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    Method, apparatus and media for performing GF(2) polynomial operations
    3.
    发明授权
    Method, apparatus and media for performing GF(2) polynomial operations 有权
    用于执行GF（2）多项式运算的方法，装置和介质

    公开(公告)号：US08375077B2

    公开(公告)日：2013-02-12

    申请号：US12239927

    申请日：2008-09-29

    Applicant: Pierre Laurent

    Inventor： Pierre Laurent

    IPC: G06F7/00

    CPC classification number: G06F7/726

    Abstract: 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.

    Abstract translation: 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。

    Efficient method and apparatus for modular inverses
    5.
    发明申请
    Efficient method and apparatus for modular inverses 有权
    模块化逆变器的高效方法和装置

    公开(公告)号：US20100119057A1

    公开(公告)日：2010-05-13

    申请号：US12291318

    申请日：2008-11-07

    Applicant: Pierre Laurent ,  Vinodh Gopal

    Inventor： Pierre Laurent ,  Vinodh Gopal

    IPC: H04L9/28

    CPC classification number: G06F7/727 ,  G06F7/721 ,  H04L9/3093 ,  H04N7/1675 ,  H04N21/2383

    Abstract: 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.

    Abstract translation: 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。

    Roll of tissue paper sheets, and associated manufacturing method
    6.
    发明授权
    Roll of tissue paper sheets, and associated manufacturing method 失效
    卷纸薄纸和相关制造方法

    公开(公告)号：US06884492B2

    公开(公告)日：2005-04-26

    申请号：US10636531

    申请日：2003-08-08

    Applicant: Michel Basler ,  Sébastien Jeannot ,  Pierre Laurent

    Inventor： Michel Basler ,  Sébastien Jeannot ,  Pierre Laurent

    IPC: A47K10/16 ,  B31F1/07 ,  D21F11/00 ,  B32B3/00 ,  B31F1/22 ,  D21H11/00

    CPC classification number: B31F1/07 ,  A47K10/16 ,  B31F2201/0733 ,  B31F2201/0738 ,  B31F2201/0761 ,  D21F11/006 ,  Y10S428/906 ,  Y10T156/1023 ,  Y10T428/24562 ,  Y10T428/24612 ,  Y10T428/24777 ,  Y10T428/24967

    Abstract: The invention relates to a roll constituted by a plurality of tissue paper sheets each having a specific surface weight between 10 and 40 g/m2 and exhibiting thick zones (4) separated over at least 90% of their periphery by thinner zones (5). According to the invention, and as regards at least the outermost turns of the roll, the thick zones are at least partly superposed one on the other in a way to add the thicknesses cumulatively and hence to create height differentials on the roll's outside. The invention also relates to a method for making a roll, wherein a strip composed of a plurality of juxtaposed tissue paper sheets exhibiting thick zones separated by thinner zones will be wound on itself. According to the invention, the winding of the roll is such that the thick zones (4) of the outermost roll turns are at least partly superposed in order to constitute a salient topography on the roll's outside.

    Abstract translation: 本发明涉及一种由多个薄纸组成的卷，每个薄纸各自具有10至40g / m 2之间的比表面积，并且显示出在其至少90％的分辨率上分离的厚区（4） 周边由薄区（5）。 根据本发明，至少对于辊的最外圈，厚区域至少部分地叠加在另一个上，以便累积地增加厚度，从而在辊的外侧产生高度差。 本发明还涉及一种用于制造卷的方法，其中，由多个并排的薄纸组合的条带，其表现出由较薄区域分隔的厚区域。 根据本发明，辊的卷绕使得最外侧辊匝的厚区域（4）至少部分地重叠，以便在辊的外部构成显着的形貌。

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