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    • 3. 发明授权
    • Method for obtaining encryption keys corresponding terminals, server and computer program products
    • 用于获取对应终端,服务器和计算机程序产品的加密密钥的方法
    • US08966266B2
    • 2015-02-24
    • US13699043
    • 2011-05-16
    • Eric BrierThomas Peyrin
    • Eric BrierThomas Peyrin
    • H04L9/32H04L9/08
    • H04L9/0819H04L9/0838H04L9/0869H04L2209/38
    • A method and apparatus for obtaining an encryption key for an item of data transmitted from a client to a server. The method includes: determining a number R of registers available within the client for carrying out a plurality of calculations of encryption keys; determining a maximum number N of iterations necessary for obtaining at least one encryption key at the server; obtaining a structure of data representative of a key calculation state effected within the R available registers; calculating the at least one encryption key as a function: —of the number of available registers R, by performing at most N calls to a pseudo-random function F and —of the data structure; so that the at least one encryption key can be obtained from a combination of at most T=CR+NN−1 encryption keys based on a secret previously shared between the server and client.
    • 一种用于获得从客户端发送到服务器的数据项的加密密钥的方法和装置。 该方法包括:确定客户端内可用的寄存器数量R,以执行加密密钥的多个计算; 确定在所述服务器处获得至少一个加密密钥所需的迭代的最大数量N; 获得表示在R可用寄存器内实现的密钥计算状态的数据结构; 通过对伪随机函数F和数据结构执行至多N个调用来计算至少一个加密密钥作为可用寄存器R的数量的函数; 使得可以基于先前在服务器和客户端之间共享的秘密从最多T = CR + NN-1加密密钥的组合中获得至少一个加密密钥。
    • 4. 发明申请
    • CRYPTOGRAPHIC METHOD USING A NON-SUPERSINGULAR ELLIPTIC CURVE E IN CHARACTERISTIC 3
    • 特征3中的非超级电路曲线E的折射方法
    • US20140105384A1
    • 2014-04-17
    • US12964382
    • 2010-12-09
    • Eric Brier
    • Eric Brier
    • H04L9/28
    • H04L9/28H04L9/002H04L9/3066
    • A cryptographic method is provided of a type with public key over a non-supersingular elliptic curve E, determined by the simplified Weirstrass equation y2=x3+a.x2+b over a finite field GF(3n), with n being an integer greater than or equal to 1. The method includes associating an element t of said finite field with a point P′ of the elliptic field. The step of associating includes: obtaining a pre-determined quadratic non-residue η on GF(3n); obtaining a pre-determined point P=(zP, yP) belonging to a conic C defined by the following equation: a.η.z2−y2+b=0; obtaining a point Q=(zQ, yQ), distinct from the point P belonging to the conic C and a straight line D defined by the following equation: y=t.z+yP−t.zP; obtaining the element ξ of GF(3n) verifying the following linear equation over GF(3): ξ3−η.ξ=(η2.zQ)/a; and associating, with the element t of the finite field, the point P′ of the elliptic curve, for which the coordinates are defined by the pair (η.zQ/ξ, yQ).
    • 提供了一种具有公钥的类型的密码方法,该公钥在非超椭圆曲线E上,由有限域GF(3n)上的简化Weirstrass方程y2 = x3 + a.x2 + b确定,其中n是更大的整数 该方法包括将所述有限域的元素t与椭圆场的点P'相关联。 关联的步骤包括:获得预定的二次非残基和eegr; 在GF(3n)上; 获得属于由以下等式定义的圆锥C的预定点P =(zP,yP):a。&eegr;。z2-y2 + b = 0; 获得与属于圆锥C的点P不同的点Q =(zQ,yQ)和由以下等式定义的直线D:y = t.z + yP-t.zP; 获取元素&xgr; GF(3n)验证GF(3)上的以下线性方程:&xgr; 3-&egrgr。。&xgr; =(&eegr; 2.zQ)/ a; 并且与有限域的元素t相关联的椭圆曲线的点P',其坐标由对(&eegr; .zQ /&xgr; yQ)定义。
    • 6. 发明授权
    • Process for generating an elliptic curve, application in a cryptographic process, and cryptographic process using such a curve
    • 用于生成椭圆曲线的过程,加密处理中的应用以及使用这样的曲线的密码处理
    • US08165285B2
    • 2012-04-24
    • US11336816
    • 2006-01-23
    • Eric Brier
    • Eric Brier
    • H04K1/00
    • G06F7/725H04L9/3073H04L2209/08
    • The invention relates, mainly to a cryptographic process using an elliptic curve represented by means of an equation containing first and second parameters (a, b), a bilinear matching, and calculations in a finite group of integers constructed around at least one first reduction rule reducing each integer to its remainder in a whole division by a first prime number (p) that constitutes a third parameter, the elements of the finite group being in bijection with points selected on the elliptic curve, and the number of which is linked to a fourth parameter (q), where this process uses public and private keys, each of which is represented by a given point of the elliptic curve or by a multiplication factor between two points of this curve.According to the invention, the first reduction rule is the only reduction rule implemented, and the elliptic curve is obtained through a step-by-step construction process, directly allocating to the finite group q*q q-order points in the elliptic curve.
    • 本发明主要涉及使用由包含第一和第二参数(a,b)的方程表示的椭圆曲线的密码处理,双线性匹配以及围绕至少一个第一简化规则构造的有限整数组中的计算 将每个整数除以整数除以构成第三参数的第一素数(p),将有限组的元素与椭圆曲线上选择的点相对应,并将其数量与 第四个参数(q),其中该过程使用公钥和私钥,其中每一个由椭圆曲线的给定点或该曲线的两个点之间的乘积因子表示。 根据本发明,第一简化规则是实现的唯一的减少规则,并且椭圆曲线通过逐步构造过程获得,直接分配给椭圆曲线中的有限群q * q q个点。
    • 8. 发明申请
    • METHOD FOR OBTAINING ENCRYPTION KEYS CORRESPONDING TERMINALS, SERVER AND COMPUTER PROGRAM PRODUCTS
    • 用于获取加密终端,服务器和计算机程序产品的方法
    • US20140149744A1
    • 2014-05-29
    • US13699043
    • 2011-05-16
    • Eric BrierThomas Peyrin
    • Eric BrierThomas Peyrin
    • H04L9/08
    • H04L9/0819H04L9/0838H04L9/0869H04L2209/38
    • A method and apparatus for obtaining an encryption key for an item of data transmitted from a client to a server. The method includes: determining a number R of registers available within the client for carrying out a plurality of calculations of encryption keys; determining a maximum number N of iterations necessary for obtaining at least one encryption key at the server; obtaining a structure of data representative of a key calculation state effected within the R available registers; calculating the at least one encryption key as a function: —of the number of available registers R, by performing at most N calls to a pseudo-random function F and —of the data structure; so that the at least one encryption key can be obtained from a combination of at most T=CR+NN−1 encryption keys based on a secret previously shared between the server and client.
    • 一种用于获得从客户端发送到服务器的数据项的加密密钥的方法和装置。 该方法包括:确定客户端内可用的寄存器数量R,以执行加密密钥的多个计算; 确定在所述服务器处获得至少一个加密密钥所需的迭代的最大数量N; 获得表示在R可用寄存器内实现的密钥计算状态的数据结构; 通过对伪随机函数F和数据结构执行至多N个调用来计算至少一个加密密钥作为可用寄存器R的数量的函数; 使得可以基于先前在服务器和客户端之间共享的秘密从最多T = CR + NN-1加密密钥的组合中获得至少一个加密密钥。