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    • 5. 发明申请
    • A DEVICE, METHOD AND A COMPUTER PROGRAM PRODUCT FOR CALCULATING ADDITIONS OF POINTS ON ELLIPTIC CURVES IN EDWARDS FORM
    • 一种用于计算EDWARDS表格中ELLIPTIC曲线点的附加值的装置,方法和计算机程序产品
    • WO2009095491A1
    • 2009-08-06
    • PCT/EP2009/051096
    • 2009-01-30
    • THOMSON LICENSINGJOYE, Marc
    • JOYE, Marc
    • G06F7/72
    • G06F7/725G06F2207/7261
    • A device (100) for calculations on elliptic curves. The elliptic curve in generalized Edwards form is projected on a projective form so that a point P = (x 1 , y 1 ) on the elliptic curve is represented by the tuple (x 1 Z 1 : y 1 Z 1 : Z 1 ) for any Z 1 ≠ 0. An addition of two projective points (X 1 : V 1 : Z 1 ) and (X 2 : V 2 : Z 2 ) is given by X 3 = Z 1 Z 2 (X 1 Y 2 + X 2 Y 1 )M, Y 3 = Z 1 Z 2 (Y 1 Y 2 - e X 1 X 2 )N, and Z 3 = MN, where M = f Z 1 2 Z 2 2 - d X 1 X 2 Y 1 Y 2 and N = f Z 1 2 Z 2 2 + d X 1 X 2 Y 1 Y 2 . By rewriting X 1 Y 2 + X 2 Y 1 as (X 1 + Y 1 )(X 2 + Y 2 ) - X 1 Y 1 - X 2 Y 2 , this costs 10M+ 1 S + 1 d + 1 e + 1 f where M denotes a field multiplication, S denotes a field squaring, and d, e, f denote respectively a multiplication by constants d, e, f . Also provided is a special doubling formula, a method, and a computer program (140).
    • 用于在椭圆曲线上计算的装置(100)。 广义爱德华兹形式的椭圆曲线投影在投影形式上,使得椭圆曲线上的点P =(x1,y1)由任何Z1的元组(x1Z1:y1Z1:Z1)表示。 通过X3 = Z1Z2(X1 Y2 + X2Y1)M,Y3 = Z1Z2(Y1 Y2-e X1X2)N给出两个投影点(X1:V1:Z1)和(X2:V2:Z2)的相加, Z3 = MN,其中M = f Z1 2Z2 2 -d X1X2Y1Y2和N = f Z1 2Z2 2 + d X1X2Y1 Y2。 通过将X1 Y2 + X2Y1重写为(X1 + Y1)(X2 + Y2)-X1 Y1-X2Y2,则成本为10M + 1 S + 1 d + 1 e + 1 f其中M表示场乘法,S表示场平方, d,e,f分别表示常数d,e,f的相乘。 还提供了特殊的加倍公式,方法和计算机程序(140)。
    • 7. 发明申请
    • A METHOD AND A DEVICE FOR PERFORMING TORUS-BASED CRYPTOGRAPHY
    • 一种用于执行基于多普勒频率分析的方法和装置
    • WO2010145983A1
    • 2010-12-23
    • PCT/EP2010/058131
    • 2010-06-10
    • THOMSON LICENSINGJOYE, Marc
    • JOYE, Marc
    • H04L9/30H04L9/32
    • H04L9/3013H04L9/302H04L9/3255H04L2209/12H04L2209/30
    • At CRYPTO 2003, Rubin and Silverberg introduced the concept of torus-based cryptography over a finite field. The present invention extends their setting to the ring of integers modulo N , thus obtaining compact representations for cryptographic systems that base their security on the discrete logarithm problem and the factoring problem. This can result in small key sizes and substantial savings in memory and bandwidth. However, unlike the case of finite field, analogous trace-based compression methods cannot be adapted to accommodate the extended setting of the invention when the underlying systems require more than a mere exponentiation. The invention finds particular application in a torus-based implementation of the ACJT group signature scheme. Also provided is a processor (10).
    • 在CRYPTO 2003年,Rubin和Silverberg在有限的领域上介绍了基于环面的加密技术的概念。 本发明将它们的设置扩展到模N的整数环,从而获得基于离散对数问题和保理问题的安全性的密码系统的紧凑表示。 这可能导致小的密钥大小,并显着节省内存和带宽。 然而,与有限域的情况不同,当底层系统需要的不仅仅是求幂时,类似的基于跟踪的压缩方法不能适应于适应本发明的扩展设置。 本发明在ACJT组签名方案的基于环面的实现中发现具体应用。 还提供了处理器(10)。
    • 9. 发明申请
    • METHOD AND APPARATUS FOR GENERATING A SIGNATURE FOR A MESSAGE AND METHOD AND APPARATUS FOR VERIFYING SUCH A SIGNATURE
    • 用于生成消息签名的方法和装置以及用于验证这样的签名的装置
    • WO2010000552A1
    • 2010-01-07
    • PCT/EP2009/056759
    • 2009-06-02
    • THOMSON LICENSINGJOYE, Marc
    • JOYE, Marc
    • H04L9/32H04L9/30
    • H04L9/3249H04L9/302H04L2209/56H04L2209/80
    • A method of generating a signature σ for a message m, the method enabling online/offline signatures. Two random primes p and q are generated, with N = pq ; two random quadratic residues g and x are chosen in Z* N , and, for an integer z, h = g -Z mod N is calculated. This gives the public key { g,h,x,N } and the private key { p,q,z }. Then, an integer t and a prime e are chosen. The offline signature part y may then be calculated as: equation (I) where b is an integer bigger than 0, predetermined in the signature scheme. The online part k of the signature on message m is then calculated as k = t + mz and the signature σ on message m is generated as σ = ( k, y, e ) and returned. To verify the signature, it is checked that 1) e is an odd IE -bit integer, 2) k is an I κ-bit integer, and 3) equation (II). An advantage of the method is that it may be performed without hashing. Also provided are a signing device (210), a verification device (310), and computer program supports (260; 360).
    • 生成消息m的签名s的方法,该方法启用在线/离线签名。 产生两个随机素数p和q,其中N = pq; 在Z * N中选择两个随机二次残差g和x,对于整数z,计算h = g-Z mod N。 这给出公钥{g,h,x,N}和私钥{p,q,z}。 然后,选择整数t和素数e。 离线签名部分y然后可以被计算为:等式(I)其中b是大于0的整数,在签名方案中是预定的。 然后将消息m上的签名的在线部分k计算为k = t + mz,并且生成消息m上的签名s作为s =(k,y,e)并返回。 为了验证签名,检查1)e是奇数IE比特整数,2)k是I比特整数,以及3)等式(II)。 该方法的优点在于可以不进行散列来执行。 还提供了签名设备(210),验证设备(310)和计算机程序支持(260; 360)。