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    • 8. 发明授权
    • Method, apparatus and media for performing GF(2) polynomial operations
    • 用于执行GF(2)多项式运算的方法,装置和介质
    • US08375077B2
    • 2013-02-12
    • US12239927
    • 2008-09-29
    • Pierre Laurent
    • Pierre Laurent
    • G06F7/00
    • G06F7/726
    • Methods, apparatus and media for performing polynomial arithmetic operations over a Galois field having characteristic 2 and size 1 are disclosed. Such methods, apparatus and media include generating a binary representation of a polynomial over a Galois field having characteristic 2 and size 1, generating a plurality of right shifted binary representations of the first polynomial, and generating a binary representation of the polynomial reciprocal based upon a bitwise exclusive-OR of the binary representation of the polynomial and one or more right shifted binary representations selected from the plurality of right shifted binary representations.
    • 公开了在具有特征2和尺寸1的伽罗瓦域上执行多项式算术运算的方法,装置和介质。 这样的方法,装置和媒体包括在具有特征2和尺寸1的伽罗瓦域上生成多项式的二进制表示,产生第一多项式的多个右移二进制表示,并且基于一个多项式互逆生成多项式互逆的二进制表示 多项式的二进制表示和从多个右移二进制表示中选择的一个或多个右移二进制表示的按位异或。
    • 10. 发明申请
    • Efficient method and apparatus for modular inverses
    • 模块化逆变器的高效方法和装置
    • US20100119057A1
    • 2010-05-13
    • US12291318
    • 2008-11-07
    • Pierre LaurentVinodh Gopal
    • Pierre LaurentVinodh Gopal
    • H04L9/28
    • G06F7/727G06F7/721H04L9/3093H04N7/1675H04N21/2383
    • Methods and apparatus are described for computing modular inverses of odd input values modulo 2N (or modulo xN, for example in some Galois field) to perform a modular multiplication in cryptographic processing systems. In one embodiment an approximation is computed having 2k bits of the modular inverse of the odd input value without multiplications, for example using a binary extended Euclidean algorithm. A sequence of log2N−k Newton-Raphson or similarly quadratically convergent iterations are applied to the approximation using an extended precision multiplier to generate the modular inverse of the odd input value modulo 2N (or modulo xN), the modular inverse having up to N bits of precision. The modular inverse of the odd input value is then used in a modular multiplication to perform cryptographic operations and/or cyclic redundancy checks on communication data.
    • 描述的方法和装置用于计算模2N的奇数输入值(或者例如在一些伽罗瓦域中的模xN)以在密码处理系统中执行模乘。 在一个实施例中,计算具有奇数输入值的模数逆的2k位的近似,而不进行乘法,例如使用二进制扩展的欧几里德算法。 使用扩展精度乘数将log2N-k Newton-Raphson或类似的二次收敛迭代的序列应用于近似,以产生模2N(或模xN)的奇数输入值的模逆,该模逆向具有多达N位 的精度。 然后,以模数乘法将奇数输入值的模数反向用于对通信数据执行加密操作和/或循环冗余校验。