Independent Submission S. Kiyomoto
Request for Comments: 7008 W. Shin
Category: Informational KDDI R&D Laboratories, Inc.
ISSN: 2070-1721 August 2013
Independent Submission S. Kiyomoto
Request for Comments: 7008 W. Shin
Category: Informational KDDI R&D Laboratories, Inc.
ISSN: 2070-1721 August 2013
A Description of the KCipher-2 Encryption Algorithm
KCipher-2加密算法的描述
Abstract
摘要
This document describes the KCipher-2 encryption algorithm. KCipher-2 is a stream cipher with a 128-bit key and a 128-bit initialization vector. Since the algorithm for KCipher-2 was published in 2007, security and efficiency have been rigorously evaluated through academic and industrial studies. As of the publication of this document, no security vulnerabilities have been found. KCipher-2 offers fast encryption and decryption by means of simple operations that enable efficient implementation. KCipher-2 has been used for industrial applications, especially for mobile health monitoring and diagnostic services in Japan.
本文档介绍KCipher-2加密算法。KCipher-2是一种具有128位密钥和128位初始化向量的流密码。自2007年KCipher-2算法发布以来，通过学术和工业研究对其安全性和效率进行了严格评估。截至本文件发布之日，未发现任何安全漏洞。KCipher-2通过简单的操作提供快速加密和解密，从而实现高效实现。KCipher-2已用于工业应用，特别是在日本用于移动健康监测和诊断服务。
Status of This Memo
关于下段备忘
This document is not an Internet Standards Track specification; it is published for informational purposes.
本文件不是互联网标准跟踪规范；它是为了提供信息而发布的。
This is a contribution to the RFC Series, independently of any other RFC stream. The RFC Editor has chosen to publish this document at its discretion and makes no statement about its value for implementation or deployment. Documents approved for publication by the RFC Editor are not a candidate for any level of Internet Standard; see Section 2 of RFC 5741.
这是对RFC系列的贡献，独立于任何其他RFC流。RFC编辑器已选择自行发布此文档，并且未声明其对实现或部署的价值。RFC编辑批准发布的文件不适用于任何级别的互联网标准；见RFC 5741第2节。
Information about the current status of this document, any errata, and how to provide feedback on it may be obtained at http://www.rfc-editor.org/info/rfc7008.
有关本文件当前状态、任何勘误表以及如何提供反馈的信息，请访问http://www.rfc-editor.org/info/rfc7008.
Copyright Notice
版权公告
Copyright (c) 2013 IETF Trust and the persons identified as the document authors. All rights reserved.
版权所有（c）2013 IETF信托基金和确定为文件作者的人员。版权所有。
This document is subject to BCP 78 and the IETF Trust's Legal Provisions Relating to IETF Documents (http://trustee.ietf.org/license-info) in effect on the date of publication of this document. Please review these documents carefully, as they describe your rights and restrictions with respect to this document.
本文件受BCP 78和IETF信托有关IETF文件的法律规定的约束(http://trustee.ietf.org/license-info)自本文件出版之日起生效。请仔细阅读这些文件，因为它们描述了您对本文件的权利和限制。
Table of Contents
目录
1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . 3
2. Algorithm Description . . . . . . . . . . . . . . . . . . . . 3
2.1. Notations . . . . . . . . . . . . . . . . . . . . . . . . 4
2.2. Internal State . . . . . . . . . . . . . . . . . . . . . . 4
2.2.1. Feedback Shift Registers . . . . . . . . . . . . . . . 4
2.2.2. Internal Registers . . . . . . . . . . . . . . . . . . 5
2.3. Operations . . . . . . . . . . . . . . . . . . . . . . . . 5
2.3.1. next() . . . . . . . . . . . . . . . . . . . . . . . . 5
2.3.2. init() . . . . . . . . . . . . . . . . . . . . . . . . 7
2.3.3. stream() . . . . . . . . . . . . . . . . . . . . . . . 8
2.4. Subroutines . . . . . . . . . . . . . . . . . . . . . . . 9
2.4.1. NLF() . . . . . . . . . . . . . . . . . . . . . . . . 9
2.4.2. sub_K2() . . . . . . . . . . . . . . . . . . . . . . . 9
2.4.3. S_box() . . . . . . . . . . . . . . . . . . . . . . . 10
2.4.4. Multiplications in GF(2#32) . . . . . . . . . . . . . 11
2.5. Encryption and Decryption Scheme . . . . . . . . . . . . . 13
2.5.1. Key Stream Generation . . . . . . . . . . . . . . . . 13
2.5.2. Encryption and Decryption of a Message . . . . . . . . 14
3. Security Considerations . . . . . . . . . . . . . . . . . . . 14
4. References . . . . . . . . . . . . . . . . . . . . . . . . . . 14
4.1. Normative References . . . . . . . . . . . . . . . . . . . 14
4.2. Informative References . . . . . . . . . . . . . . . . . . 14
Appendix A. Tables for Multiplication in GF(2#32) . . . . . . . . 16
A.1. The table amul0 . . . . . . . . . . . . . . . . . . . . . 16
A.2. The table amul1 . . . . . . . . . . . . . . . . . . . . . 17
A.3. The table amul2 . . . . . . . . . . . . . . . . . . . . . 19
A.4. The table amul3 . . . . . . . . . . . . . . . . . . . . . 20
Appendix B. A Simple Implementation Example of KCipher-2 . . . . 22
B.1. Code Components I - Definitions and Declarations . . . . . 22
B.2. Code Components II - Functions . . . . . . . . . . . . . . 23
B.3. Use Case . . . . . . . . . . . . . . . . . . . . . . . . . 28
Appendix C. Test Vectors . . . . . . . . . . . . . . . . . . . . 28
C.1. Key Stream Generation Examples . . . . . . . . . . . . . . 28
C.2. Another Key Stream Generation with the State Values . . . 29
C.2.1. S after init(1) . . . . . . . . . . . . . . . . . . . 30
C.2.2. S after init(2) . . . . . . . . . . . . . . . . . . . 30
C.2.3. S after init(3) . . . . . . . . . . . . . . . . . . . 30
C.2.4. S after init(4) . . . . . . . . . . . . . . . . . . . 31
C.2.5. S after init(5) . . . . . . . . . . . . . . . . . . . 31
C.2.6. S after init(6) . . . . . . . . . . . . . . . . . . . 31
C.2.7. S after init(7) . . . . . . . . . . . . . . . . . . . 31
C.2.8. S after init(8) . . . . . . . . . . . . . . . . . . . 32
C.2.9. S after init(9) . . . . . . . . . . . . . . . . . . . 32
C.2.10. S after init(10) . . . . . . . . . . . . . . . . . . . 32
C.2.11. S after init(11) . . . . . . . . . . . . . . . . . . . 32
C.2.12. S after init(12) . . . . . . . . . . . . . . . . . . . 33
1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . 3
2. Algorithm Description . . . . . . . . . . . . . . . . . . . . 3
2.1. Notations . . . . . . . . . . . . . . . . . . . . . . . . 4
2.2. Internal State . . . . . . . . . . . . . . . . . . . . . . 4
2.2.1. Feedback Shift Registers . . . . . . . . . . . . . . . 4
2.2.2. Internal Registers . . . . . . . . . . . . . . . . . . 5
2.3. Operations . . . . . . . . . . . . . . . . . . . . . . . . 5
2.3.1. next() . . . . . . . . . . . . . . . . . . . . . . . . 5
2.3.2. init() . . . . . . . . . . . . . . . . . . . . . . . . 7
2.3.3. stream() . . . . . . . . . . . . . . . . . . . . . . . 8
2.4. Subroutines . . . . . . . . . . . . . . . . . . . . . . . 9
2.4.1. NLF() . . . . . . . . . . . . . . . . . . . . . . . . 9
2.4.2. sub_K2() . . . . . . . . . . . . . . . . . . . . . . . 9
2.4.3. S_box() . . . . . . . . . . . . . . . . . . . . . . . 10
2.4.4. Multiplications in GF(2#32) . . . . . . . . . . . . . 11
2.5. Encryption and Decryption Scheme . . . . . . . . . . . . . 13
2.5.1. Key Stream Generation . . . . . . . . . . . . . . . . 13
2.5.2. Encryption and Decryption of a Message . . . . . . . . 14
3. Security Considerations . . . . . . . . . . . . . . . . . . . 14
4. References . . . . . . . . . . . . . . . . . . . . . . . . . . 14
4.1. Normative References . . . . . . . . . . . . . . . . . . . 14
4.2. Informative References . . . . . . . . . . . . . . . . . . 14
Appendix A. Tables for Multiplication in GF(2#32) . . . . . . . . 16
A.1. The table amul0 . . . . . . . . . . . . . . . . . . . . . 16
A.2. The table amul1 . . . . . . . . . . . . . . . . . . . . . 17
A.3. The table amul2 . . . . . . . . . . . . . . . . . . . . . 19
A.4. The table amul3 . . . . . . . . . . . . . . . . . . . . . 20
Appendix B. A Simple Implementation Example of KCipher-2 . . . . 22
B.1. Code Components I - Definitions and Declarations . . . . . 22
B.2. Code Components II - Functions . . . . . . . . . . . . . . 23
B.3. Use Case . . . . . . . . . . . . . . . . . . . . . . . . . 28
Appendix C. Test Vectors . . . . . . . . . . . . . . . . . . . . 28
C.1. Key Stream Generation Examples . . . . . . . . . . . . . . 28
C.2. Another Key Stream Generation with the State Values . . . 29
C.2.1. S after init(1) . . . . . . . . . . . . . . . . . . . 30
C.2.2. S after init(2) . . . . . . . . . . . . . . . . . . . 30
C.2.3. S after init(3) . . . . . . . . . . . . . . . . . . . 30
C.2.4. S after init(4) . . . . . . . . . . . . . . . . . . . 31
C.2.5. S after init(5) . . . . . . . . . . . . . . . . . . . 31
C.2.6. S after init(6) . . . . . . . . . . . . . . . . . . . 31
C.2.7. S after init(7) . . . . . . . . . . . . . . . . . . . 31
C.2.8. S after init(8) . . . . . . . . . . . . . . . . . . . 32
C.2.9. S after init(9) . . . . . . . . . . . . . . . . . . . 32
C.2.10. S after init(10) . . . . . . . . . . . . . . . . . . . 32
C.2.11. S after init(11) . . . . . . . . . . . . . . . . . . . 32
C.2.12. S after init(12) . . . . . . . . . . . . . . . . . . . 33
C.2.13. S after init(13) . . . . . . . . . . . . . . . . . . . 33
C.2.14. S after init(14) . . . . . . . . . . . . . . . . . . . 33
C.2.15. S after init(15) . . . . . . . . . . . . . . . . . . . 33
C.2.16. S after init(16) . . . . . . . . . . . . . . . . . . . 34
C.2.17. S after init(17) . . . . . . . . . . . . . . . . . . . 34
C.2.18. S after init(18) . . . . . . . . . . . . . . . . . . . 34
C.2.19. S after init(19) . . . . . . . . . . . . . . . . . . . 34
C.2.20. S after init(20) . . . . . . . . . . . . . . . . . . . 35
C.2.21. S after init(21) . . . . . . . . . . . . . . . . . . . 35
C.2.22. S after init(22) . . . . . . . . . . . . . . . . . . . 35
C.2.23. S after init(23) . . . . . . . . . . . . . . . . . . . 35
C.2.24. S(0) after init(24) . . . . . . . . . . . . . . . . . 36
C.2.25. S(1) and the Key Stream at S(1) . . . . . . . . . . . 36
C.2.26. S(2) and the Key Stream at S(2) . . . . . . . . . . . 37
C.2.13. S after init(13) . . . . . . . . . . . . . . . . . . . 33
C.2.14. S after init(14) . . . . . . . . . . . . . . . . . . . 33
C.2.15. S after init(15) . . . . . . . . . . . . . . . . . . . 33
C.2.16. S after init(16) . . . . . . . . . . . . . . . . . . . 34
C.2.17. S after init(17) . . . . . . . . . . . . . . . . . . . 34
C.2.18. S after init(18) . . . . . . . . . . . . . . . . . . . 34
C.2.19. S after init(19) . . . . . . . . . . . . . . . . . . . 34
C.2.20. S after init(20) . . . . . . . . . . . . . . . . . . . 35
C.2.21. S after init(21) . . . . . . . . . . . . . . . . . . . 35
C.2.22. S after init(22) . . . . . . . . . . . . . . . . . . . 35
C.2.23. S after init(23) . . . . . . . . . . . . . . . . . . . 35
C.2.24. S(0) after init(24) . . . . . . . . . . . . . . . . . 36
C.2.25. S(1) and the Key Stream at S(1) . . . . . . . . . . . 36
C.2.26. S(2) and the Key Stream at S(2) . . . . . . . . . . . 37
KCipher-2 is a stream cipher that uses a 128-bit secret key and a 128-bit initialization vector. Since the algorithm for KCipher-2 was published in 2007 [SASC07], it has been evaluated in academic and industrial studies. The security and performance of KCipher-2 have been rigorously evaluated by its developers and other institutions [SECRYPT07] [ICETE07] [CRYPTEC] [SIIS11]. As of the publication of this document, no attack on KCipher-2 has been successful. KCipher-2 can be efficiently implemented in software to provide fast encryption and decryption, owing to its uncomplicated design. Only four simple operations are used: exclusive-OR, addition, shift, and table lookup. When the algorithm is implemented in hardware, internal computations can be parallel to yield greater efficiency. Moreover, since its internal state representation only amounts to several hundred bits, KCipher-2 is suitable for resource-limited environments. KCipher-2 has been actively used in several industrial applications in Japan, has been published by an international standardization body (ISO/IEC 18033-4 [ISO18033]), and has been designated a Japanese e-Government recommended cipher [CRYPTECLIST].
KCipher-2是一种使用128位密钥和128位初始化向量的流密码。自从KCipher-2的算法于2007年发表[SASC07]以来，已经在学术和工业研究中对其进行了评估。KCipher-2的安全性和性能已由其开发商和其他机构进行了严格评估[SECRYPT07][ICETE07][CRYPTEC][SIIS11]。截至本文件发布之日，对KCipher-2的攻击尚未成功。KCipher-2设计简单，可以在软件中高效实现，以提供快速加密和解密。仅使用四个简单操作：异或、加法、移位和表查找。当算法在硬件中实现时，内部计算可以并行，从而产生更高的效率。此外，由于其内部状态表示仅为几百位，KCipher-2适用于资源有限的环境。KCipher-2在日本的多个工业应用中得到了积极的应用，由国际标准化机构（ISO/IEC 18033-4[ISO18033]）发布，并被指定为日本电子政府推荐的密码[密码列表]。
In this section, we describe the internal components of KCipher-2 and define the operations for deriving key streams from an input key and an initialization vector. We illustrate the detailed operations, mostly in pseudocode format, but also provide code snippets written in the C language syntax when necessary.
在本节中，我们将描述KCipher-2的内部组件，并定义从输入密钥和初始化向量导出密钥流的操作。我们演示了详细的操作，主要是伪代码格式，但必要时还提供了用C语言语法编写的代码片段。
All values in this document are stored in big-endian order (aka network byte order). We use the following notations in the description of KCipher-2.
本文档中的所有值都以大端顺序（也称为网络字节顺序）存储。我们在KCipher-2的描述中使用以下符号。
^ Bitwise exclusive-OR
^位异或
n#m mth power of n
n#m n的m次方
+n Integer addition modulo 2#n
+n模2#n的整数加法
<<_r n n-bit left circular shift in an r-bit register
<<\r位寄存器中的n位左循环移位
0x Hexadecimal representation
0x十六进制表示法
E[i] The (i + 1)th element of E when E is composed of consecutive multiple elements
E[i]当E由连续的多个元素组成时，E的第（i+1）个元素
GF Galois field. GF(n#m) means the finite field of exactly n#m elements
GF伽罗瓦场。GF（n#m）表示n#m元素的有限域
** Multiplication of elements on the finite field GF(2#32)
** Multiplication of elements on the finite field GF(2#32)
NOTE: Many texts denote "the mth power of n" by "n^m", but we write it using '#', instead of '^', to avoid reader confusion with the power operator and the XOR operator of the C language syntax.
注意：许多文本用“n^m”表示“n的第m次幂”，但我们使用“#”而不是“^”来编写它，以避免读者混淆C语言语法中的幂运算符和异或运算符。
The internal state of KCipher-2 can be denoted by S. The internal
state consists of six sub-components: two feedback shift registers,
FSR-A and FSR-B, and four internal registers, L1, R1, L2, and R2.
We, therefore, often write S = (A, B, L1, R1, L2, R2), where A and B
refer to FSR-A and FSR-B, respectively.
The internal state of KCipher-2 can be denoted by S. The internal
state consists of six sub-components: two feedback shift registers,
FSR-A and FSR-B, and four internal registers, L1, R1, L2, and R2.
We, therefore, often write S = (A, B, L1, R1, L2, R2), where A and B
refer to FSR-A and FSR-B, respectively.
The two feedback shift registers (FSRs) are separately called Feedback Shift Register A (FSR-A) and Feedback Shift Register B (FSR-B). FSR-A is composed of five 32-bit units that are consecutively arranged. Each unit can be identified by A[0], A[1], A[2], A[3], and A[4]. Likewise, FSR-B is composed of eleven consecutive 32-bit units, B[0], ..., B[10]. All values stored in each 32-bit unit of FSR is in GF(2#32).
这两个反馈移位寄存器（FSR）分别称为反馈移位寄存器A（FSR-A）和反馈移位寄存器B（FSR-B）。FSR-A由五个连续排列的32位单元组成。每个单元都可以用[0]、[1]、[2]、[3]和[4]来标识。类似地，FSR-B由十一个连续的32位单元B[0]、…、B[10]组成。存储在FSR的每个32位单元中的所有值都以GF（2#32）为单位。
Besides FSR, KCipher-2 has four internal registers to store intermediate computation results during operation. The four registers are named L1, R1, L2, and R2.
除了FSR之外，KCipher-2还有四个内部寄存器，用于存储操作期间的中间计算结果。这四个寄存器分别命名为L1、R1、L2和R2。
Three major operations constitute the behavior of KCipher-2: init(), next(), and stream(). The init() operation initializes the internal values of the system. The next() operation derives new values of S' from the values of S, where S' and S refer to the internal state. The stream() operation derives a key stream from the current state S.
KCipher-2的行为由三个主要操作组成：init（）、next（）和stream（）。init（）操作初始化系统的内部值。next（）操作从S的值派生S'的新值，其中S'和S表示内部状态。stream（）操作从当前状态派生密钥流。
The next() operation takes the current state S = (A, B, L1, R1, L2,
R2) as input. The size of the input amounts to twenty of the 32-bit
units in total (five units for A, eleven for B, and one for L1, R1,
L2, and R2). It produces the next state S' = (A', B', L1', R1', L2',
R2'). This operation is mainly used to generate secure key streams
by applying non-linear functions (NLFs) for every cycle of KCipher-2.
Additionally, it is used to initialize the system. The behaviors are
distinguished by the input parameter that indicates the operation
modes.
The next() operation takes the current state S = (A, B, L1, R1, L2,
R2) as input. The size of the input amounts to twenty of the 32-bit
units in total (five units for A, eleven for B, and one for L1, R1,
L2, and R2). It produces the next state S' = (A', B', L1', R1', L2',
R2'). This operation is mainly used to generate secure key streams
by applying non-linear functions (NLFs) for every cycle of KCipher-2.
Additionally, it is used to initialize the system. The behaviors are
distinguished by the input parameter that indicates the operation
modes.
Inside the next() operation, the internal registers are updated by the result of the substitution function described in Section 2.4.2. The feedback shift registers are also updated by feedback functions. The feedback functions include the multiplication of register units and the fixed elements a0, a1, a2, and a3 in a finite field. The fixed elements a0, ..., a3 are carefully chosen to provide the maximum length of the feedback shift registers. The theory behind the selection of fixed elements and the way to simplify the necessary multiplications are briefly described in Section 2.4.4.
在next（）操作中，内部寄存器由第2.4.2节中描述的替换函数的结果更新。反馈移位寄存器也通过反馈功能进行更新。反馈函数包括寄存器单元与有限域中的固定元素a0、a1、a2和a3的乘法。仔细选择固定元件a0、…、a3，以提供反馈移位寄存器的最大长度。第2.4.4节简要介绍了选择固定元素背后的理论以及简化必要乘法的方法。
The operation takes the following inputs:
该操作采用以下输入：
o S = (A, B, L1, R1, L2, R2)
o S=（A，B，L1，R1，L2，R2）
o mode = {INIT, NORMAL}, where INIT means the operation is used for initialization, and NORMAL means it is used for generating secure key streams.
o mode={INIT，NORMAL}，其中INIT表示操作用于初始化，NORMAL表示用于生成安全密钥流。
The operation outputs a new state,
操作输出一个新状态，
o S' = (A', B', L1', R1', L2', R2')
o S'=（A'，B'，L1'，R1'，L2'，R2'）
by performing the following steps:
通过执行以下步骤：
1. Set registers in the nonlinear functions
1. 非线性函数中的寄存器集
L1' = sub_K2(R2 +32 B[4]);
R1' = sub_K2(L2 +32 B[9]);
L2' = sub_K2(L1);
R2' = sub_K2(R1);
L1' = sub_K2(R2 +32 B[4]);
R1' = sub_K2(L2 +32 B[9]);
L2' = sub_K2(L1);
R2' = sub_K2(R1);
for m from 0 to 3 A'[m] = A[m + 1];
对于从0到3的m，'[m]=A[m+1]；
for m from 0 to 9 B'[m] = B[m + 1];
对于从0到9的m，B'[m]=B[m+1]；
NOTE: sub_K2 is a substitution function described in Section 2.4.2.
注：sub_K2是第2.4.2节中描述的替代函数。
2. Depending on the value of the operation mode, do the following:
2. 根据操作模式的值，执行以下操作：
a. When the mode is NORMAL, A'[4] and B'[10] are computed as follows:
a. 当模式正常时，A'[4]和B'[10]的计算如下：
A'[4] = (a0 ** A[0]) ^ A[3];
A'[4] = (a0 ** A[0]) ^ A[3];
if A[2][30] is 1:
if A[2][31] is 1:
B'[10] = (a1 ** B[0]) ^ B[1] ^ B[6] ^ (a3 ** B[8]);
else if A[2][31] is 0:
B'[10] = (a1 ** B[0]) ^ B[1] ^ B[6] ^ B[8];
else if A[2][30] is 0:
if A[2][31] is 1:
B'[10] = (a2 ** B[0]) ^ B[1] ^ B[6] ^ (a3 ** B[8]);
else if A[2][31] is 0:
B'[10] = (a2 ** B[0]) ^ B[1] ^ B[6] ^ B[8];
if A[2][30] is 1:
if A[2][31] is 1:
B'[10] = (a1 ** B[0]) ^ B[1] ^ B[6] ^ (a3 ** B[8]);
else if A[2][31] is 0:
B'[10] = (a1 ** B[0]) ^ B[1] ^ B[6] ^ B[8];
else if A[2][30] is 0:
if A[2][31] is 1:
B'[10] = (a2 ** B[0]) ^ B[1] ^ B[6] ^ (a3 ** B[8]);
else if A[2][31] is 0:
B'[10] = (a2 ** B[0]) ^ B[1] ^ B[6] ^ B[8];
b. When the mode is INIT, A'[4] and B'[10] are XOR-ed with the non-linear function output described in Section 2.4.1.
b. 当模式为INIT时，A'[4]和B'[10]与第2.4.1节中描述的非线性函数输出进行异或运算。
A'[4] = (a0 ** A[0]) ^ A[3] ^ NLF(B[0], R2, R1, A[4]);
A'[4] = (a0 ** A[0]) ^ A[3] ^ NLF(B[0], R2, R1, A[4]);
if A[2][30] is 1:
if A[2][31] is 1:
B'[10] = (a1 ** B[0]) ^ B[1] ^ B[6] ^ (a3 ** B[8]) ^
NLF(B[10], L2, L1, A[0]);
else if A[2][31] is 0:
B'[10] = (a1 ** B[0]) ^ B[1] ^ B[6] ^ B[8] ^
NLF(B[10], L2, L1, A[0]);
if A[2][30] is 1:
if A[2][31] is 1:
B'[10] = (a1 ** B[0]) ^ B[1] ^ B[6] ^ (a3 ** B[8]) ^
NLF(B[10], L2, L1, A[0]);
else if A[2][31] is 0:
B'[10] = (a1 ** B[0]) ^ B[1] ^ B[6] ^ B[8] ^
NLF(B[10], L2, L1, A[0]);
else if A[2][30] is 0:
if A[2][31] is 1:
B'[10] = (a2 ** B[0]) ^ B[1] ^ B[6] ^ (a3 ** B[8]) ^
NLF(B[10], L2, L1, A[0]);
else if A[2][31] is 0:
B'[10] = (a2 ** B[0]) ^ B[1] ^ B[6] ^ B[8] ^
NLF(B[10], L2, L1, A[0]);
else if A[2][30] is 0:
if A[2][31] is 1:
B'[10] = (a2 ** B[0]) ^ B[1] ^ B[6] ^ (a3 ** B[8]) ^
NLF(B[10], L2, L1, A[0]);
else if A[2][31] is 0:
B'[10] = (a2 ** B[0]) ^ B[1] ^ B[6] ^ B[8] ^
NLF(B[10], L2, L1, A[0]);
3. Output S' = (A', B', L1', R1', L2', R2').
3. 输出S'=（A'，B'，L1'，R1'，L2'，R2'）。
Note that A[2] is a 32-bit unit. Thus, A[2][j] is the value of the jth least significant bit of A[2], where 0 <= j <= 31.
请注意，[2]是一个32位单元。因此，A[2][j]是A[2]的第j个最低有效位的值，其中0<=j<=31。
The corresponding code snippets written in the C language syntax can be found in Section 2.4.4 and Appendix B.
在第2.4.4节和附录B中可以找到用C语言语法编写的相应代码段。
The init() operation takes a 128-bit key (K) and a 128-bit initialization vector (IV) and prepares the values of the state variables for generating key streams.
init（）操作接受128位密钥（K）和128位初始化向量（IV），并准备状态变量的值以生成密钥流。
o K = (K[0], K[1], K[2], K[3]), where each K[i] is a 32-bit unit and 0 <= i <= 3
o K=（K[0]，K[1]，K[2]，K[3]），其中每个K[i]是32位单元且0<=i<=3
o IV =(IV[0], IV[1], IV[2], IV[3]), where each IV[i] is a 32-bit unit and 0 <= i <= 3,
o IV=（IV[0]、IV[1]、IV[2]、IV[3]），其中每个IV[i]是32位单元且0<=i<=3，
and the output is an initialized state S, which will be referenced as S(0). The output is derived from the following steps:
输出是一个初始化状态S，它将被引用为S（0）。输出来自以下步骤：
1. Expand K to the 384-bit internal key IK = (IK[0], ..., IK[11]), where IK[i] is a 32-bit unit and 0 <= i <= 11. The expansion procedure is as follows:
1. 将K扩展到384位内部关键点IK=（IK[0]，…，IK[11]），其中IK[i]是32位单位，0<=i<=11。展开程序如下：
for m from 0 to 11
if m is 0, 1, 2, or 3:
IK[m] = K[m];
else if m is 5, 6, 7, 9, 10, or 11:
IK[m] = IK[m - 4] ^ IK[m - 1];
else if m is 4:
IK[4] = IK[0] ^ sub_K2(IK[3] <<_32 8) ^
(0x01, 0x00, 0x00, 0x00);
else if m is 8:
IK[8] = IK[4] ^ sub_K2(IK[7] <<_32 8) ^
(0x02, 0x00, 0x00, 0x00);
for m from 0 to 11
if m is 0, 1, 2, or 3:
IK[m] = K[m];
else if m is 5, 6, 7, 9, 10, or 11:
IK[m] = IK[m - 4] ^ IK[m - 1];
else if m is 4:
IK[4] = IK[0] ^ sub_K2(IK[3] <<_32 8) ^
(0x01, 0x00, 0x00, 0x00);
else if m is 8:
IK[8] = IK[4] ^ sub_K2(IK[7] <<_32 8) ^
(0x02, 0x00, 0x00, 0x00);
NOTE: sub_K2 is the substitution function described in Section 2.4.2.
注：sub_K2是第2.4.2节中描述的替代函数。
2. Initialize the feedback shift registers and the internal registers using the values of IK and IV as follows:
2. 使用IK和IV值初始化反馈移位寄存器和内部寄存器，如下所示：
for m from 0 to 4 A[m] = IK[4 - m];
对于从0到4的m，A[m]=IK[4-m]；
B[0] = IK[10]; B[1] = IK[11]; B[2] = IV[0]; B[3] = IV[1];
B[4] = IK[8]; B[5] = IK[9]; B[6] = IV[2]; B[7] = IV[3];
B[8] = IK[7]; B[9] = IK[5]; B[10] = IK[6];
B[0] = IK[10]; B[1] = IK[11]; B[2] = IV[0]; B[3] = IV[1];
B[4] = IK[8]; B[5] = IK[9]; B[6] = IV[2]; B[7] = IV[3];
B[8] = IK[7]; B[9] = IK[5]; B[10] = IK[6];
L1 = R1 = L2 = R2 = 0x00000000;
L1 = R1 = L2 = R2 = 0x00000000;
Set S as (A, B, L1, R1, L2, R2).
将S设置为（A、B、L1、R1、L2、R2）。
3. Prepare the state values by applying the next() operation 24 times as follows:
3. 通过应用next（）操作24次来准备状态值，如下所示：
for m from 1 to 24
Set S' as next(S, INIT);
Set S as S';
for m from 1 to 24
Set S' as next(S, INIT);
Set S as S';
4. Output S.
4. 输出S。
The stream() function derives a 64-bit key stream, Z, from the state values. Its input is an initialized state,
函数的作用是：从状态值中导出64位密钥流Z。它的输入是一个初始化状态，
o S = (A, B, L1, R1, L2, R2)
o S=（A，B，L1，R1，L2，R2）
and its output is Z = (ZH, ZL), where ZH and ZL are 32-bit units.
stream() performs the following:
and its output is Z = (ZH, ZL), where ZH and ZL are 32-bit units.
stream() performs the following:
1. Set register values
1. 设置寄存器值
ZH = NLF(B[10], L2, L1, A[0]);
ZL = NLF(B[0], R2, R1, A[4]);
ZH = NLF(B[10], L2, L1, A[0]);
ZL = NLF(B[0], R2, R1, A[4]);
2. Output Z = (ZH, ZL).
2. 输出Z=（ZH，ZL）。
NOTE: The function NLF is described in Section 2.4.1.
注：第2.4.1节描述了NLF功能。
We explain the functions used above: sub_K2(), NLF(), and S_box().
我们解释上面使用的函数：sub_K2（）、NLF（）和S_box（）。
NLF() is a non-linear function that takes the four 32-bit values, A, B, C, D, and outputs the 32-bit value, Q. The output Q is calculated as follows.
NLF（）是一个非线性函数，它接受四个32位值a、B、C、D，并输出32位值Q。输出Q的计算如下。
Q = (A +32 B) ^ C ^ D;
Q = (A +32 B) ^ C ^ D;
sub_K2() is a substitution function that is a permutation of GF(2#32), based on components from the Advanced Encryption Standard (AES) [FIPS-AES]. Its input is a 32-bit value divided into four 8-bit strings. Inside sub_K2(), an 8-to-8-bit substitution function, S_box(), is applied to each 8-bit string separately, and then a 32- to-32-bit linear permutation is applied to the whole 32-bit string. Our S_box() function is identical to the S-Box operation of AES, and our linear permutation is identical to the AES Mix Column operation.
sub_K2（）是一个替换函数，它是GF（2#32）的置换，基于高级加密标准（AES）[FIPS-AES]中的组件。它的输入是一个32位值，分为四个8位字符串。在sub_K2（）内部，对每个8位字符串分别应用8到8位替换函数S_box（），然后对整个32位字符串应用32到32位线性置换。我们的S_box（）函数与AES的S-box操作相同，我们的线性置换与AES的混合列操作相同。
Consider the input of sub_K2 as a 32-bit value W = (w[3], w[2], w[1],
w[0]), where each subelement of w is an 8-bit unit. Prepare two
32-bit temporary storages, T = (t[3], t[2], t[1], t[0]) and Q =
(q[3], q[2], q[1], q[0]), where t[i] and q[i] are 8-bit units and 0
<= i <= 3.
Consider the input of sub_K2 as a 32-bit value W = (w[3], w[2], w[1],
w[0]), where each subelement of w is an 8-bit unit. Prepare two
32-bit temporary storages, T = (t[3], t[2], t[1], t[0]) and Q =
(q[3], q[2], q[1], q[0]), where t[i] and q[i] are 8-bit units and 0
<= i <= 3.
The 32-bit output Q is obtained from the following procedures:
通过以下步骤获得32位输出Q：
1. Apply S_box() to each 8-bit input string. Note that S_box() is defined in Section 2.4.3.
1. 将S_box（）应用于每个8位输入字符串。请注意，S_box（）在第2.4.3节中有定义。
for m from 0 to 3 t[m] = S_box(w[m]);
对于从0到3t[m]=S_盒（w[m]）；
2. Calculate q by the matrix multiplication, Q = M * T in GF(2#8) of the irreducible polynomial f(x) = x#8 + x#4 + x#3 + x + 1, where
2. 通过不可约多项式f（x）=x#8+x#4+x#3+x+1的GF（2#8）中的矩阵乘法计算q，其中
o Q is a 1x4 matrix, (q[0], q[1], q[2], q[3))
o Q是一个1x4矩阵，（Q[0]，Q[1]，Q[2]，Q[3））
o M is a 4x4 matrix,
o M是一个4x4矩阵，
(02, 03, 01, 01, 01, 02, 03, 01, 01, 01, 02, 03, 03, 01, 01, 02)
(02, 03, 01, 01, 01, 02, 03, 01, 01, 01, 02, 03, 03, 01, 01, 02)
o T is a 1x4 matrix, (t[0], t[1], t[2], t[3]).
o T是一个1x4矩阵，（T[0]，T[1]，T[2]，T[3]）。
Namely, the procedure that calculates (q[3], q[2], q[1], q[0]) can be written in the C language syntax as:
即，计算（q[3]、q[2]、q[1]、q[0]）的过程可以用C语言语法编写为：
q[0] = GF_mult_by_2(t[0]) ^ GF_mult_by_3(t[1]) ^ t[2] ^ t[3];
q[1] = t[0] ^ GF_mult_by_2(t[1]) ^ GF_mult_by_3(t[2]) ^ t[3];
q[2] = t[0] ^ t[1] ^ GF_mult_by_2(t[2]) ^ GF_mult_by_3(t[3]);
q[3] = GF_mult_by_3(t[0]) ^ t[1] ^ t[2] ^ GF_mult_by_2(t[3]);
q[0] = GF_mult_by_2(t[0]) ^ GF_mult_by_3(t[1]) ^ t[2] ^ t[3];
q[1] = t[0] ^ GF_mult_by_2(t[1]) ^ GF_mult_by_3(t[2]) ^ t[3];
q[2] = t[0] ^ t[1] ^ GF_mult_by_2(t[2]) ^ GF_mult_by_3(t[3]);
q[3] = GF_mult_by_3(t[0]) ^ t[1] ^ t[2] ^ GF_mult_by_2(t[3]);
where GF_mult_by_2 and GF_mult_by_3 are multiplication functions in GF(2#8), defined as follows:
其中GF_mult_by_2和GF_mult_by_3是GF（2#8）中的乘法函数，定义如下：
o The function GF_mult_by_2(t) multiplies 2 by the given 8-bit value t in GF(2#8) and returns an 8-bit value q as follows (lq is a temporary 32-bit variable):
o 函数GF_mult_by_2（t）将2乘以GF（2#8）中给定的8位值t，并返回一个8位值q，如下所示（lq是一个临时32位变量）：
lq = t << 1;
if ((lq & 0x100) != 0) lq ^= 0x011B;
q = lq ^ 0xFF;
lq = t << 1;
if ((lq & 0x100) != 0) lq ^= 0x011B;
q = lq ^ 0xFF;
o The function GF_mult_by_3(t) multiplies 3 by the given 8-bit value t in GF(2#8) and returns an 8-bit value q as follows (lq is a temporary 32-bit variable):
o 函数GF_mult_乘以_3（t）将3乘以GF（2#8）中给定的8位值t，并返回一个8位值q，如下所示（lq是一个临时32位变量）：
lq = (t << 1) ^ t;
if ((lq & 0x100) != 0) lq ^= 0x011B;
q = lq ^ 0xFF;
lq = (t << 1) ^ t;
if ((lq & 0x100) != 0) lq ^= 0x011B;
q = lq ^ 0xFF;
3. Output Q = (q[3], q[2], q[1], q[0]).
3. 输出Q=（Q[3]，Q[2]，Q[1]，Q[0]）。
S_box() is a substitution that can be done by a simple table lookup operation. Thus, S_box() can be defined by the following value table:
S_box（）是一种替换，可以通过简单的表查找操作完成。因此，S_box（）可以由以下值表定义：
S_box[256] = {
0x63, 0x7c, 0x77, 0x7b, 0xf2, 0x6b, 0x6f, 0xc5,
0x30, 0x01, 0x67, 0x2b, 0xfe, 0xd7, 0xab, 0x76,
0xca, 0x82, 0xc9, 0x7d, 0xfa, 0x59, 0x47, 0xf0,
0xad, 0xd4, 0xa2, 0xaf, 0x9c, 0xa4, 0x72, 0xc0,
0xb7, 0xfd, 0x93, 0x26, 0x36, 0x3f, 0xf7, 0xcc,
0x34, 0xa5, 0xe5, 0xf1, 0x71, 0xd8, 0x31, 0x15,
0x04, 0xc7, 0x23, 0xc3, 0x18, 0x96, 0x05, 0x9a,
0x07, 0x12, 0x80, 0xe2, 0xeb, 0x27, 0xb2, 0x75,
0x09, 0x83, 0x2c, 0x1a, 0x1b, 0x6e, 0x5a, 0xa0,
0x52, 0x3b, 0xd6, 0xb3, 0x29, 0xe3, 0x2f, 0x84,
S_box[256] = {
0x63, 0x7c, 0x77, 0x7b, 0xf2, 0x6b, 0x6f, 0xc5,
0x30, 0x01, 0x67, 0x2b, 0xfe, 0xd7, 0xab, 0x76,
0xca, 0x82, 0xc9, 0x7d, 0xfa, 0x59, 0x47, 0xf0,
0xad, 0xd4, 0xa2, 0xaf, 0x9c, 0xa4, 0x72, 0xc0,
0xb7, 0xfd, 0x93, 0x26, 0x36, 0x3f, 0xf7, 0xcc,
0x34, 0xa5, 0xe5, 0xf1, 0x71, 0xd8, 0x31, 0x15,
0x04, 0xc7, 0x23, 0xc3, 0x18, 0x96, 0x05, 0x9a,
0x07, 0x12, 0x80, 0xe2, 0xeb, 0x27, 0xb2, 0x75,
0x09, 0x83, 0x2c, 0x1a, 0x1b, 0x6e, 0x5a, 0xa0,
0x52, 0x3b, 0xd6, 0xb3, 0x29, 0xe3, 0x2f, 0x84,
0x53, 0xd1, 0x00, 0xed, 0x20, 0xfc, 0xb1, 0x5b, 0x6a, 0xcb, 0xbe, 0x39, 0x4a, 0x4c, 0x58, 0xcf, 0xd0, 0xef, 0xaa, 0xfb, 0x43, 0x4d, 0x33, 0x85, 0x45, 0xf9, 0x02, 0x7f, 0x50, 0x3c, 0x9f, 0xa8, 0x51, 0xa3, 0x40, 0x8f, 0x92, 0x9d, 0x38, 0xf5, 0xbc, 0xb6, 0xda, 0x21, 0x10, 0xff, 0xf3, 0xd2, 0xcd, 0x0c, 0x13, 0xec, 0x5f, 0x97, 0x44, 0x17, 0xc4, 0xa7, 0x7e, 0x3d, 0x64, 0x5d, 0x19, 0x73, 0x60, 0x81, 0x4f, 0xdc, 0x22, 0x2a, 0x90, 0x88, 0x46, 0xee, 0xb8, 0x14, 0xde, 0x5e, 0x0b, 0xdb, 0xe0, 0x32, 0x3a, 0x0a, 0x49, 0x06, 0x24, 0x5c, 0xc2, 0xd3, 0xac, 0x62, 0x91, 0x95, 0xe4, 0x79, 0xe7, 0xc8, 0x37, 0x6d, 0x8d, 0xd5, 0x4e, 0xa9, 0x6c, 0x56, 0xf4, 0xea, 0x65, 0x7a, 0xae, 0x08, 0xba, 0x78, 0x25, 0x2e, 0x1c, 0xa6, 0xb4, 0xc6, 0xe8, 0xdd, 0x74, 0x1f, 0x4b, 0xbd, 0x8b, 0x8a, 0x70, 0x3e, 0xb5, 0x66, 0x48, 0x03, 0xf6, 0x0e, 0x61, 0x35, 0x57, 0xb9, 0x86, 0xc1, 0x1d, 0x9e, 0xe1, 0xf8, 0x98, 0x11, 0x69, 0xd9, 0x8e, 0x94, 0x9b, 0x1e, 0x87, 0xe9, 0xce, 0x55, 0x28, 0xdf, 0x8c, 0xa1, 0x89, 0x0d, 0xbf, 0xe6, 0x42, 0x68, 0x41, 0x99, 0x2d, 0x0f, 0xb0, 0x54, 0xbb, 0x16 };
0x53，0x53，0xd1，0x53，0xd1，0x00，0x0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0啊,，0x19，0x73，0x22，0x22，0x2a，0x22，0x2a，0x2a，0x90，0x90，0x88，0x88，0x88，0x46，0x88，0x46，0xE E，0xE，0xE，0x8 8个，0x6 6，0x6，0x7，0x7，0x7，0x7，0x7，0x7 7，0x7，0x7，0x7，0x6，0x22，0x22，0x22，0x22，0x2，0x2，0x2，0x2，0x2，0x2，0x2a，0x2a，0x2，0x2，0x2，0x2a，0x2，0x2a，0x2，0x2，0x2a，0x2a，0x20，0x2a，0x20，0x20，0x20，0xA，0xA，0xA，0xA，0x20，0xA，0xA，0xA，0xA，0xac，0xac，0x62，0x62，0x62，0x62，0x62，0x62，0x62，0x62，0x62，0x2e，0x1、0x4、0x8、0x8、0x8、0x88、0x8、0x8、0x8、0x8、0x8、0x8、0x8、0x8、0x8、0x8、0x8、0x8 8、0x8、0x8、0x8、0x8、0x8、0x6、0x6、0x6、0x6、0x6、0x6、0x6、0x6、0x7、0x16、0x7、0x7、0x8、0x8、0x8、0x8、0x8、0x88、0x8、0x8、0x8、0x8、0x8、0x8、0x8、0x8、0x8、0x8、0x8、0x8、0x8、0x8、0x8、0x8、0x8、0x8、0x8、0x8、0x8、0x8、0x8、0x8、0x8、0x8、0x8、0x8、0x8、0x8、0x8、0x8、0x8、0x8、0x8、0x8、0x8、0x8、0x，0xb0，0x54，0xbb，0x16}；
FSR-A and FSR-B are word-oriented linear feedback shift registers (LFSRs). In the next() operation of Section 2.3.1, the feedback functions to the two LFSRs are shown, which include multiplication of fixed elements a0, a1, a2, or a3 in GF(2#32). The fixed elements are carefully chosen to maximize the period of the key stream generated by the two registers. Here, we briefly explain how we obtain the fixed elements. Further details and theories can be found in [SECRYPT07].
FSR-A和FSR-B是面向字的线性反馈移位寄存器（LFSR）。在第2.3.1节的下一个（）操作中，显示了两个LFSR的反馈函数，其中包括GF（2#32）中固定元素a0、a1、a2或a3的乘法。仔细选择固定元素，以最大化两个寄存器生成的密钥流的周期。这里，我们简要说明如何获得固定元素。更多细节和理论见[SECRYPT07]。
We obtain a0 as follows. First, to guarantee that the period is maximized for an 8-bit unit, we consider p as the root of the primitive polynomial:
我们得到a0如下。首先，为了保证一个8位单元的周期最大化，我们认为P是本原多项式的根：
x#8 + x#7 + x#6, + x + 1 in GF(2).
GF（2）中的x#8+x#7+x#6，+x+1。
Therefore, an 8-bit string y = (y7, ..., y0), where y7 is the most
significant bit, can be written as:
Therefore, an 8-bit string y = (y7, ..., y0), where y7 is the most
significant bit, can be written as:
y = y7(p#7) + y6(p#6) + ... + y1(p) + y0
y = y7(p#7) + y6(p#6) + ... + y1(p) + y0
Next, a0 is the root of irreducible polynomial of degree four:
接下来，a0是四次不可约多项式的根：
x#4 + p#24(x#3) + p#3(x#2) + p#12(x) + p#71 in GF(2#8).
GF（2#8）中的x#4+p#24（x#3）+p#3（x#2）+p#12（x）+p#71。
Then, hierarchically, a 32-bit unit Y = (Y3, Y2, Y1, Y0), where Y3 is
the most significant byte, can be written as:
Then, hierarchically, a 32-bit unit Y = (Y3, Y2, Y1, Y0), where Y3 is
the most significant byte, can be written as:
Y3(a0#3) + Y2(a0#2) + Y1(a0) + Y0
Y3(a0#3) + Y2(a0#2) + Y1(a0) + Y0
The feedback polynomial to FSR-A,
FSR-A的反馈多项式，
f(x) = a0(x#5) + x#2 + 1
f(x) = a0(x#5) + x#2 + 1
produces the maximum-length period of the key stream with a0.
使用a0生成密钥流的最大长度周期。
Similarly, a1, a2, and a3 are the roots of irreducible polynomials of degree four of
类似地，a1、a2和a3是四次不可约多项式的根
x#4 + q#230(x#3) + q#156(x#2) + q#93(x) + q#29 in GF(2#8)
x#4 + r#34(x#3) + r#16(x#2) + r#199(x) + r#248 in GF(2#8)
x#4 + s#157(x#3) + s#253(x#2) + s#56(x) + s#16 in GF(2#8)
x#4 + q#230(x#3) + q#156(x#2) + q#93(x) + q#29 in GF(2#8)
x#4 + r#34(x#3) + r#16(x#2) + r#199(x) + r#248 in GF(2#8)
x#4 + s#157(x#3) + s#253(x#2) + s#56(x) + s#16 in GF(2#8)
respectively. The feedback polynomial to FSR-B that uses a1, a2, and a3 can produce the maximum-length period. The feedback polynomials to FSR-A and FSR-B are as written in Step 2 of the next() operation, and the mathematical notations of these polynomials can also be found in [SECRYPT07].
分别地使用a1、a2和a3的FSR-B反馈多项式可以产生最大长度周期。FSR-A和FSR-B的反馈多项式如next（）操作的步骤2所述，这些多项式的数学符号也可在[SECRYPT07]中找到。
Calculation of the original feedback polynomials might be time-consuming because it includes multiplications in finite fields. However, these multiplications can be done faster if the multiples of a0, ..., a3 were already calculated for all possible inputs. The tables of amul0, ..., amul3 in Appendix A provide such pre-calculation results. As shown in Step 2 of next(), we can utilize these tables to finish the necessary calculations efficiently.
原始反馈多项式的计算可能很耗时，因为它包括有限域中的乘法。但是，如果已经为所有可能的输入计算了a0、…、a3的倍数，则可以更快地进行这些乘法运算。附录A中的amul0、…、amul3表提供了此类预计算结果。如next（）的步骤2所示，我们可以利用这些表高效地完成必要的计算。
For example, consider the input as a 32-bit value w, which represents an element of GF(2#32). The 32-bit output string w' = a0 ** w can be obtained using the amul0 table in Appendix A.1 as follows:
例如，考虑输入为32位值W，它代表GF（2×32）的元素。可使用附录A.1中的amul0表获得32位输出字符串w'=a0**w，如下所示：
w' = (w << 8) ^ amul0[w >> 24];
w' = (w << 8) ^ amul0[w >> 24];
Likewise, multiplications of (a1 ** w), (a2 ** w), and (a3 ** w) can be obtained in the same way, simply by using the amul1, amul2, and amul3 tables that we provide in Appendixes A.2, A.3, and A.4.
类似地，（a1**w）、（a2**w）和（a3**w）的乘法可以通过相同的方式获得，只需使用附录A.2、A.3和A.4中提供的amul1、amul2和amul3表即可。
Eventually, Step 2 of the next() operation, which updates A'[4] and B'[10], can be written in the C language syntax as follows. Note that nA[4] and nB[10] correspond to A'[4] and B'[10], respectively, and temp1 and temp2 are 32-bit variables.
最后，next（）操作的第2步（更新A'[4]和B'[10]）可以用C语言语法编写，如下所示。注意，nA[4]和nB[10]分别对应于A'[4]和B'[10]，并且temp1和temp2是32位变量。
nA[4] = ((A[0] << 8) ^ amul0[(A[0] >> 24)]) ^ A[3];
if (mode == INIT)
nA[4] ^= NLF(B[0], R2, R1, A[4]);
nA[4] = ((A[0] << 8) ^ amul0[(A[0] >> 24)]) ^ A[3];
if (mode == INIT)
nA[4] ^= NLF(B[0], R2, R1, A[4]);
if (A[2] & 0x40000000) {
temp1 = (B[0] << 8) ^ amul1[(B[0] >> 24)];
} else {
temp1 = (B[0] << 8) ^ amul2[(B[0] >> 24)];
}
if (A[2] & 0x40000000) {
temp1 = (B[0] << 8) ^ amul1[(B[0] >> 24)];
} else {
temp1 = (B[0] << 8) ^ amul2[(B[0] >> 24)];
}
if (A[2] & 0x80000000) {
temp2 = (B[8] << 8) ^ amul3[(B[8] >> 24)];
} else {
temp2 = B[8];
}
if (A[2] & 0x80000000) {
temp2 = (B[8] << 8) ^ amul3[(B[8] >> 24)];
} else {
temp2 = B[8];
}
nB[10] = temp1 ^ B[1] ^ B[6] ^ temp2;
if (mode == INIT)
nB[10] ^= NLF(B[10], L2, L1, A[0]);
nB[10] = temp1 ^ B[1] ^ B[6] ^ temp2;
if (mode == INIT)
nB[10] ^= NLF(B[10], L2, L1, A[0]);
In this section, we use the notation S(i) to specifically reference the values of the internal state at i (where i >= 0), which is an arbitrary, discrete temporal moment (aka cycle) after the initialization.
在本节中，我们使用符号S（i）专门引用i处的内部状态值（其中i>=0），这是初始化后的任意离散时间矩（也称为周期）。
Given a 128-bit key K, a 128-bit initialization vector (IV), KCipher-2 is initialized as follows:
给定128位密钥K和128位初始化向量（IV），KCipher-2的初始化如下：
S(0) = init(K, IV);
S(0) = init(K, IV);
where S(0) is a state representation. With an initialized state S(i), where i >= 0, a 64-bit key stream X(i) can be obtained using the stream() operation, as follows:
其中S（0）是状态表示。对于初始化状态S（i），其中i>=0，可以使用stream（）操作获得64位密钥流X（i），如下所示：
X(i) = stream(S(i));
X(i) = stream(S(i));
To generate a new key stream X(i + 1), use the next() operation and the stream() operation as follows:
要生成新的密钥流X（i+1），请按如下所示使用next（）操作和stream（）操作：
S(i + 1) = next(S(i), NORMAL);
X(i + 1) = stream(S(i + 1));
S(i + 1) = next(S(i), NORMAL);
X(i + 1) = stream(S(i + 1));
Given a 64-bit message block M and a key stream X, an encrypted message E is obtained by
给定64位消息块M和密钥流X，通过以下方式获得加密消息E：
E = M ^ X;
E = M ^ X;
Conversely, the decrypted message D is obtained by
相反，解密的消息D通过以下方式获得：
D = E ^ X;
D = E ^ X;
The original message M and the decrypted message D are identical when the same key stream is used.
当使用相同的密钥流时，原始消息M和解密消息D是相同的。
We recommend reinitializing and rekeying after 2#58 cycles of KCipher-2, which means after generating 2#64 key stream bits. It is important to make sure that no IV is ever reused under the same key.
我们建议在KCipher-2的2#58个周期之后重新初始化和重新设置密钥，这意味着在生成2#64个密钥流位之后。重要的是要确保在同一个密钥下不会重复使用任何IV。
[ISO18033] "Information technology -- Security techniques -- Encryption algorithms -- Part 4: Stream ciphers", ISO/ IEC 18033-4:2012 Ed. 2, December 2012.
[ISO18033]“信息技术——安全技术——加密算法——第4部分：流密码”，ISO/IEC 18033-4:2012第2版，2012年12月。
[FIPS-AES] National Institute of Standards and Technology, "Advanced Encryption Standard (AES)", FIPS PUB 197, November 2001, <http://csrc.nist.gov/publications/ fips/fips197/fips-197.pdf>.
[FIPS-AES]国家标准与技术研究所，“高级加密标准（AES）”，FIPS PUB 197，2001年11月<http://csrc.nist.gov/publications/ fips/fips197/fips-197.pdf>。
[SECRYPT07] Kiyomoto, S., Tanaka, T., and K. Sakurai, "K2: A Stream Cipher Algorithm Using Dynamic Feedback Control", Proc. SECRYPT 2007, pp. 204-213.
[SECRYPT07]Kiyomoto，S.，Tanaka，T.，和K.Sakurai，“K2：使用动态反馈控制的流密码算法”，Proc。《2007年部长会议》，第204-213页。
[ICETE07] Kiyomoto, S., Tanaka, T., and K. Sakurai, "K2 Stream Cipher", Proc. ICETE 2007, pp. 214-226.
[ICETE07]Kiyomoto，S.，Tanaka，T.，和K.Sakurai，“K2流密码”，Proc。ICETE 2007，第214-226页。
[CRYPTEC] Bogdanov, A., Preneel, B., and V. Rijmen, "Security Evaluation of the K2 Stream Cipher", 2010, <http://www.cryptrec.go.jp/english/estimation.html>.
[CRYPTEC]Bogdanov，A.，Preneel，B.，和V.Rijmen，“K2流密码的安全评估”，2010年<http://www.cryptrec.go.jp/english/estimation.html>.
[CRYPTECLIST] "Cryptography Research and Evaluation Committees", <http://www.cryptrec.go.jp/english/estimation.html>.
[密码列表]“密码研究和评估委员会”<http://www.cryptrec.go.jp/english/estimation.html>.
[SIIS11] Priemuth-Schmid, D., "Attacks on Simplified Versions of K2", Proc. SIIS 2011, LNCS 7053, pp. 117-127.
[SIIS11]Priemuth Schmid，D.，“对K2简化版本的攻击”，Proc。SIIS 2011，LNCS 7053，第117-127页。
[SASC07] Kiyomoto, S., Tanaka, T., and K. Sakurai, "A Word-Oriented Stream Cipher Using Clock Control", Proc. SASC 2007, pp. 260-274.
[SASC07]Kiyomoto，S.，Tanaka，T.，和K.Sakurai，“使用时钟控制的面向字的流密码”，Proc。国资委2007年，第260-274页。
Appendix A. Tables for Multiplication in GF(2#32)
附录A.GF（2#32）中的乘法表
amul0[256] = {
0x00000000,0xB6086D1A,0xAF10DA34,0x1918B72E,
0x9D207768,0x2B281A72,0x3230AD5C,0x8438C046,
0xF940EED0,0x4F4883CA,0x565034E4,0xE05859FE,
0x646099B8,0xD268F4A2,0xCB70438C,0x7D782E96,
0x31801F63,0x87887279,0x9E90C557,0x2898A84D,
0xACA0680B,0x1AA80511,0x03B0B23F,0xB5B8DF25,
0xC8C0F1B3,0x7EC89CA9,0x67D02B87,0xD1D8469D,
0x55E086DB,0xE3E8EBC1,0xFAF05CEF,0x4CF831F5,
0x62C33EC6,0xD4CB53DC,0xCDD3E4F2,0x7BDB89E8,
0xFFE349AE,0x49EB24B4,0x50F3939A,0xE6FBFE80,
0x9B83D016,0x2D8BBD0C,0x34930A22,0x829B6738,
0x06A3A77E,0xB0ABCA64,0xA9B37D4A,0x1FBB1050,
0x534321A5,0xE54B4CBF,0xFC53FB91,0x4A5B968B,
0xCE6356CD,0x786B3BD7,0x61738CF9,0xD77BE1E3,
0xAA03CF75,0x1C0BA26F,0x05131541,0xB31B785B,
0x3723B81D,0x812BD507,0x98336229,0x2E3B0F33,
0xC4457C4F,0x724D1155,0x6B55A67B,0xDD5DCB61,
0x59650B27,0xEF6D663D,0xF675D113,0x407DBC09,
0x3D05929F,0x8B0DFF85,0x921548AB,0x241D25B1,
0xA025E5F7,0x162D88ED,0x0F353FC3,0xB93D52D9,
0xF5C5632C,0x43CD0E36,0x5AD5B918,0xECDDD402,
0x68E51444,0xDEED795E,0xC7F5CE70,0x71FDA36A,
0x0C858DFC,0xBA8DE0E6,0xA39557C8,0x159D3AD2,
0x91A5FA94,0x27AD978E,0x3EB520A0,0x88BD4DBA,
0xA6864289,0x108E2F93,0x099698BD,0xBF9EF5A7,
0x3BA635E1,0x8DAE58FB,0x94B6EFD5,0x22BE82CF,
0x5FC6AC59,0xE9CEC143,0xF0D6766D,0x46DE1B77,
0xC2E6DB31,0x74EEB62B,0x6DF60105,0xDBFE6C1F,
0x97065DEA,0x210E30F0,0x381687DE,0x8E1EEAC4,
0x0A262A82,0xBC2E4798,0xA536F0B6,0x133E9DAC,
0x6E46B33A,0xD84EDE20,0xC156690E,0x775E0414,
0xF366C452,0x456EA948,0x5C761E66,0xEA7E737C,
0x4B8AF89E,0xFD829584,0xE49A22AA,0x52924FB0,
0xD6AA8FF6,0x60A2E2EC,0x79BA55C2,0xCFB238D8,
0xB2CA164E,0x04C27B54,0x1DDACC7A,0xABD2A160,
0x2FEA6126,0x99E20C3C,0x80FABB12,0x36F2D608,
0x7A0AE7FD,0xCC028AE7,0xD51A3DC9,0x631250D3,
0xE72A9095,0x5122FD8F,0x483A4AA1,0xFE3227BB,
0x834A092D,0x35426437,0x2C5AD319,0x9A52BE03,
0x1E6A7E45,0xA862135F,0xB17AA471,0x0772C96B,
0x2949C658,0x9F41AB42,0x86591C6C,0x30517176,
0xB469B130,0x0261DC2A,0x1B796B04,0xAD71061E,
0xD0092888,0x66014592,0x7F19F2BC,0xC9119FA6,
amul0[256] = {
0x00000000,0xB6086D1A,0xAF10DA34,0x1918B72E,
0x9D207768,0x2B281A72,0x3230AD5C,0x8438C046,
0xF940EED0,0x4F4883CA,0x565034E4,0xE05859FE,
0x646099B8,0xD268F4A2,0xCB70438C,0x7D782E96,
0x31801F63,0x87887279,0x9E90C557,0x2898A84D,
0xACA0680B,0x1AA80511,0x03B0B23F,0xB5B8DF25,
0xC8C0F1B3,0x7EC89CA9,0x67D02B87,0xD1D8469D,
0x55E086DB,0xE3E8EBC1,0xFAF05CEF,0x4CF831F5,
0x62C33EC6,0xD4CB53DC,0xCDD3E4F2,0x7BDB89E8,
0xFFE349AE,0x49EB24B4,0x50F3939A,0xE6FBFE80,
0x9B83D016,0x2D8BBD0C,0x34930A22,0x829B6738,
0x06A3A77E,0xB0ABCA64,0xA9B37D4A,0x1FBB1050,
0x534321A5,0xE54B4CBF,0xFC53FB91,0x4A5B968B,
0xCE6356CD,0x786B3BD7,0x61738CF9,0xD77BE1E3,
0xAA03CF75,0x1C0BA26F,0x05131541,0xB31B785B,
0x3723B81D,0x812BD507,0x98336229,0x2E3B0F33,
0xC4457C4F,0x724D1155,0x6B55A67B,0xDD5DCB61,
0x59650B27,0xEF6D663D,0xF675D113,0x407DBC09,
0x3D05929F,0x8B0DFF85,0x921548AB,0x241D25B1,
0xA025E5F7,0x162D88ED,0x0F353FC3,0xB93D52D9,
0xF5C5632C,0x43CD0E36,0x5AD5B918,0xECDDD402,
0x68E51444,0xDEED795E,0xC7F5CE70,0x71FDA36A,
0x0C858DFC,0xBA8DE0E6,0xA39557C8,0x159D3AD2,
0x91A5FA94,0x27AD978E,0x3EB520A0,0x88BD4DBA,
0xA6864289,0x108E2F93,0x099698BD,0xBF9EF5A7,
0x3BA635E1,0x8DAE58FB,0x94B6EFD5,0x22BE82CF,
0x5FC6AC59,0xE9CEC143,0xF0D6766D,0x46DE1B77,
0xC2E6DB31,0x74EEB62B,0x6DF60105,0xDBFE6C1F,
0x97065DEA,0x210E30F0,0x381687DE,0x8E1EEAC4,
0x0A262A82,0xBC2E4798,0xA536F0B6,0x133E9DAC,
0x6E46B33A,0xD84EDE20,0xC156690E,0x775E0414,
0xF366C452,0x456EA948,0x5C761E66,0xEA7E737C,
0x4B8AF89E,0xFD829584,0xE49A22AA,0x52924FB0,
0xD6AA8FF6,0x60A2E2EC,0x79BA55C2,0xCFB238D8,
0xB2CA164E,0x04C27B54,0x1DDACC7A,0xABD2A160,
0x2FEA6126,0x99E20C3C,0x80FABB12,0x36F2D608,
0x7A0AE7FD,0xCC028AE7,0xD51A3DC9,0x631250D3,
0xE72A9095,0x5122FD8F,0x483A4AA1,0xFE3227BB,
0x834A092D,0x35426437,0x2C5AD319,0x9A52BE03,
0x1E6A7E45,0xA862135F,0xB17AA471,0x0772C96B,
0x2949C658,0x9F41AB42,0x86591C6C,0x30517176,
0xB469B130,0x0261DC2A,0x1B796B04,0xAD71061E,
0xD0092888,0x66014592,0x7F19F2BC,0xC9119FA6,
0x4D295FE0,0xFB2132FA,0xE23985D4,0x5431E8CE, 0x18C9D93B,0xAEC1B421,0xB7D9030F,0x01D16E15, 0x85E9AE53,0x33E1C349,0x2AF97467,0x9CF1197D, 0xE18937EB,0x57815AF1,0x4E99EDDF,0xF89180C5, 0x7CA94083,0xCAA12D99,0xD3B99AB7,0x65B1F7AD, 0x8FCF84D1,0x39C7E9CB,0x20DF5EE5,0x96D733FF, 0x12EFF3B9,0xA4E79EA3,0xBDFF298D,0x0BF74497, 0x768F6A01,0xC087071B,0xD99FB035,0x6F97DD2F, 0xEBAF1D69,0x5DA77073,0x44BFC75D,0xF2B7AA47, 0xBE4F9BB2,0x0847F6A8,0x115F4186,0xA7572C9C, 0x236FECDA,0x956781C0,0x8C7F36EE,0x3A775BF4, 0x470F7562,0xF1071878,0xE81FAF56,0x5E17C24C, 0xDA2F020A,0x6C276F10,0x753FD83E,0xC337B524, 0xED0CBA17,0x5B04D70D,0x421C6023,0xF4140D39, 0x702CCD7F,0xC624A065,0xDF3C174B,0x69347A51, 0x144C54C7,0xA24439DD,0xBB5C8EF3,0x0D54E3E9, 0x896C23AF,0x3F644EB5,0x267CF99B,0x90749481, 0xDC8CA574,0x6A84C86E,0x739C7F40,0xC594125A, 0x41ACD21C,0xF7A4BF06,0xEEBC0828,0x58B46532, 0x25CC4BA4,0x93C426BE,0x8ADC9190,0x3CD4FC8A, 0xB8EC3CCC,0x0EE451D6,0x17FCE6F8,0xA1F48BE2 };
0x18C9D93B，0xAE1BB421，0xB7B7B77D93B，0xAEC1B1B421，0xB7B7D9030F，0x01D1616 16 16 16 16 16 15，0x85E9 EEE5 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 16 16 16 16 16 16 16 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 497，0x768F6A01，0xC087071B，10亿B7 7 7亿BFC75D，0亿F7 7 7 7 7 7 7 7 7 BBBBCC75D，0亿B7 7 7 7 7 7 7 7 7 AA47，0亿BB7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 BB7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 174B，0x69347A51，0x144C54C7、0xA24439DD、0xBB5C8EF3、0x0D54E3E9、0x896C23AF、0x3F644EB5、0x267CF99B、0x90749481、0xDC8CA574、0x6A84C86E、0x739C7F40、0xC594125A、0x41ACD21C、0xF7A4BF06、0xEEBC0828、0x58B46532、0x25CC4BA4、0x93C426BE、0x8ADC9190、0x3CD4FC8A、0xB8ECC、0xEE451D6F6A17E2、0xB17FCC；
amul1[256] = {
0x00000000,0xA0F5FC2E,0x6DC7D55C,0xCD322972,
0xDAA387B8,0x7A567B96,0xB76452E4,0x1791AECA,
0x996B235D,0x399EDF73,0xF4ACF601,0x54590A2F,
0x43C8A4E5,0xE33D58CB,0x2E0F71B9,0x8EFA8D97,
0x1FD646BA,0xBF23BA94,0x721193E6,0xD2E46FC8,
0xC575C102,0x65803D2C,0xA8B2145E,0x0847E870,
0x86BD65E7,0x264899C9,0xEB7AB0BB,0x4B8F4C95,
0x5C1EE25F,0xFCEB1E71,0x31D93703,0x912CCB2D,
0x3E818C59,0x9E747077,0x53465905,0xF3B3A52B,
0xE4220BE1,0x44D7F7CF,0x89E5DEBD,0x29102293,
0xA7EAAF04,0x071F532A,0xCA2D7A58,0x6AD88676,
0x7D4928BC,0xDDBCD492,0x108EFDE0,0xB07B01CE,
0x2157CAE3,0x81A236CD,0x4C901FBF,0xEC65E391,
0xFBF44D5B,0x5B01B175,0x96339807,0x36C66429,
0xB83CE9BE,0x18C91590,0xD5FB3CE2,0x750EC0CC,
0x629F6E06,0xC26A9228,0x0F58BB5A,0xAFAD4774,
0x7C2F35B2,0xDCDAC99C,0x11E8E0EE,0xB11D1CC0,
0xA68CB20A,0x06794E24,0xCB4B6756,0x6BBE9B78,
0xE54416EF,0x45B1EAC1,0x8883C3B3,0x28763F9D,
0x3FE79157,0x9F126D79,0x5220440B,0xF2D5B825,
0x63F97308,0xC30C8F26,0x0E3EA654,0xAECB5A7A,
0xB95AF4B0,0x19AF089E,0xD49D21EC,0x7468DDC2,
0xFA925055,0x5A67AC7B,0x97558509,0x37A07927,
amul1[256] = {
0x00000000,0xA0F5FC2E,0x6DC7D55C,0xCD322972,
0xDAA387B8,0x7A567B96,0xB76452E4,0x1791AECA,
0x996B235D,0x399EDF73,0xF4ACF601,0x54590A2F,
0x43C8A4E5,0xE33D58CB,0x2E0F71B9,0x8EFA8D97,
0x1FD646BA,0xBF23BA94,0x721193E6,0xD2E46FC8,
0xC575C102,0x65803D2C,0xA8B2145E,0x0847E870,
0x86BD65E7,0x264899C9,0xEB7AB0BB,0x4B8F4C95,
0x5C1EE25F,0xFCEB1E71,0x31D93703,0x912CCB2D,
0x3E818C59,0x9E747077,0x53465905,0xF3B3A52B,
0xE4220BE1,0x44D7F7CF,0x89E5DEBD,0x29102293,
0xA7EAAF04,0x071F532A,0xCA2D7A58,0x6AD88676,
0x7D4928BC,0xDDBCD492,0x108EFDE0,0xB07B01CE,
0x2157CAE3,0x81A236CD,0x4C901FBF,0xEC65E391,
0xFBF44D5B,0x5B01B175,0x96339807,0x36C66429,
0xB83CE9BE,0x18C91590,0xD5FB3CE2,0x750EC0CC,
0x629F6E06,0xC26A9228,0x0F58BB5A,0xAFAD4774,
0x7C2F35B2,0xDCDAC99C,0x11E8E0EE,0xB11D1CC0,
0xA68CB20A,0x06794E24,0xCB4B6756,0x6BBE9B78,
0xE54416EF,0x45B1EAC1,0x8883C3B3,0x28763F9D,
0x3FE79157,0x9F126D79,0x5220440B,0xF2D5B825,
0x63F97308,0xC30C8F26,0x0E3EA654,0xAECB5A7A,
0xB95AF4B0,0x19AF089E,0xD49D21EC,0x7468DDC2,
0xFA925055,0x5A67AC7B,0x97558509,0x37A07927,
0x2031D7ED,0x80C42BC3,0x4DF602B1,0xED03FE9F, 0x42AEB9EB,0xE25B45C5,0x2F696CB7,0x8F9C9099, 0x980D3E53,0x38F8C27D,0xF5CAEB0F,0x553F1721, 0xDBC59AB6,0x7B306698,0xB6024FEA,0x16F7B3C4, 0x01661D0E,0xA193E120,0x6CA1C852,0xCC54347C, 0x5D78FF51,0xFD8D037F,0x30BF2A0D,0x904AD623, 0x87DB78E9,0x272E84C7,0xEA1CADB5,0x4AE9519B, 0xC413DC0C,0x64E62022,0xA9D40950,0x0921F57E, 0x1EB05BB4,0xBE45A79A,0x73778EE8,0xD38272C6, 0xF85E6A49,0x58AB9667,0x9599BF15,0x356C433B, 0x22FDEDF1,0x820811DF,0x4F3A38AD,0xEFCFC483, 0x61354914,0xC1C0B53A,0x0CF29C48,0xAC076066, 0xBB96CEAC,0x1B633282,0xD6511BF0,0x76A4E7DE, 0xE7882CF3,0x477DD0DD,0x8A4FF9AF,0x2ABA0581, 0x3D2BAB4B,0x9DDE5765,0x50EC7E17,0xF0198239, 0x7EE30FAE,0xDE16F380,0x1324DAF2,0xB3D126DC, 0xA4408816,0x04B57438,0xC9875D4A,0x6972A164, 0xC6DFE610,0x662A1A3E,0xAB18334C,0x0BEDCF62, 0x1C7C61A8,0xBC899D86,0x71BBB4F4,0xD14E48DA, 0x5FB4C54D,0xFF413963,0x32731011,0x9286EC3F, 0x851742F5,0x25E2BEDB,0xE8D097A9,0x48256B87, 0xD909A0AA,0x79FC5C84,0xB4CE75F6,0x143B89D8, 0x03AA2712,0xA35FDB3C,0x6E6DF24E,0xCE980E60, 0x406283F7,0xE0977FD9,0x2DA556AB,0x8D50AA85, 0x9AC1044F,0x3A34F861,0xF706D113,0x57F32D3D, 0x84715FFB,0x2484A3D5,0xE9B68AA7,0x49437689, 0x5ED2D843,0xFE27246D,0x33150D1F,0x93E0F131, 0x1D1A7CA6,0xBDEF8088,0x70DDA9FA,0xD02855D4, 0xC7B9FB1E,0x674C0730,0xAA7E2E42,0x0A8BD26C, 0x9BA71941,0x3B52E56F,0xF660CC1D,0x56953033, 0x41049EF9,0xE1F162D7,0x2CC34BA5,0x8C36B78B, 0x02CC3A1C,0xA239C632,0x6F0BEF40,0xCFFE136E, 0xD86FBDA4,0x789A418A,0xB5A868F8,0x155D94D6, 0xBAF0D3A2,0x1A052F8C,0xD73706FE,0x77C2FAD0, 0x6053541A,0xC0A6A834,0x0D948146,0xAD617D68, 0x239BF0FF,0x836E0CD1,0x4E5C25A3,0xEEA9D98D, 0xF9387747,0x59CD8B69,0x94FFA21B,0x340A5E35, 0xA5269518,0x05D36936,0xC8E14044,0x6814BC6A, 0x7F8512A0,0xDF70EE8E,0x1242C7FC,0xB2B73BD2, 0x3C4DB645,0x9CB84A6B,0x518A6319,0xF17F9F37, 0xE6EE31FD,0x461BCDD3,0x8B29E4A1,0x2BDC188F };
0.42AEB9EB，0.255B5B555C55，0.2F5B55B5B55B5555，0.2F696 6 6 CB7，0.8F9 9 9 9 9 9 9 9 9 9 9 9 9 9 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 13DC0C，0x1EB05BBB4，0xBE45AA7 9A，0x738 8 8 8 8 8 8 8 8 8 8 8 10 9 9 9 9 9 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 0x50EC7E17,0xF0198239，10月7日EEE3030FAE，10月16日F380，10月1324-4-4-4-4-4-16，10月A4408816，0 0 0 0 B747438，0 0 0 C987516-7 10 10-7 EEEE7-7-7-7-7-7-7-7-7-7-7-7-7-7-10-10-7-7-30-10-10-10-10-10-10-10-10-10 10-7-7-7-10-7-7-10-7-7-7-7-7-7-7-7-7-7-7-7-7-7-7-7-7-7个EEEE7-7-7-7-7-7-7-7-10 10 10 10-10 10 10 10 10-10 10-10-10-10-10-10-10 10-10-10-10-10-10-10 10-10 10-10-A35FDB3C，0x6E6DF24E，0xCE980 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 0 0 0 0 6 6 6 6 6 6 6 6 6 10 10 10 10 10 10 10 10 10 10 10 10 10 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 10 10 10 10 10 10 10 10 10 10 10 10 10 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 56953033，0x41049EF9、0xE1F162D7、0x2CC34BA5、0x8C36B78B、0x02CC3A1C、0xA239C632、0x6F0BEF40、0xCFFE136E、0xD86FBDA4、0x789A418A、0xB5A868F8、0x155D94D6、0xBAF0D3A2、0x1A052F8C、0xD73706FE、0x77C2FAD0、0x6053541A、0xC0A6A834、0x0D948146、0xAD617D68、0x239BFFF、0x836E0CD1、0xE5E5FFA940B7D、0xE57459B9B9E757B9E5F947D、0xB9B9B9B9B9B9B9B9E、0xB9B9B9B9B9B9B9B9B9B9B9E、0xB9B9B9B，0xA5269518、0x05D36936、0xC8E14044、0x6814BC6A、0x7F8512A0、0xDF70EE8E、0x1242C7FC、0xB2B73BD2、0x3C4DB645、0x9CB84A6B、0x518A6319、0xF17F9F37、0xE6EE31FD、0x461BCDD3、0x8B29E4A1、0x2BDC188F}；
amul2[256] = {
0x00000000,0x5BF87F93,0xB6BDFE6B,0xED4581F8,
0x2137B1D6,0x7ACFCE45,0x978A4FBD,0xCC72302E,
0x426E2FE1,0x19965072,0xF4D3D18A,0xAF2BAE19,
0x63599E37,0x38A1E1A4,0xD5E4605C,0x8E1C1FCF,
0x84DC5E8F,0xDF24211C,0x3261A0E4,0x6999DF77,
0xA5EBEF59,0xFE1390CA,0x13561132,0x48AE6EA1,
0xC6B2716E,0x9D4A0EFD,0x700F8F05,0x2BF7F096,
0xE785C0B8,0xBC7DBF2B,0x51383ED3,0x0AC04140,
0x45F5BC53,0x1E0DC3C0,0xF3484238,0xA8B03DAB,
0x64C20D85,0x3F3A7216,0xD27FF3EE,0x89878C7D,
0x079B93B2,0x5C63EC21,0xB1266DD9,0xEADE124A,
0x26AC2264,0x7D545DF7,0x9011DC0F,0xCBE9A39C,
0xC129E2DC,0x9AD19D4F,0x77941CB7,0x2C6C6324,
0xE01E530A,0xBBE62C99,0x56A3AD61,0x0D5BD2F2,
0x8347CD3D,0xD8BFB2AE,0x35FA3356,0x6E024CC5,
0xA2707CEB,0xF9880378,0x14CD8280,0x4F35FD13,
0x8AA735A6,0xD15F4A35,0x3C1ACBCD,0x67E2B45E,
0xAB908470,0xF068FBE3,0x1D2D7A1B,0x46D50588,
0xC8C91A47,0x933165D4,0x7E74E42C,0x258C9BBF,
0xE9FEAB91,0xB206D402,0x5F4355FA,0x04BB2A69,
0x0E7B6B29,0x558314BA,0xB8C69542,0xE33EEAD1,
0x2F4CDAFF,0x74B4A56C,0x99F12494,0xC2095B07,
0x4C1544C8,0x17ED3B5B,0xFAA8BAA3,0xA150C530,
0x6D22F51E,0x36DA8A8D,0xDB9F0B75,0x806774E6,
0xCF5289F5,0x94AAF666,0x79EF779E,0x2217080D,
0xEE653823,0xB59D47B0,0x58D8C648,0x0320B9DB,
0x8D3CA614,0xD6C4D987,0x3B81587F,0x607927EC,
0xAC0B17C2,0xF7F36851,0x1AB6E9A9,0x414E963A,
0x4B8ED77A,0x1076A8E9,0xFD332911,0xA6CB5682,
0x6AB966AC,0x3141193F,0xDC0498C7,0x87FCE754,
0x09E0F89B,0x52188708,0xBF5D06F0,0xE4A57963,
0x28D7494D,0x732F36DE,0x9E6AB726,0xC592C8B5,
0x59036A01,0x02FB1592,0xEFBE946A,0xB446EBF9,
0x7834DBD7,0x23CCA444,0xCE8925BC,0x95715A2F,
0x1B6D45E0,0x40953A73,0xADD0BB8B,0xF628C418,
0x3A5AF436,0x61A28BA5,0x8CE70A5D,0xD71F75CE,
0xDDDF348E,0x86274B1D,0x6B62CAE5,0x309AB576,
0xFCE88558,0xA710FACB,0x4A557B33,0x11AD04A0,
0x9FB11B6F,0xC44964FC,0x290CE504,0x72F49A97,
0xBE86AAB9,0xE57ED52A,0x083B54D2,0x53C32B41,
0x1CF6D652,0x470EA9C1,0xAA4B2839,0xF1B357AA,
0x3DC16784,0x66391817,0x8B7C99EF,0xD084E67C,
0x5E98F9B3,0x05608620,0xE82507D8,0xB3DD784B,
0x7FAF4865,0x245737F6,0xC912B60E,0x92EAC99D,
0x982A88DD,0xC3D2F74E,0x2E9776B6,0x756F0925,
amul2[256] = {
0x00000000,0x5BF87F93,0xB6BDFE6B,0xED4581F8,
0x2137B1D6,0x7ACFCE45,0x978A4FBD,0xCC72302E,
0x426E2FE1,0x19965072,0xF4D3D18A,0xAF2BAE19,
0x63599E37,0x38A1E1A4,0xD5E4605C,0x8E1C1FCF,
0x84DC5E8F,0xDF24211C,0x3261A0E4,0x6999DF77,
0xA5EBEF59,0xFE1390CA,0x13561132,0x48AE6EA1,
0xC6B2716E,0x9D4A0EFD,0x700F8F05,0x2BF7F096,
0xE785C0B8,0xBC7DBF2B,0x51383ED3,0x0AC04140,
0x45F5BC53,0x1E0DC3C0,0xF3484238,0xA8B03DAB,
0x64C20D85,0x3F3A7216,0xD27FF3EE,0x89878C7D,
0x079B93B2,0x5C63EC21,0xB1266DD9,0xEADE124A,
0x26AC2264,0x7D545DF7,0x9011DC0F,0xCBE9A39C,
0xC129E2DC,0x9AD19D4F,0x77941CB7,0x2C6C6324,
0xE01E530A,0xBBE62C99,0x56A3AD61,0x0D5BD2F2,
0x8347CD3D,0xD8BFB2AE,0x35FA3356,0x6E024CC5,
0xA2707CEB,0xF9880378,0x14CD8280,0x4F35FD13,
0x8AA735A6,0xD15F4A35,0x3C1ACBCD,0x67E2B45E,
0xAB908470,0xF068FBE3,0x1D2D7A1B,0x46D50588,
0xC8C91A47,0x933165D4,0x7E74E42C,0x258C9BBF,
0xE9FEAB91,0xB206D402,0x5F4355FA,0x04BB2A69,
0x0E7B6B29,0x558314BA,0xB8C69542,0xE33EEAD1,
0x2F4CDAFF,0x74B4A56C,0x99F12494,0xC2095B07,
0x4C1544C8,0x17ED3B5B,0xFAA8BAA3,0xA150C530,
0x6D22F51E,0x36DA8A8D,0xDB9F0B75,0x806774E6,
0xCF5289F5,0x94AAF666,0x79EF779E,0x2217080D,
0xEE653823,0xB59D47B0,0x58D8C648,0x0320B9DB,
0x8D3CA614,0xD6C4D987,0x3B81587F,0x607927EC,
0xAC0B17C2,0xF7F36851,0x1AB6E9A9,0x414E963A,
0x4B8ED77A,0x1076A8E9,0xFD332911,0xA6CB5682,
0x6AB966AC,0x3141193F,0xDC0498C7,0x87FCE754,
0x09E0F89B,0x52188708,0xBF5D06F0,0xE4A57963,
0x28D7494D,0x732F36DE,0x9E6AB726,0xC592C8B5,
0x59036A01,0x02FB1592,0xEFBE946A,0xB446EBF9,
0x7834DBD7,0x23CCA444,0xCE8925BC,0x95715A2F,
0x1B6D45E0,0x40953A73,0xADD0BB8B,0xF628C418,
0x3A5AF436,0x61A28BA5,0x8CE70A5D,0xD71F75CE,
0xDDDF348E,0x86274B1D,0x6B62CAE5,0x309AB576,
0xFCE88558,0xA710FACB,0x4A557B33,0x11AD04A0,
0x9FB11B6F,0xC44964FC,0x290CE504,0x72F49A97,
0xBE86AAB9,0xE57ED52A,0x083B54D2,0x53C32B41,
0x1CF6D652,0x470EA9C1,0xAA4B2839,0xF1B357AA,
0x3DC16784,0x66391817,0x8B7C99EF,0xD084E67C,
0x5E98F9B3,0x05608620,0xE82507D8,0xB3DD784B,
0x7FAF4865,0x245737F6,0xC912B60E,0x92EAC99D,
0x982A88DD,0xC3D2F74E,0x2E9776B6,0x756F0925,
0xB91D390B,0xE2E54698,0x0FA0C760,0x5458B8F3, 0xDA44A73C,0x81BCD8AF,0x6CF95957,0x370126C4, 0xFB7316EA,0xA08B6979,0x4DCEE881,0x16369712, 0xD3A45FA7,0x885C2034,0x6519A1CC,0x3EE1DE5F, 0xF293EE71,0xA96B91E2,0x442E101A,0x1FD66F89, 0x91CA7046,0xCA320FD5,0x27778E2D,0x7C8FF1BE, 0xB0FDC190,0xEB05BE03,0x06403FFB,0x5DB84068, 0x57780128,0x0C807EBB,0xE1C5FF43,0xBA3D80D0, 0x764FB0FE,0x2DB7CF6D,0xC0F24E95,0x9B0A3106, 0x15162EC9,0x4EEE515A,0xA3ABD0A2,0xF853AF31, 0x34219F1F,0x6FD9E08C,0x829C6174,0xD9641EE7, 0x9651E3F4,0xCDA99C67,0x20EC1D9F,0x7B14620C, 0xB7665222,0xEC9E2DB1,0x01DBAC49,0x5A23D3DA, 0xD43FCC15,0x8FC7B386,0x6282327E,0x397A4DED, 0xF5087DC3,0xAEF00250,0x43B583A8,0x184DFC3B, 0x128DBD7B,0x4975C2E8,0xA4304310,0xFFC83C83, 0x33BA0CAD,0x6842733E,0x8507F2C6,0xDEFF8D55, 0x50E3929A,0x0B1BED09,0xE65E6CF1,0xBDA61362, 0x71D4234C,0x2A2C5CDF,0xC769DD27,0x9C91A2B4 };
0xD44A7C，0x8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 7 7 7 7 7 7 7 7 7 7 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 807退潮，0x2-4 E95，0x9 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 16 16 EC9，0x4 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 EEEEEEEEEE15 15 15 15 15 15 15 A，10 10 10 10 10 10 10 10 10 10 10 10 10 EEEEEEEEEEEEEEEEEEEEEEEEEEEEEE15 A，0x6 15 15 A，0x10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 15 A，0xA310 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 B583A8,0x184DFC3B，0x128DBD7B，0x4975C2E8、0xA4304310、0xFFC83C83、0x33BA0CAD、0x6842733E、0x8507F2C6、0xDEFF8D55、0x50E3929A、0x0B1BED09、0xE65E6CF1、0xBDA61362、0x71D4234C、0x2A22C5CDF、0xC769DD27、0x9C91A2B4}；
amul3[256] = {
0x00000000,0x4559568B,0x8AB2AC73,0xCFEBFAF8,
0x71013DE6,0x34586B6D,0xFBB39195,0xBEEAC71E,
0xE2027AA9,0xA75B2C22,0x68B0D6DA,0x2DE98051,
0x9303474F,0xD65A11C4,0x19B1EB3C,0x5CE8BDB7,
0xA104F437,0xE45DA2BC,0x2BB65844,0x6EEF0ECF,
0xD005C9D1,0x955C9F5A,0x5AB765A2,0x1FEE3329,
0x43068E9E,0x065FD815,0xC9B422ED,0x8CED7466,
0x3207B378,0x775EE5F3,0xB8B51F0B,0xFDEC4980,
0x27088D6E,0x6251DBE5,0xADBA211D,0xE8E37796,
0x5609B088,0x1350E603,0xDCBB1CFB,0x99E24A70,
0xC50AF7C7,0x8053A14C,0x4FB85BB4,0x0AE10D3F,
0xB40BCA21,0xF1529CAA,0x3EB96652,0x7BE030D9,
0x860C7959,0xC3552FD2,0x0CBED52A,0x49E783A1,
0xF70D44BF,0xB2541234,0x7DBFE8CC,0x38E6BE47,
0x640E03F0,0x2157557B,0xEEBCAF83,0xABE5F908,
0x150F3E16,0x5056689D,0x9FBD9265,0xDAE4C4EE,
0x4E107FDC,0x0B492957,0xC4A2D3AF,0x81FB8524,
0x3F11423A,0x7A4814B1,0xB5A3EE49,0xF0FAB8C2,
0xAC120575,0xE94B53FE,0x26A0A906,0x63F9FF8D,
0xDD133893,0x984A6E18,0x57A194E0,0x12F8C26B,
0xEF148BEB,0xAA4DDD60,0x65A62798,0x20FF7113,
0x9E15B60D,0xDB4CE086,0x14A71A7E,0x51FE4CF5,
0x0D16F142,0x484FA7C9,0x87A45D31,0xC2FD0BBA,
0x7C17CCA4,0x394E9A2F,0xF6A560D7,0xB3FC365C,
0x6918F2B2,0x2C41A439,0xE3AA5EC1,0xA6F3084A,
amul3[256] = {
0x00000000,0x4559568B,0x8AB2AC73,0xCFEBFAF8,
0x71013DE6,0x34586B6D,0xFBB39195,0xBEEAC71E,
0xE2027AA9,0xA75B2C22,0x68B0D6DA,0x2DE98051,
0x9303474F,0xD65A11C4,0x19B1EB3C,0x5CE8BDB7,
0xA104F437,0xE45DA2BC,0x2BB65844,0x6EEF0ECF,
0xD005C9D1,0x955C9F5A,0x5AB765A2,0x1FEE3329,
0x43068E9E,0x065FD815,0xC9B422ED,0x8CED7466,
0x3207B378,0x775EE5F3,0xB8B51F0B,0xFDEC4980,
0x27088D6E,0x6251DBE5,0xADBA211D,0xE8E37796,
0x5609B088,0x1350E603,0xDCBB1CFB,0x99E24A70,
0xC50AF7C7,0x8053A14C,0x4FB85BB4,0x0AE10D3F,
0xB40BCA21,0xF1529CAA,0x3EB96652,0x7BE030D9,
0x860C7959,0xC3552FD2,0x0CBED52A,0x49E783A1,
0xF70D44BF,0xB2541234,0x7DBFE8CC,0x38E6BE47,
0x640E03F0,0x2157557B,0xEEBCAF83,0xABE5F908,
0x150F3E16,0x5056689D,0x9FBD9265,0xDAE4C4EE,
0x4E107FDC,0x0B492957,0xC4A2D3AF,0x81FB8524,
0x3F11423A,0x7A4814B1,0xB5A3EE49,0xF0FAB8C2,
0xAC120575,0xE94B53FE,0x26A0A906,0x63F9FF8D,
0xDD133893,0x984A6E18,0x57A194E0,0x12F8C26B,
0xEF148BEB,0xAA4DDD60,0x65A62798,0x20FF7113,
0x9E15B60D,0xDB4CE086,0x14A71A7E,0x51FE4CF5,
0x0D16F142,0x484FA7C9,0x87A45D31,0xC2FD0BBA,
0x7C17CCA4,0x394E9A2F,0xF6A560D7,0xB3FC365C,
0x6918F2B2,0x2C41A439,0xE3AA5EC1,0xA6F3084A,
0x1819CF54,0x5D4099DF,0x92AB6327,0xD7F235AC, 0x8B1A881B,0xCE43DE90,0x01A82468,0x44F172E3, 0xFA1BB5FD,0xBF42E376,0x70A9198E,0x35F04F05, 0xC81C0685,0x8D45500E,0x42AEAAF6,0x07F7FC7D, 0xB91D3B63,0xFC446DE8,0x33AF9710,0x76F6C19B, 0x2A1E7C2C,0x6F472AA7,0xA0ACD05F,0xE5F586D4, 0x5B1F41CA,0x1E461741,0xD1ADEDB9,0x94F4BB32, 0x9C20FEDD,0xD979A856,0x169252AE,0x53CB0425, 0xED21C33B,0xA87895B0,0x67936F48,0x22CA39C3, 0x7E228474,0x3B7BD2FF,0xF4902807,0xB1C97E8C, 0x0F23B992,0x4A7AEF19,0x859115E1,0xC0C8436A, 0x3D240AEA,0x787D5C61,0xB796A699,0xF2CFF012, 0x4C25370C,0x097C6187,0xC6979B7F,0x83CECDF4, 0xDF267043,0x9A7F26C8,0x5594DC30,0x10CD8ABB, 0xAE274DA5,0xEB7E1B2E,0x2495E1D6,0x61CCB75D, 0xBB2873B3,0xFE712538,0x319ADFC0,0x74C3894B, 0xCA294E55,0x8F7018DE,0x409BE226,0x05C2B4AD, 0x592A091A,0x1C735F91,0xD398A569,0x96C1F3E2, 0x282B34FC,0x6D726277,0xA299988F,0xE7C0CE04, 0x1A2C8784,0x5F75D10F,0x909E2BF7,0xD5C77D7C, 0x6B2DBA62,0x2E74ECE9,0xE19F1611,0xA4C6409A, 0xF82EFD2D,0xBD77ABA6,0x729C515E,0x37C507D5, 0x892FC0CB,0xCC769640,0x039D6CB8,0x46C43A33, 0xD2308101,0x9769D78A,0x58822D72,0x1DDB7BF9, 0xA331BCE7,0xE668EA6C,0x29831094,0x6CDA461F, 0x3032FBA8,0x756BAD23,0xBA8057DB,0xFFD90150, 0x4133C64E,0x046A90C5,0xCB816A3D,0x8ED83CB6, 0x73347536,0x366D23BD,0xF986D945,0xBCDF8FCE, 0x023548D0,0x476C1E5B,0x8887E4A3,0xCDDEB228, 0x91360F9F,0xD46F5914,0x1B84A3EC,0x5EDDF567, 0xE0373279,0xA56E64F2,0x6A859E0A,0x2FDCC881, 0xF5380C6F,0xB0615AE4,0x7F8AA01C,0x3AD3F697, 0x84393189,0xC1606702,0x0E8B9DFA,0x4BD2CB71, 0x173A76C6,0x5263204D,0x9D88DAB5,0xD8D18C3E, 0x663B4B20,0x23621DAB,0xEC89E753,0xA9D0B1D8, 0x543CF858,0x1165AED3,0xDE8E542B,0x9BD702A0, 0x253DC5BE,0x60649335,0xAF8F69CD,0xEAD63F46, 0xB63E82F1,0xF367D47A,0x3C8C2E82,0x79D57809, 0xC73FBF17,0x8266E99C,0x4D8D1364,0x08D445EF };
0x8B1881B，0xCE10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 FEDD，0xD979A856,0x169252AE，0x6-676 6-6 6-6 6-6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 7 CFCF10 12，0x4 4 257 7B7B7B7B7B7BB7B7B7BB7B7B7B7B7B7B7B7B7B7BBBBD2FF，0xF494 907 7 7 7 7 7 7 7-78B7B7BBBBBBBBBBBBBBB7D2D2D6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 B75D，0xCA294 5，0xCA4 5 5 5，0x8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 CB，0xD78A，0x58822 72，0x1DB7BB7BF9，0x8 8 8 8 8 8 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 BBBBBBBBBBBBBB7 FFF9 9 9 9 9 9，0 7 7 7 7 7 7 7 7 9，0 6 6 7 7 7 7 7 7 7 7 9，10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 BBBBBB7 7 7 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 0x1B84A3EC，0x5EDDF567，0.F53380C6F，0 0 0 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 F，0 0 0 6 6 6 6 6 10 10 AE4，0 0 7 7 7 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 82F1,0xF367D47A，0x3C8C2E82,0x79D57809,0xC73FBF17,0x8266E99C,0x4D8D1364,0x08D445EF}；
We provide an example implementation of KCipher-2 written in C. The implementation is simple; we do not consider storage or time complexity, nor do we consider software engineering-related issues, such as encapsulation, modularity, and so on.
我们提供了一个用C编写的KCipher-2的示例实现；我们不考虑存储或时间复杂度，也不考虑软件工程相关的问题，例如封装、模块化等。
#include <stdio.h>
#include <stdint.h>
#include <stdio.h>
#include <stdint.h>
#define INIT 0 #define NORMAL 1
#定义初始0#定义法线1
void init (unsigned int *, unsigned int *);
void next(int);
void stream (unsigned int *, unsigned int *);
void init (unsigned int *, unsigned int *);
void next(int);
void stream (unsigned int *, unsigned int *);
static const uint8_t S_box[256] = {
...
// as defined in Section 2.4.3
};
static const uint8_t S_box[256] = {
...
// as defined in Section 2.4.3
};
static const uint32_t amul0[256] = {
...
// as defined in Appendix A.1
};
static const uint32_t amul0[256] = {
...
// as defined in Appendix A.1
};
static const uint32_t amul1[256] = {
...
// as defined in Appendix A.2
};
static const uint32_t amul1[256] = {
...
// as defined in Appendix A.2
};
static const uint32_t amul2[256] = {
...
// as defined in Appendix A.3
};
static const uint32_t amul2[256] = {
...
// as defined in Appendix A.3
};
static const uint32_t amul3[256] = {
...
// as defined in Appendix A.4
};
static const uint32_t amul3[256] = {
...
// as defined in Appendix A.4
};
/* Global variables */
/* Global variables */
// State S
uint32_t A[5]; // five 32-bit units
// State S
uint32_t A[5]; // five 32-bit units
uint32_t B[11]; // eleven 32-bit units
uint32_t L1, R1, L2, R2; // one 32-bit unit for each
uint32_t B[11]; // eleven 32-bit units
uint32_t L1, R1, L2, R2; // one 32-bit unit for each
// The internal key (IK) and the initialization vector (IV)
uint32_t IK[12]; // (12*32) bits
uint32_t IV[4]; // (4*32) bits
// The internal key (IK) and the initialization vector (IV)
uint32_t IK[12]; // (12*32) bits
uint32_t IV[4]; // (4*32) bits
/**
* Do multiplication in GF(2#8) of the irreducible polynomial,
* f(x) = x#8 + x#4 + x#3 + x + 1. The given parameter is multiplied
* by 2.
* @param t : (INPUT). 8 bits. The number will be multiplied by 2
* @return : (OUTPUT). 8 bits. The multiplication result
*/
uint8_t GF_mult_by_2 (uint8_t t) {
uint8_t q;
uint32_t lq;
/**
* Do multiplication in GF(2#8) of the irreducible polynomial,
* f(x) = x#8 + x#4 + x#3 + x + 1. The given parameter is multiplied
* by 2.
* @param t : (INPUT). 8 bits. The number will be multiplied by 2
* @return : (OUTPUT). 8 bits. The multiplication result
*/
uint8_t GF_mult_by_2 (uint8_t t) {
uint8_t q;
uint32_t lq;
lq = t << 1;
if ((lq & 0x100) != 0) lq ^= 0x011B;
q = lq ^ 0xFF;
lq = t << 1;
if ((lq & 0x100) != 0) lq ^= 0x011B;
q = lq ^ 0xFF;
return q;
}
return q;
}
/**
* Do multiplication in GF(2#8) of the irreducible polynomial,
* f(x) = x#8 + x#4 + x#3 + x + 1. The given parameter is multiplied
* by 3.
* @param t : (INPUT). 8 bits. The number will be multiplied by 3
* @return : (OUTPUT). 8 bits. The multiplication result
*/
uint8_t GF_mult_by_3 (uint8_t t) {
uint8_t q;
uint32_t lq;
/**
* Do multiplication in GF(2#8) of the irreducible polynomial,
* f(x) = x#8 + x#4 + x#3 + x + 1. The given parameter is multiplied
* by 3.
* @param t : (INPUT). 8 bits. The number will be multiplied by 3
* @return : (OUTPUT). 8 bits. The multiplication result
*/
uint8_t GF_mult_by_3 (uint8_t t) {
uint8_t q;
uint32_t lq;
lq = (t << 1) ^ t;
if ((lq & 0x100) != 0) lq ^= 0x011B;
q = lq ^ 0xFF;
lq = (t << 1) ^ t;
if ((lq & 0x100) != 0) lq ^= 0x011B;
q = lq ^ 0xFF;
return q;
}
return q;
}
/**
* Do substitution on a given input. See Section 2.4.2.
* @param t : (INPUT), (1*32) bits
* @return : (OUTPUT), (1*32) bits
*/
uint32_t sub_k2 (uint32_t in) {
uint32_t out;
/**
* Do substitution on a given input. See Section 2.4.2.
* @param t : (INPUT), (1*32) bits
* @return : (OUTPUT), (1*32) bits
*/
uint32_t sub_k2 (uint32_t in) {
uint32_t out;
uint8_t w0 = in & 0x000000ff;
uint8_t w1 = (in >> 8) & 0x000000ff;
uint8_t w2 = (in >> 16) & 0x000000ff;
uint8_t w3 = (in >> 24) & 0x000000ff;
uint8_t w0 = in & 0x000000ff;
uint8_t w1 = (in >> 8) & 0x000000ff;
uint8_t w2 = (in >> 16) & 0x000000ff;
uint8_t w3 = (in >> 24) & 0x000000ff;
uint8_t t3, t2, t1, t0;
uint8_t q3, q2, q1, q0;
uint8_t t3, t2, t1, t0;
uint8_t q3, q2, q1, q0;
t0 = S_box[w0]; t1 = S_box[w1]; t2 = S_box[w2]; t3 = S_box[w3];
t0 = S_box[w0]; t1 = S_box[w1]; t2 = S_box[w2]; t3 = S_box[w3];
q0 = GF_mult_by_2(t0) ^ GF_mult_by_3(t1) ^ t2 ^ t3;
q1 = t0 ^ GF_mult_by_2(t1) ^ GF_mult_by_3(t2) ^ t3;
q2 = t0 ^ t1 ^ GF_mult_by_2(t2) ^ GF_mult_by_3(t3);
q3 = GF_mult_by_3(t0) ^ t1 ^ t2 ^ GF_mult_by_2(t3);
q0 = GF_mult_by_2(t0) ^ GF_mult_by_3(t1) ^ t2 ^ t3;
q1 = t0 ^ GF_mult_by_2(t1) ^ GF_mult_by_3(t2) ^ t3;
q2 = t0 ^ t1 ^ GF_mult_by_2(t2) ^ GF_mult_by_3(t3);
q3 = GF_mult_by_3(t0) ^ t1 ^ t2 ^ GF_mult_by_2(t3);
out = (q3 << 24) | (q2 << 16) | (q1 << 8) | q0;
out = (q3 << 24) | (q2 << 16) | (q1 << 8) | q0;
return out;
}
return out;
}
/**
* Expand a given 128-bit key (K) to a 384-bit internal key
* information (IK).
* See Step 1 of init() in Section 2.3.2.
* @param key[4] : (INPUT), (4*32) bits
* @param iv[4] : (INPUT), (4*32) bits
* @modify IK[12] : (OUTPUT), (12*32) bits
* @modify IV[12] : (OUTPUT), (4*32) bits
*/
void key_expansion (uint32_t *key, uint32_t *iv) {
// copy iv to IV
IV[0] = iv[0]; IV[1] = iv[1]; IV[2] = iv[2]; IV[3] = iv[3];
/**
* Expand a given 128-bit key (K) to a 384-bit internal key
* information (IK).
* See Step 1 of init() in Section 2.3.2.
* @param key[4] : (INPUT), (4*32) bits
* @param iv[4] : (INPUT), (4*32) bits
* @modify IK[12] : (OUTPUT), (12*32) bits
* @modify IV[12] : (OUTPUT), (4*32) bits
*/
void key_expansion (uint32_t *key, uint32_t *iv) {
// copy iv to IV
IV[0] = iv[0]; IV[1] = iv[1]; IV[2] = iv[2]; IV[3] = iv[3];
// m = 0 ... 3
IK[0] = key[0]; IK[1] = key[1];
IK[2] = key[2]; IK[3] = key[3];
// m = 4
IK[4] = IK[0] ^ sub_k2((IK[3] << 8) ^ (IK[3] >> 24)) ^
0x01000000;
// m = 0 ... 3
IK[0] = key[0]; IK[1] = key[1];
IK[2] = key[2]; IK[3] = key[3];
// m = 4
IK[4] = IK[0] ^ sub_k2((IK[3] << 8) ^ (IK[3] >> 24)) ^
0x01000000;
// m = 4 ... 11, but not 4 nor 8
IK[5] = IK[1] ^ IK[4]; IK[6] = IK[2] ^ IK[5];
IK[7] = IK[3] ^ IK[6];
// m = 4 ... 11, but not 4 nor 8
IK[5] = IK[1] ^ IK[4]; IK[6] = IK[2] ^ IK[5];
IK[7] = IK[3] ^ IK[6];
// m = 8
IK[8] = IK[4] ^ sub_k2((IK[7] << 8) ^ (IK[7] >> 24)) ^
0x02000000;
// m = 8
IK[8] = IK[4] ^ sub_k2((IK[7] << 8) ^ (IK[7] >> 24)) ^
0x02000000;
// m = 4 ... 11, but not 4 nor 8
IK[9] = IK[5] ^ IK[8]; IK[10] = IK[6] ^ IK[9];
IK[11] = IK[7] ^ IK[10];
}
// m = 4 ... 11, but not 4 nor 8
IK[9] = IK[5] ^ IK[8]; IK[10] = IK[6] ^ IK[9];
IK[11] = IK[7] ^ IK[10];
}
/**
* Set up the initial state value using IK and IV. See Step 2 of
* init() in Section 2.3.2.
* @param key[4] : (INPUT), (4*32) bits
* @param iv[4] : (INPUT), (4*32) bits
* @modify S : (OUTPUT), (A, B, L1, R1, L2, R2)
*/
void setup_state_values (uint32_t *key, uint32_t *iv) {
// setting up IK and IV by calling key_expansion(key, iv)
key_expansion(key, iv);
/**
* Set up the initial state value using IK and IV. See Step 2 of
* init() in Section 2.3.2.
* @param key[4] : (INPUT), (4*32) bits
* @param iv[4] : (INPUT), (4*32) bits
* @modify S : (OUTPUT), (A, B, L1, R1, L2, R2)
*/
void setup_state_values (uint32_t *key, uint32_t *iv) {
// setting up IK and IV by calling key_expansion(key, iv)
key_expansion(key, iv);
// setting up the internal state values
A[0] = IK[4]; A[1] = IK[3]; A[2] = IK[2];
A[3] = IK[1]; A[4] = IK[0];
// setting up the internal state values
A[0] = IK[4]; A[1] = IK[3]; A[2] = IK[2];
A[3] = IK[1]; A[4] = IK[0];
B[0] = IK[10]; B[1] = IK[11]; B[2] = IV[0]; B[3] = IV[1];
B[4] = IK[8]; B[5] = IK[9]; B[6] = IV[2]; B[7] = IV[3];
B[8] = IK[7]; B[9] = IK[5]; B[10] = IK[6];
B[0] = IK[10]; B[1] = IK[11]; B[2] = IV[0]; B[3] = IV[1];
B[4] = IK[8]; B[5] = IK[9]; B[6] = IV[2]; B[7] = IV[3];
B[8] = IK[7]; B[9] = IK[5]; B[10] = IK[6];
L1 = R1 = L2 = R2 = 0x00000000;
}
L1 = R1 = L2 = R2 = 0x00000000;
}
/**
* Initialize the system with a 128-bit key (K) and a 128-bit
* initialization vector (IV). It sets up the internal state value
* and invokes next(INIT) iteratively 24 times. After this,
* the system is ready to produce key streams. See Section 2.3.2.
* @param key[12] : (INPUT), (4*32) bits
* @param iv[4] : (INPUT), (4*32) bits
* @modify IK : (12*32) bits, by calling setup_state_values()
* @modify IV : (4*32) bits, by calling setup_state_values()
* @modify S : (OUTPUT), (A, B, L1, R1, L2, R2)
*/
void init (uint32_t *k, uint32_t *iv) {
int i;
/**
* Initialize the system with a 128-bit key (K) and a 128-bit
* initialization vector (IV). It sets up the internal state value
* and invokes next(INIT) iteratively 24 times. After this,
* the system is ready to produce key streams. See Section 2.3.2.
* @param key[12] : (INPUT), (4*32) bits
* @param iv[4] : (INPUT), (4*32) bits
* @modify IK : (12*32) bits, by calling setup_state_values()
* @modify IV : (4*32) bits, by calling setup_state_values()
* @modify S : (OUTPUT), (A, B, L1, R1, L2, R2)
*/
void init (uint32_t *k, uint32_t *iv) {
int i;
setup_state_values(k, iv);
设置状态值（k，iv）；
for(i=0; i < 24; i++) {
next(INIT);
}
}
for(i=0; i < 24; i++) {
next(INIT);
}
}
/**
* Non-linear function. See Section 2.4.1.
* @param A : (INPUT), 8 bits
* @param B : (INPUT), 8 bits
* @param C : (INPUT), 8 bits
* @param D : (INPUT), 8 bits
* @return : (OUTPUT), 8 bits
*/
uint32_t NLF (uint32_t A, uint32_t B,
uint32_t C, uint32_t D ) {
uint32_t Q;
/**
* Non-linear function. See Section 2.4.1.
* @param A : (INPUT), 8 bits
* @param B : (INPUT), 8 bits
* @param C : (INPUT), 8 bits
* @param D : (INPUT), 8 bits
* @return : (OUTPUT), 8 bits
*/
uint32_t NLF (uint32_t A, uint32_t B,
uint32_t C, uint32_t D ) {
uint32_t Q;
Q = (A + B) ^ C ^ D;
Q = (A + B) ^ C ^ D;
return Q;
}
return Q;
}
/**
* Derive a new state from the current state values.
* See Section 2.3.1.
* @param mode : (INPUT) INIT (= 0) or NORMAL (= 1)
* @modify S : (OUTPUT)
*/
void next (int mode) {
uint32_t nA[5];
uint32_t nB[11];
uint32_t nL1, nR1, nL2, nR2;
uint32_t temp1, temp2;
/**
* Derive a new state from the current state values.
* See Section 2.3.1.
* @param mode : (INPUT) INIT (= 0) or NORMAL (= 1)
* @modify S : (OUTPUT)
*/
void next (int mode) {
uint32_t nA[5];
uint32_t nB[11];
uint32_t nL1, nR1, nL2, nR2;
uint32_t temp1, temp2;
nL1 = sub_k2(R2 + B[4]);
nR1 = sub_k2(L2 + B[9]);
nL2 = sub_k2(L1);
nR2 = sub_k2(R1);
nL1 = sub_k2(R2 + B[4]);
nR1 = sub_k2(L2 + B[9]);
nL2 = sub_k2(L1);
nR2 = sub_k2(R1);
// m = 0 ... 3
nA[0] = A[1]; nA[1] = A[2]; nA[2] = A[3]; nA[3] = A[4];
// m = 0 ... 3
nA[0] = A[1]; nA[1] = A[2]; nA[2] = A[3]; nA[3] = A[4];
// m = 0 ... 9
nB[0] = B[1]; nB[1] = B[2]; nB[2] = B[3]; nB[3] = B[4];
nB[4] = B[5]; nB[5] = B[6]; nB[6] = B[7]; nB[7] = B[8];
nB[8] = B[9]; nB[9] = B[10];
// m = 0 ... 9
nB[0] = B[1]; nB[1] = B[2]; nB[2] = B[3]; nB[3] = B[4];
nB[4] = B[5]; nB[5] = B[6]; nB[6] = B[7]; nB[7] = B[8];
nB[8] = B[9]; nB[9] = B[10];
// update nA[4]
temp1 = (A[0] << 8) ^ amul0[(A[0] >> 24)];
nA[4] = temp1 ^ A[3];
if (mode == INIT)
nA[4] ^= NLF(B[0], R2, R1, A[4]);
// update nA[4]
temp1 = (A[0] << 8) ^ amul0[(A[0] >> 24)];
nA[4] = temp1 ^ A[3];
if (mode == INIT)
nA[4] ^= NLF(B[0], R2, R1, A[4]);
// update nB[10]
if (A[2] & 0x40000000) /* if A[2][30] == 1 */ {
temp1 = (B[0] << 8) ^ amul1[(B[0] >> 24)];
} else /*if A[2][30] == 0*/ {
temp1 = (B[0] << 8) ^ amul2[(B[0] >> 24)];
}
// update nB[10]
if (A[2] & 0x40000000) /* if A[2][30] == 1 */ {
temp1 = (B[0] << 8) ^ amul1[(B[0] >> 24)];
} else /*if A[2][30] == 0*/ {
temp1 = (B[0] << 8) ^ amul2[(B[0] >> 24)];
}
if (A[2] & 0x80000000) /* if A[2][31] == 1 */ {
temp2 = (B[8] << 8) ^ amul3[(B[8] >> 24)];
} else /* if A[2][31] == 0 */ {
temp2 = B[8];
}
if (A[2] & 0x80000000) /* if A[2][31] == 1 */ {
temp2 = (B[8] << 8) ^ amul3[(B[8] >> 24)];
} else /* if A[2][31] == 0 */ {
temp2 = B[8];
}
nB[10] = temp1 ^ B[1] ^ B[6] ^ temp2;
nB[10] = temp1 ^ B[1] ^ B[6] ^ temp2;
if (mode == INIT)
nB[10] ^= NLF(B[10], L2, L1, A[0]);
if (mode == INIT)
nB[10] ^= NLF(B[10], L2, L1, A[0]);
/* copy S' to S */
A[0] = nA[0]; A[1] = nA[1]; A[2] = nA[2];
A[3] = nA[3]; A[4] = nA[4];
/* copy S' to S */
A[0] = nA[0]; A[1] = nA[1]; A[2] = nA[2];
A[3] = nA[3]; A[4] = nA[4];
B[0] = nB[0]; B[1] = nB[1]; B[2] = nB[2]; B[3] = nB[3];
B[4] = nB[4]; B[5] = nB[5]; B[6] = nB[6]; B[7] = nB[7];
B[8] = nB[8]; B[9] = nB[9]; B[10] = nB[10];
B[0] = nB[0]; B[1] = nB[1]; B[2] = nB[2]; B[3] = nB[3];
B[4] = nB[4]; B[5] = nB[5]; B[6] = nB[6]; B[7] = nB[7];
B[8] = nB[8]; B[9] = nB[9]; B[10] = nB[10];
L1 = nL1; R1 = nR1; L2 = nL2; R2 = nR2;
}
L1 = nL1; R1 = nR1; L2 = nL2; R2 = nR2;
}
/**
* Obtain a key stream = (ZH, ZL) from the current state values.
* See Section 2.3.3.
* @param ZH : (OUTPUT) (1 * 32)-bit
* @modify ZL : (OUTPUT) (1 * 32)-bit
*/
void stream (uint32_t *ZH, uint32_t *ZL) {
*ZH = NLF(B[10], L2, L1, A[0]);
*ZL = NLF(B[0], R2, R1, A[4]);
}
/**
* Obtain a key stream = (ZH, ZL) from the current state values.
* See Section 2.3.3.
* @param ZH : (OUTPUT) (1 * 32)-bit
* @modify ZL : (OUTPUT) (1 * 32)-bit
*/
void stream (uint32_t *ZH, uint32_t *ZL) {
*ZH = NLF(B[10], L2, L1, A[0]);
*ZL = NLF(B[0], R2, R1, A[4]);
}
void main (void) {
真空总管（真空）{
// Set the key and the iv
uint32_t key[4] = ...;
uint32_t iv[4] = ...;
// Set the key and the iv
uint32_t key[4] = ...;
uint32_t iv[4] = ...;
init(key, iv);
init（键，iv）；
// produce a key stream
stream(&zh, &zl);
next(NORMAL);
// produce a key stream
stream(&zh, &zl);
next(NORMAL);
// produce another key stream
stream(&zh, &zl);
next(NORMAL);
...
}
// produce another key stream
stream(&zh, &zl);
next(NORMAL);
...
}
This appendix provides running examples of KCipher-2 obtained from the naive implementation. All values are written in hexadecimal form.
本附录提供了从naive实现中获得的KCipher-2的运行示例。所有值均以十六进制形式写入。
The following is a series of the 64-bit key streams generated from the given 8-bit keys (K) and 128-bit initialization vectors (IVs).
以下是从给定的8位密钥（K）和128位初始化向量（IVs）生成的一系列64位密钥流。
- K : 00000000 00000000 00000000 00000000 - IV: 00000000 00000000 00000000 00000000 - Generated key streams at S(i) are as follows S(0): F871EBEF 945B7272 S(1): E40C0494 1DFF0537 S(2): 0B981A59 FBC8AC57 S(3): 566D3B02 C179DBB4 S(4): 3B46F1F0 33554C72 S(5): 5DE68BCC 9872858F S(6): 57549602 4062F0E9 S(7): F932C998 226DB6BA ...
- K:00000000000000000000000000000000000000-IV:00000000000000000000000000-在S（i）生成的关键流如下S（0）：F871EBEF 945B7272 S（1）：E40C0494 1DF0537 S（2）：0B981A59 FBC8AC57 S（3）：566D3B02 C179DBB4 S（4）：3B46F1F0 33554C72 S（5）：5DE68BCC 9872858F S（6）：57549602 4062F09 S（7）：F932C998 2266BA。。。
- K : A37B7D01 2F897076 FE08C22D 142BB2CF - IV: 33A6EE60 E57927E0 8B45CC4C A30EDE4A - Generated key streams at S(i) are as follows S(0): 60E9A6B6 7B4C2524
- K:A37B7D01 2F8970776 FE08C22D 142BB2CF-IV:33A6EE60 E57927E0 8B45CC4C A30EDE4A-在S（i）处生成的密钥流如下S（0）：60E9A6B6 7B4C2524
S(1): FE726D44 AD5B402E S(2): 31D0D1BA 5CA233A4 S(3): AFC74BE7 D6069D36 S(4): 4A75BB6C D8D5B7F0 S(5): 38AAAA28 4AE4CD2F S(6): E2E5313D FC6CCD8F S(7): 9D2484F2 0F86C50D ...
S（1）：FE726D44 AD5B402E S（2）：31D0D1BA 5CA233A4 S（3）：AFC74BE7 D6069D36 S（4）：4A75BB6C D8D5B7F0 S（5）：38AAAA28 4AE4CD2F S（6）：E2E5313D FC6CCD8F S（7）：9D2484F2 0F86C50D。。。
- K : 3D62E9B1 8E5B042F 42DF43CC 7175C96E - IV: 777CEFE4 541300C8 ADCACA8A 0B48CD55 - Generated key streams at S(i) are as follows S(0): 690F108D 84F44AC7 S(1): BF257BD7 E394F6C9 S(2): AA1192C3 8E200C6E S(3): 073C8078 AC18AAD1 S(4): D4B8DADE 68802368 S(5): 2FA42076 83DEA5A4 S(6): 4C1D95EA E959F5B4 S(7): 2611F41E A40F0A58 ...
- K:3D62E9B1 8E5B042F 42DF43CC 7175C96E-IV:777CEFE4 541300C8 ADCACA8A 0B48CD55-在S（i）处生成的关键流如下S（0）：690F108D 84F44AC7 S（1）：BF257BD7 E394F6C9 S（2）：AA1192C3 8E200C6E S（3）：073C8078 AC18AAD1 S（4）：D4B8DADE 68802368（5）：2FA42076 835A4 S（6）：4C951DEA E95B4F4F9C9 S（F08）：A11F4。。。
In this section, the initialization procedure and the key stream generation are illustrated in detail. The given 128-bit key (K) and the 128-bit initialization vector (IV) are as follows:
在本节中，详细说明了初始化过程和密钥流生成。给定的128位密钥（K）和128位初始化向量（IV）如下所示：
- K : 0F1E2D3C 4B5A6978 8796A5B4 C3D2E1F0 - IV: F0E0D0C0 B0A09080 70605040 30201000.
- K:0F1E2D3C 4B5A6978 8796A5B4 C3D2E1F0-IV:F0E0D0C0 B0A09080 70605040 30201000。
Based on K and IV, the init() operation (Section 2.3.2) sets up
the internal state values, S = (A, B, L1, R1, L2, R2), as follows:
Based on K and IV, the init() operation (Section 2.3.2) sets up
the internal state values, S = (A, B, L1, R1, L2, R2), as follows:
A[0]: 7993A6A2 A[1]: C3D2E1F0 A[2]: 8796A5B4
A[3]: 4B5A6978 A[4]: 0F1E2D3C
A[0]: 7993A6A2 A[1]: C3D2E1F0 A[2]: 8796A5B4
A[3]: 4B5A6978 A[4]: 0F1E2D3C
B[0]: 38AB371B B[1] : 4E26BC85 B[2]: F0E0D0C0
B[3]: B0A09080 B[4] : BF3D92AF B[5]: 8DF45D75
B[6]: 70605040 B[7] : 30201000 B[8]: 768D8B9E
B[9]: 32C9CFDA B[10]: B55F6A6E
B[0]: 38AB371B B[1] : 4E26BC85 B[2]: F0E0D0C0
B[3]: B0A09080 B[4] : BF3D92AF B[5]: 8DF45D75
B[6]: 70605040 B[7] : 30201000 B[8]: 768D8B9E
B[9]: 32C9CFDA B[10]: B55F6A6E
L1: 00000000 R1: 00000000 L2: 00000000 R2: 00000000
L1: 00000000 R1: 00000000 L2: 00000000 R2: 00000000
To complete the initialization, the next() operation is applied to the state values 24 times (in Section 2.3.2, Step 3). Let us denote each repeated application of the next() operation by init(i), where 1 <= i <= 24. The internal state values resulting from each init(i) are shown in Appendixes C.2.1 - C.2.24.
要完成初始化，将next（）操作应用于状态值24次（在第2.3.2节，步骤3中）。让我们用init（i）表示下一个（）操作的每次重复应用，其中1<=i<=24。附录C.2.1-C.2.24中显示了每个初始（i）产生的内部状态值。
A[0]: C3D2E1F0 A[1]: 8796A5B4 A[2]: 4B5A6978
A[3]: 0F1E2D3C A[4]: 37070F7F
A[0]: C3D2E1F0 A[1]: 8796A5B4 A[2]: 4B5A6978
A[3]: 0F1E2D3C A[4]: 37070F7F
B[0]: 4E26BC85 B[1] : F0E0D0C0 B[2]: B0A09080
B[3]: BF3D92AF B[4] : 8DF45D75 B[5]: 70605040
B[6]: 30201000 B[7] : 768D8B9E B[8]: 32C9CFDA
B[9]: B55F6A6E B[10]: 64DEFF24
B[0]: 4E26BC85 B[1] : F0E0D0C0 B[2]: B0A09080
B[3]: BF3D92AF B[4] : 8DF45D75 B[5]: 70605040
B[6]: 30201000 B[7] : 768D8B9E B[8]: 32C9CFDA
B[9]: B55F6A6E B[10]: 64DEFF24
L1: F360860C R1: E81907D5 L2: 63636363 R2: 63636363
L1: F360860C R1: E81907D5 L2: 63636363 R2: 63636363
A[0]: 8796A5B4 A[1]: 4B5A6978 A[2]: 0F1E2D3C
A[3]: 37070F7F A[4]: 25BCF981
A[0]: 8796A5B4 A[1]: 4B5A6978 A[2]: 0F1E2D3C
A[3]: 37070F7F A[4]: 25BCF981
B[0]: F0E0D0C0 B[1] : B0A09080 B[2]: BF3D92AF
B[3]: 8DF45D75 B[4] : 70605040 B[5]: 30201000
B[6]: 768D8B9E B[7] : 32C9CFDA B[8]: B55F6A6E
B[9]: 64DEFF24 B[10]: 7E65CB6A
B[0]: F0E0D0C0 B[1] : B0A09080 B[2]: BF3D92AF
B[3]: 8DF45D75 B[4] : 70605040 B[5]: 30201000
B[6]: 768D8B9E B[7] : 32C9CFDA B[8]: B55F6A6E
B[9]: 64DEFF24 B[10]: 7E65CB6A
L1: 1B9542ED R1: 9B259D28 L2: 971610F6 R2: 39C36E1D
L1: 1B9542ED R1: 9B259D28 L2: 971610F6 R2: 39C36E1D
A[0]: 4B5A6978 A[1]: 0F1E2D3C A[2]: 37070F7F
A[3]: 25BCF981 A[4]: FA2DD9D3
A[0]: 4B5A6978 A[1]: 0F1E2D3C A[2]: 37070F7F
A[3]: 25BCF981 A[4]: FA2DD9D3
B[0]: B0A09080 B[1] : BF3D92AF B[2]: 8DF45D75
B[3]: 70605040 B[4] : 30201000 B[5]: 768D8B9E
B[6]: 32C9CFDA B[7] : B55F6A6E B[8]: 64DEFF24
B[9]: 7E65CB6A B[10]: 08573732
B[0]: B0A09080 B[1] : BF3D92AF B[2]: 8DF45D75
B[3]: 70605040 B[4] : 30201000 B[5]: 768D8B9E
B[6]: 32C9CFDA B[7] : B55F6A6E B[8]: 64DEFF24
B[9]: 7E65CB6A B[10]: 08573732
L1: 1F41CDFB R1: CFAE13F3 L2: BCC7DC5B R2: 1528DDA1
L1: 1F41CDFB R1: CFAE13F3 L2: BCC7DC5B R2: 1528DDA1
A[0]: 0F1E2D3C A[1]: 37070F7F A[2]: 25BCF981
A[3]: FA2DD9D3 A[4]: AB820031
A[0]: 0F1E2D3C A[1]: 37070F7F A[2]: 25BCF981
A[3]: FA2DD9D3 A[4]: AB820031
B[0]: BF3D92AF B[1] : 8DF45D75 B[2]: 70605040
B[3]: 30201000 B[4] : 768D8B9E B[5]: 32C9CFDA
B[6]: B55F6A6E B[7] : 64DEFF24 B[8]: 7E65CB6A
B[9]: 08573732 B[10]: 40941D82
B[0]: BF3D92AF B[1] : 8DF45D75 B[2]: 70605040
B[3]: 30201000 B[4] : 768D8B9E B[5]: 32C9CFDA
B[6]: B55F6A6E B[7] : 64DEFF24 B[8]: 7E65CB6A
B[9]: 08573732 B[10]: 40941D82
L1: 8D7100A7 R1: AA6C8F89 L2: B4F43081 R2: 81264AF3
L1: 8D7100A7 R1: AA6C8F89 L2: B4F43081 R2: 81264AF3
A[0]: 37070F7F A[1]: 25BCF981 A[2]: FA2DD9D3
A[3]: AB820031 A[4]: D8F5995F
A[0]: 37070F7F A[1]: 25BCF981 A[2]: FA2DD9D3
A[3]: AB820031 A[4]: D8F5995F
B[0]: 8DF45D75 B[1] : 70605040 B[2]: 30201000
B[3]: 768D8B9E B[4] : 32C9CFDA B[5]: B55F6A6E
B[6]: 64DEFF24 B[7] : 7E65CB6A B[8]: 08573732
B[9]: 40941D82 B[10]: 1A8DA7FB
B[0]: 8DF45D75 B[1] : 70605040 B[2]: 30201000
B[3]: 768D8B9E B[4] : 32C9CFDA B[5]: B55F6A6E
B[6]: 64DEFF24 B[7] : 7E65CB6A B[8]: 08573732
B[9]: 40941D82 B[10]: 1A8DA7FB
L1: D315A91D R1: 751BC887 L2: 9E8539E3 R2: 929B1D3C
L1: D315A91D R1: 751BC887 L2: 9E8539E3 R2: 929B1D3C
A[0]: 25BCF981 A[1]: FA2DD9D3 A[2]: AB820031
A[3]: D8F5995F A[4]: F697B5BB
A[0]: 25BCF981 A[1]: FA2DD9D3 A[2]: AB820031
A[3]: D8F5995F A[4]: F697B5BB
B[0]: 70605040 B[1] : 30201000 B[2]: 768D8B9E
B[3]: 32C9CFDA B[4] : B55F6A6E B[5]: 64DEFF24
B[6]: 7E65CB6A B[7] : 08573732 B[8]: 40941D82
B[9]: 1A8DA7FB B[10]: 13B5E7F3
B[0]: 70605040 B[1] : 30201000 B[2]: 768D8B9E
B[3]: 32C9CFDA B[4] : B55F6A6E B[5]: 64DEFF24
B[6]: 7E65CB6A B[7] : 08573732 B[8]: 40941D82
B[9]: 1A8DA7FB B[10]: 13B5E7F3
L1: 88658E94 R1: 7F1C023D L2: B16F9402 R2: 5F06AB3F
L1: 88658E94 R1: 7F1C023D L2: B16F9402 R2: 5F06AB3F
A[0]: FA2DD9D3 A[1]: AB820031 A[2]: D8F5995F
A[3]: F697B5BB A[4]: 6B0A7012
A[0]: FA2DD9D3 A[1]: AB820031 A[2]: D8F5995F
A[3]: F697B5BB A[4]: 6B0A7012
B[0]: 30201000 B[1] : 768D8B9E B[2]: 32C9CFDA
B[3]: B55F6A6E B[4] : 64DEFF24 B[5]: 7E65CB6A
B[6]: 08573732 B[7] : 40941D82 B[8]: 1A8DA7FB
B[9]: 13B5E7F3 B[10]: D76ABD2C
B[0]: 30201000 B[1] : 768D8B9E B[2]: 32C9CFDA
B[3]: B55F6A6E B[4] : 64DEFF24 B[5]: 7E65CB6A
B[6]: 08573732 B[7] : 40941D82 B[8]: 1A8DA7FB
B[9]: 13B5E7F3 B[10]: D76ABD2C
L1: 21BF8813 R1: 743F68DE L2: A1F603E6 R2: 3D1EA499
L1: 21BF8813 R1: 743F68DE L2: A1F603E6 R2: 3D1EA499
A[0]: AB820031 A[1]: D8F5995F A[2]: F697B5BB
A[3]: 6B0A7012 A[4]: 23995B7E
A[0]: AB820031 A[1]: D8F5995F A[2]: F697B5BB
A[3]: 6B0A7012 A[4]: 23995B7E
B[0]: 768D8B9E B[1] : 32C9CFDA B[2]: B55F6A6E
B[3]: 64DEFF24 B[4] : 7E65CB6A B[5]: 08573732
B[6]: 40941D82 B[7] : 1A8DA7FB B[8]: 13B5E7F3
B[9]: D76ABD2C B[10]: 997C3F70
B[0]: 768D8B9E B[1] : 32C9CFDA B[2]: B55F6A6E
B[3]: 64DEFF24 B[4] : 7E65CB6A B[5]: 08573732
B[6]: 40941D82 B[7] : 1A8DA7FB B[8]: 13B5E7F3
B[9]: D76ABD2C B[10]: 997C3F70
L1: B48EA08C R1: 657C8FFD L2: AAB50B58 R2: 281F9A12
L1: B48EA08C R1: 657C8FFD L2: AAB50B58 R2: 281F9A12
A[0]: D8F5995F A[1]: F697B5BB A[2]: 6B0A7012
A[3]: 23995B7E A[4]: F8532F87
A[0]: D8F5995F A[1]: F697B5BB A[2]: 6B0A7012
A[3]: 23995B7E A[4]: F8532F87
B[0]: 32C9CFDA B[1] : B55F6A6E B[2]: 64DEFF24
B[3]: 7E65CB6A B[4] : 08573732 B[5]: 40941D82
B[6]: 1A8DA7FB B[7] : 13B5E7F3 B[8]: D76ABD2C
B[9]: 997C3F70 B[10]: 95FFF657
B[0]: 32C9CFDA B[1] : B55F6A6E B[2]: 64DEFF24
B[3]: 7E65CB6A B[4] : 08573732 B[5]: 40941D82
B[6]: 1A8DA7FB B[7] : 13B5E7F3 B[8]: D76ABD2C
B[9]: 997C3F70 B[10]: 95FFF657
L1: A2040C44 R1: EF19DC4E L2: 543A1967 R2: 05D0CF60
L1: A2040C44 R1: EF19DC4E L2: 543A1967 R2: 05D0CF60
A[0]: F697B5BB A[1]: 6B0A7012 A[2]: 23995B7E
A[3]: F8532F87 A[4]: BEDF1DEF
A[0]: F697B5BB A[1]: 6B0A7012 A[2]: 23995B7E
A[3]: F8532F87 A[4]: BEDF1DEF
B[0]: B55F6A6E B[1] : 64DEFF24 B[2]: 7E65CB6A
B[3]: 08573732 B[4] : 40941D82 B[5]: 1A8DA7FB
B[6]: 13B5E7F3 B[7] : D76ABD2C B[8]: 997C3F70
B[9]: 95FFF657 B[10]: 6D2C2FA3
B[0]: B55F6A6E B[1] : 64DEFF24 B[2]: 7E65CB6A
B[3]: 08573732 B[4] : 40941D82 B[5]: 1A8DA7FB
B[6]: 13B5E7F3 B[7] : D76ABD2C B[8]: 997C3F70
B[9]: 95FFF657 B[10]: 6D2C2FA3
L1: C7AE66B0 R1: 9C075DB9 L2: 5554CBE7 R2: 866080C4
L1: C7AE66B0 R1: 9C075DB9 L2: 5554CBE7 R2: 866080C4
A[0]: 6B0A7012 A[1]: 23995B7E A[2]: F8532F87 A[3]: BEDF1DEF A[4]: 983D37.
A[0]：6B0A7012 A[1]：23995B7E A[2]：F8532F87 A[3]：BEDF1DEF A[4]：983D37。
B[0]: 64DEFF24 B[1] : 7E65CB6A B[2]: 08573732
B[3]: 40941D82 B[4] : 1A8DA7FB B[5]: 13B5E7F3
B[6]: D76ABD2C B[7] : 997C3F70 B[8]: 95FFF657
B[9]: 6D2C2FA3 B[10]: A02127BE
B[0]: 64DEFF24 B[1] : 7E65CB6A B[2]: 08573732
B[3]: 40941D82 B[4] : 1A8DA7FB B[5]: 13B5E7F3
B[6]: D76ABD2C B[7] : 997C3F70 B[8]: 95FFF657
B[9]: 6D2C2FA3 B[10]: A02127BE
L1: 29F322A2 R1: 01F771D9 L2: 725670A2 R2: D4F24463
L1: 29F322A2 R1: 01F771D9 L2: 725670A2 R2: D4F24463
A[0]: 23995B7E A[1]: F8532F87 A[2]: BEDF1DEF
A[3]: 983D37CB A[4]: 526A110D
A[0]: 23995B7E A[1]: F8532F87 A[2]: BEDF1DEF
A[3]: 983D37CB A[4]: 526A110D
B[0]: 7E65CB6A B[1] : 08573732 B[2]: 40941D82
B[3]: 1A8DA7FB B[4] : 13B5E7F3 B[5]: D76ABD2C
B[6]: 997C3F70 B[7] : 95FFF657 B[8]: 6D2C2FA3
B[9]: A02127BE B[10]: 49F99042
B[0]: 7E65CB6A B[1] : 08573732 B[2]: 40941D82
B[3]: 1A8DA7FB B[4] : 13B5E7F3 B[5]: D76ABD2C
B[6]: 997C3F70 B[7] : 95FFF657 B[8]: 6D2C2FA3
B[9]: A02127BE B[10]: 49F99042
L1: 51536DF4 R1: 66111E6A L2: 8147B572 R2: 6CC2AC80
L1: 51536DF4 R1: 66111E6A L2: 8147B572 R2: 6CC2AC80
A[0]: F8532F87 A[1]: BEDF1DEF A[2]: 983D37CB
A[3]: 526A110D A[4]: A5EEB8AE
A[0]: F8532F87 A[1]: BEDF1DEF A[2]: 983D37CB
A[3]: 526A110D A[4]: A5EEB8AE
B[0]: 08573732 B[1] : 40941D82 B[2]: 1A8DA7FB
B[3]: 13B5E7F3 B[4] : D76ABD2C B[5]: 997C3F70
B[6]: 95FFF657 B[7] : 6D2C2FA3 B[8]: A02127BE
B[9]: 49F99042 B[10]: 406CE62C
B[0]: 08573732 B[1] : 40941D82 B[2]: 1A8DA7FB
B[3]: 13B5E7F3 B[4] : D76ABD2C B[5]: 997C3F70
B[6]: 95FFF657 B[7] : 6D2C2FA3 B[8]: A02127BE
B[9]: 49F99042 B[10]: 406CE62C
L1: 9582D912 R1: 6953AFE8 L2: B22A3A1D R2: 903A4823
L1: 9582D912 R1: 6953AFE8 L2: B22A3A1D R2: 903A4823
A[0]: BEDF1DEF A[1]: 983D37CB A[2]: 526A110D
A[3]: A5EEB8AE A[4]: 70A5B5BA
A[0]: BEDF1DEF A[1]: 983D37CB A[2]: 526A110D
A[3]: A5EEB8AE A[4]: 70A5B5BA
B[0]: 40941D82 B[1] : 1A8DA7FB B[2]: 13B5E7F3
B[3]: D76ABD2C B[4] : 997C3F70 B[5]: 95FFF657
B[6]: 6D2C2FA3 B[7] : A02127BE B[8]: 49F99042
B[9]: 406CE62C B[10]: C57BED5B
B[0]: 40941D82 B[1] : 1A8DA7FB B[2]: 13B5E7F3
B[3]: D76ABD2C B[4] : 997C3F70 B[5]: 95FFF657
B[6]: 6D2C2FA3 B[7] : A02127BE B[8]: 49F99042
B[9]: 406CE62C B[10]: C57BED5B
L1: EB77DD2D R1: 633CFD8F L2: 32A4BCEF R2: CB33BCB2
L1: EB77DD2D R1: 633CFD8F L2: 32A4BCEF R2: CB33BCB2
A[0]: 983D37CB A[1]: 526A110D A[2]: A5EEB8AE
A[3]: 70A5B5BA A[4]: B1145F18
A[0]: 983D37CB A[1]: 526A110D A[2]: A5EEB8AE
A[3]: 70A5B5BA A[4]: B1145F18
B[0]: 1A8DA7FB B[1] : 13B5E7F3 B[2]: D76ABD2C
B[3]: 997C3F70 B[4] : 95FFF657 B[5]: 6D2C2FA3
B[6]: A02127BE B[7] : 49F99042 B[8]: 406CE62C
B[9]: C57BED5B B[10]: 7BE2C520
B[0]: 1A8DA7FB B[1] : 13B5E7F3 B[2]: D76ABD2C
B[3]: 997C3F70 B[4] : 95FFF657 B[5]: 6D2C2FA3
B[6]: A02127BE B[7] : 49F99042 B[8]: 406CE62C
B[9]: C57BED5B B[10]: 7BE2C520
L1: E11420CC R1: 6730A956 L2: 8EC8ACEF R2: C7FC060A
L1: E11420CC R1: 6730A956 L2: 8EC8ACEF R2: C7FC060A
A[0]: 526A110D A[1]: A5EEB8AE A[2]: 70A5B5BA
A[3]: B1145F18 A[4]: FA752FDC
A[0]: 526A110D A[1]: A5EEB8AE A[2]: 70A5B5BA
A[3]: B1145F18 A[4]: FA752FDC
B[0]: 13B5E7F3 B[1] : D76ABD2C B[2]: 997C3F70
B[3]: 95FFF657 B[4] : 6D2C2FA3 B[5]: A02127BE
B[6]: 49F99042 B[7] : 406CE62C B[8]: C57BED5B
B[9]: 7BE2C520 B[10]: 1F48829C
B[0]: 13B5E7F3 B[1] : D76ABD2C B[2]: 997C3F70
B[3]: 95FFF657 B[4] : 6D2C2FA3 B[5]: A02127BE
B[6]: 49F99042 B[7] : 406CE62C B[8]: C57BED5B
B[9]: 7BE2C520 B[10]: 1F48829C
L1: 0D95C94D R1: 8238B05F L2: 7B00D356 R2: 0EFE8596
L1: 0D95C94D R1: 8238B05F L2: 7B00D356 R2: 0EFE8596
A[0]: A5EEB8AE A[1]: 70A5B5BA A[2]: B1145F18
A[3]: FA752FDC A[4]: DB29190A
A[0]: A5EEB8AE A[1]: 70A5B5BA A[2]: B1145F18
A[3]: FA752FDC A[4]: DB29190A
B[0]: D76ABD2C B[1] : 997C3F70 B[2]: 95FFF657
B[3]: 6D2C2FA3 B[4] : A02127BE B[5]: 49F99042
B[6]: 406CE62C B[7] : C57BED5B B[8]: 7BE2C520
B[9]: 1F48829C B[10]: F95DD14F
B[0]: D76ABD2C B[1] : 997C3F70 B[2]: 95FFF657
B[3]: 6D2C2FA3 B[4] : A02127BE B[5]: 49F99042
B[6]: 406CE62C B[7] : C57BED5B B[8]: 7BE2C520
B[9]: 1F48829C B[10]: F95DD14F
L1: 262687B5 R1: 9B9AC5E9 L2: 7C08EB5C R2: 8C1300A3
L1: 262687B5 R1: 9B9AC5E9 L2: 7C08EB5C R2: 8C1300A3
A[0]: 70A5B5BA A[1]: B1145F18 A[2]: FA752FDC
A[3]: DB29190A A[4]: 35623CDA
A[0]: 70A5B5BA A[1]: B1145F18 A[2]: FA752FDC
A[3]: DB29190A A[4]: 35623CDA
B[0]: 997C3F70 B[1] : 95FFF657 B[2]: 6D2C2FA3
B[3]: A02127BE B[4] : 49F99042 B[5]: 406CE62C
B[6]: C57BED5B B[7] : 7BE2C520 B[8]: 1F48829C
B[9]: F95DD14F B[10]: D939E13E
B[0]: 997C3F70 B[1] : 95FFF657 B[2]: 6D2C2FA3
B[3]: A02127BE B[4] : 49F99042 B[5]: 406CE62C
B[6]: C57BED5B B[7] : 7BE2C520 B[8]: 1F48829C
B[9]: F95DD14F B[10]: D939E13E
L1: E478DEF0 R1: 06F84503 L2: 71350E88 R2: 14EF8E61
L1: E478DEF0 R1: 06F84503 L2: 71350E88 R2: 14EF8E61
A[0]: B1145F18 A[1]: FA752FDC A[2]: DB29190A
A[3]: 35623CDA A[4]: 746B4AE8
A[0]: B1145F18 A[1]: FA752FDC A[2]: DB29190A
A[3]: 35623CDA A[4]: 746B4AE8
B[0]: 95FFF657 B[1] : 6D2C2FA3 B[2]: A02127BE
B[3]: 49F99042 B[4] : 406CE62C B[5]: C57BED5B
B[6]: 7BE2C520 B[7] : 1F48829C B[8]: F95DD14F
B[9]: D939E13E B[10]: 9970C980
B[0]: 95FFF657 B[1] : 6D2C2FA3 B[2]: A02127BE
B[3]: 49F99042 B[4] : 406CE62C B[5]: C57BED5B
B[6]: 7BE2C520 B[7] : 1F48829C B[8]: F95DD14F
B[9]: D939E13E B[10]: 9970C980
L1: C2AC94C4 R1: C708FAE8 L2: FC4900F1 R2: 7C260B6A
L1: C2AC94C4 R1: C708FAE8 L2: FC4900F1 R2: 7C260B6A
A[0]: FA752FDC A[1]: DB29190A A[2]: 35623CDA
A[3]: 746B4AE8 A[4]: 2EB9213A
A[0]: FA752FDC A[1]: DB29190A A[2]: 35623CDA
A[3]: 746B4AE8 A[4]: 2EB9213A
B[0]: 6D2C2FA3 B[1] : A02127BE B[2]: 49F99042
B[3]: 406CE62C B[4] : C57BED5B B[5]: 7BE2C520
B[6]: 1F48829C B[7] : F95DD14F B[8]: D939E13E
B[9]: 9970C980 B[10]: 3C517031
B[0]: 6D2C2FA3 B[1] : A02127BE B[2]: 49F99042
B[3]: 406CE62C B[4] : C57BED5B B[5]: 7BE2C520
B[6]: 1F48829C B[7] : F95DD14F B[8]: D939E13E
B[9]: 9970C980 B[10]: 3C517031
L1: 8F007DE9 R1: B2AE0889 L2: DD68D5EA R2: 3C8757AC
L1: 8F007DE9 R1: B2AE0889 L2: DD68D5EA R2: 3C8757AC
A[0]: DB29190A A[1]: 35623CDA A[2]: 746B4AE8
A[3]: 2EB9213A A[4]: BE3CA984
A[0]: DB29190A A[1]: 35623CDA A[2]: 746B4AE8
A[3]: 2EB9213A A[4]: BE3CA984
B[0]: A02127BE B[1] : 49F99042 B[2]: 406CE62C
B[3]: C57BED5B B[4] : 7BE2C520 B[5]: 1F48829C
B[6]: F95DD14F B[7] : D939E13E B[8]: 9970C980
B[9]: 3C517031 B[10]: D1439B63
B[0]: A02127BE B[1] : 49F99042 B[2]: 406CE62C
B[3]: C57BED5B B[4] : 7BE2C520 B[5]: 1F48829C
B[6]: F95DD14F B[7] : D939E13E B[8]: 9970C980
B[9]: 3C517031 B[10]: D1439B63
L1: AFC4E32F R1: 98FBC87F L2: 58B22D36 R2: 481DC7D6
L1: AFC4E32F R1: 98FBC87F L2: 58B22D36 R2: 481DC7D6
A[0]: 35623CDA A[1]: 746B4AE8 A[2]: 2EB9213A
A[3]: BE3CA984 A[4]: 974E6719
A[0]: 35623CDA A[1]: 746B4AE8 A[2]: 2EB9213A
A[3]: BE3CA984 A[4]: 974E6719
B[0]: 49F99042 B[1] : 406CE62C B[2]: C57BED5B
B[3]: 7BE2C520 B[4] : 1F48829C B[5]: F95DD14F
B[6]: D939E13E B[7] : 9970C980 B[8]: 3C517031
B[9]: D1439B63 B[10]: 9334E221
B[0]: 49F99042 B[1] : 406CE62C B[2]: C57BED5B
B[3]: 7BE2C520 B[4] : 1F48829C B[5]: F95DD14F
B[6]: D939E13E B[7] : 9970C980 B[8]: 3C517031
B[9]: D1439B63 B[10]: 9334E221
L1: F9C43357 R1: E5539EA2 L2: C0B76A7C R2: 06EE4ED5
L1: F9C43357 R1: E5539EA2 L2: C0B76A7C R2: 06EE4ED5
A[0]: 746B4AE8 A[1]: 2EB9213A A[2]: BE3CA984
A[3]: 974E6719 A[4]: 86916EFF
A[0]: 746B4AE8 A[1]: 2EB9213A A[2]: BE3CA984
A[3]: 974E6719 A[4]: 86916EFF
B[0]: 406CE62C B[1] : C57BED5B B[2]: 7BE2C520
B[3]: 1F48829C B[4] : F95DD14F B[5]: D939E13E
B[6]: 9970C980 B[7] : 3C517031 B[8]: D1439B63
B[9]: 9334E221 B[10]: 50EF13E7
B[0]: 406CE62C B[1] : C57BED5B B[2]: 7BE2C520
B[3]: 1F48829C B[4] : F95DD14F B[5]: D939E13E
B[6]: 9970C980 B[7] : 3C517031 B[8]: D1439B63
B[9]: 9334E221 B[10]: 50EF13E7
L1: 309527ED R1: C473D814 L2: 1B107B6D R2: 0180D95D
L1: 309527ED R1: C473D814 L2: 1B107B6D R2: 0180D95D
A[0]: 2EB9213A A[1]: BE3CA984 A[2]: 974E6719
A[3]: 86916EFF A[4]: F52DACF9
A[0]: 2EB9213A A[1]: BE3CA984 A[2]: 974E6719
A[3]: 86916EFF A[4]: F52DACF9
B[0]: C57BED5B B[1] : 7BE2C520 B[2]: 1F48829C
B[3]: F95DD14F B[4] : D939E13E B[5]: 9970C980
B[6]: 3C517031 B[7] : D1439B63 B[8]: 9334E221
B[9]: 50EF13E7 B[10]: E0BD9F91
B[0]: C57BED5B B[1] : 7BE2C520 B[2]: 1F48829C
B[3]: F95DD14F B[4] : D939E13E B[5]: 9970C980
B[6]: 3C517031 B[7] : D1439B63 B[8]: 9334E221
B[9]: 50EF13E7 B[10]: E0BD9F91
L1: 4370D8E6 R1: DABED76C L2: 11C1ACCB R2: C3BAAEDF
L1: 4370D8E6 R1: DABED76C L2: 11C1ACCB R2: C3BAAEDF
Note that the result of init(24) is also referred to as S(0) (in Section 2.3.2). Since the state is S(0), the stream() operation (in Section 2.3.3) can be applied and generate key streams.
注意，init（24）的结果也被称为S（0）（在第2.3.2节中）。由于状态为S（0），因此可以应用stream（）操作（在第2.3.3节中）并生成密钥流。
Key stream at S(0) : 9FB6B580A6A5E7AF
S（0）处的密钥流：9FB6B580A6A5E7AF
Henceforth, a new key stream can be produced by 1) obtaining a new state by applying the next() operation to the current state, and 2) generating a new key stream by applying the stream() operation to the new state.
此后，可以通过1）通过将next（）操作应用于当前状态来获得新状态，以及2）通过将stream（）操作应用于新状态来生成新密钥流来生成新密钥流。
A[0]: BE3CA984 A[1]: 974E6719 A[2]: 86916EFF
A[3]: F52DACF9 A[4]: 960329B5
A[0]: BE3CA984 A[1]: 974E6719 A[2]: 86916EFF
A[3]: F52DACF9 A[4]: 960329B5
B[0]: 7BE2C520 B[1] : 1F48829C B[2]: F95DD14F
B[3]: D939E13E B[4] : 9970C980 B[5]: 3C517031
B[6]: D1439B63 B[7] : 9334E221 B[8]: 50EF13E7
B[9]: E0BD9F91 B[10]: 5318AEE1
B[0]: 7BE2C520 B[1] : 1F48829C B[2]: F95DD14F
B[3]: D939E13E B[4] : 9970C980 B[5]: 3C517031
B[6]: D1439B63 B[7] : 9334E221 B[8]: 50EF13E7
B[9]: E0BD9F91 B[10]: 5318AEE1
L1: 8FD86092 R1: 4BBDC0F6 L2: 8D63A5EF R2: FEE0F24B
L1: 8FD86092 R1: 4BBDC0F6 L2: 8D63A5EF R2: FEE0F24B
Key stream at S(1) : D1989DC6A77D5E28
S（1）处的密钥流：D1989DC6A77D5E28
A[0]: 974E6719 A[1]: 86916EFF A[2]: F52DACF9
A[3]: 960329B5 A[4]: 1A3DB24E
A[0]: 974E6719 A[1]: 86916EFF A[2]: F52DACF9
A[3]: 960329B5 A[4]: 1A3DB24E
B[0]: 1F48829C B[1] : F95DD14F B[2]: D939E13E
B[3]: 9970C980 B[4] : 3C517031 B[5]: D1439B63
B[6]: 9334E221 B[7] : 50EF13E7 B[8]: E0BD9F91
B[9]: 5318AEE1 B[10]: C86C2C77
B[0]: 1F48829C B[1] : F95DD14F B[2]: D939E13E
B[3]: 9970C980 B[4] : 3C517031 B[5]: D1439B63
B[6]: 9334E221 B[7] : 50EF13E7 B[8]: E0BD9F91
B[9]: 5318AEE1 B[10]: C86C2C77
L1: 9686FE8C R1: FAF89251 L2: 86C824E7 R2: 7BC21098
L1: 9686FE8C R1: FAF89251 L2: 86C824E7 R2: 7BC21098
Key stream at S(2) : 4EFCC8CB7BCFB32B
S（2）处的密钥流：4EFCC8CB7BCFB32B
Authors' Addresses
作者地址
Shinsaku Kiyomoto KDDI R&D Laboratories, Inc. 2-1-15 Ohara Fujimino-shi, Saitama 356-8502 Japan
日本Saitama 356-8502大原藤美浓市2-1-15号新坂清本KDDI研发实验室有限公司
Phone: +81-49-278-7885
Fax: +81-49-278-7510
EMail: kiyomoto@kddilabs.jp
Phone: +81-49-278-7885
Fax: +81-49-278-7510
EMail: kiyomoto@kddilabs.jp
Wook Shin KDDI R&D Laboratories, Inc. 2-1-15 Ohara Fujimino-shi, Saitama 356-8502 Japan
旭信KDDI研发实验室有限公司2-1-15大原藤原市，日本柴达木356-8502
EMail: ohpato@hanmail.net
EMail: ohpato@hanmail.net