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    Method and apparatus for elliptic curve scalar multiplication
    6.
    发明授权
    Method and apparatus for elliptic curve scalar multiplication 有权
    椭圆曲线标量乘法的方法和装置

    公开(公告)号：US07215780B2

    公开(公告)日：2007-05-08

    申请号：US10058214

    申请日：2002-01-29

    申请人： Robert J. Lambert ,  Ashok Vadekar ,  Adrian Antipa

    发明人： Robert J. Lambert ,  Ashok Vadekar ,  Adrian Antipa

    IPC分类号： H04L9/00

    CPC分类号： G06F7/725 ,  G06F7/722

    摘要： The applicants have recognized an alternate method of performing modular reduction that admits precomputation. The precomputation is enabled by approximating the inverse of the truncator T, which does not depend on the scalar.The applicants have also recognized that the representation of a scalar in a τ-adic representation may be optimized for each scalar that is needed.The applicants have further recognized that a standard rounding algorithm may be used to perform reduction modulo the truncator.In general terms, there is provided a method of reducing a scalar modulo a truncator, by pre-computing an inverse of the truncator. Each scalar multiplication then utilizes the pre-computed inverse to enable computation of the scalar multiplication without requiring a division by the truncator for each scalar multiplication.

    摘要翻译： 申请人已经认识到承认预先计算的执行模块化减少的替代方法。 通过逼近截断器T的反向来实现预计算，其不依赖于标量。 申请人还认识到，可以针对所需的每个标量来优化标量的代表性。 申请人进一步认识到，可以使用标准舍入算法来执行缩减模数截断器。 一般而言，提供了一种通过预先计算截断器的倒数来减少标量模截断器的方法。 每个标量乘法然后利用预先计算的逆来实现标量乘法的计算，而不需要每个标量乘法的截断器的除法。

    Timing attack resistant cryptographic system
    7.
    发明授权
    Timing attack resistant cryptographic system 有权
    定时攻击加密系统

    公开(公告)号：US07020281B2

    公开(公告)日：2006-03-28

    申请号：US09761700

    申请日：2001-01-18

    申请人： Ashok Vadekar ,  Robert J. Lambert

    发明人： Ashok Vadekar ,  Robert J. Lambert

    IPC分类号： H04L9/00

    CPC分类号： G06F9/30058 ,  G06F7/4824 ,  G06F7/725 ,  G06F2207/7261 ,  H04L9/005 ,  H04L9/3066

    摘要： A method for determining a result of a group operation performed an integral number of times on a selected element of the group, the method comprises the steps of representing the integral number as a binary vector; initializing an intermediate element to the group identity element; selecting successive bits, beginning with a left most bit, of the vector. For each of the selected bits; performing the group operation on the intermediate element to derive a new intermediate element; replacing the intermediate element with the new intermediate element; performing the group operation on the intermediate element and an element, selected from the group consisting of: the group element if the selected bit is a one; and an inverse element of the group element if the selected bit is a zero; replacing the intermediate element with the new intermediate element. In a final step, performing the group operation on the intermediate value and the inverse element if the last selected bit is a zero; and replacing the intermediate element therewith, to obtain the result, whereby each of the bits of the integral is processed with substantially equal operations thereby minimizing timing attacks on the cryptographic system.

    摘要翻译： 一种用于确定组操作的结果对组的所选元素执行整数次的方法，所述方法包括以下步骤：将整数表示为二进制向量; 将中间元素初始化为组标识元素; 选择向量开始的最左位的连续位。 对于每个选定的位; 对中间元素执行组操作以导出新的中间元素; 用新的中间元件代替中间元件; 对中间元素执行组操作，以及从由以下组成的组中选择的元素：组元素，如果所选择的位是一个; 如果所选择的位为零，则组元素的反向元素; 用新的中间元件代替中间元件。 在最后一步中，对中间值执行组操作，如果最后一个选择的位为零，则执行逆元素; 并且用其替换中间元件，以获得结果，由此以大致相等的操作处理积分的每个比特，从而最小化对密码系统的定时攻击。

    Method for accelerating cryptographic operations on elliptic curves
    8.
    发明授权
    Method for accelerating cryptographic operations on elliptic curves 有权
    加速椭圆曲线加密操作的方法

    公开(公告)号：US07995752B2

    公开(公告)日：2011-08-09

    申请号：US11095542

    申请日：2005-04-01

    申请人： Robert J. Lambert ,  Ashok Vadekar

    发明人： Robert J. Lambert ,  Ashok Vadekar

    IPC分类号： H04L9/00 ,  H04L9/28 ,  H04L9/30

    CPC分类号： G06F7/725 ,  H04L9/3073

    摘要： This invention provides a method for accelerating multiplication of an elliptic curve point Q(x,y) by a scalar k, the method comprising the steps of selecting an elliptic curve over a finite field Fq where q is a prime power such that there exists an endomorphism ψ, where ψ(Q)=λ·Q for all points Q(x,y) on the elliptic curve; and using smaller representations ki of the scalar k in combination with the mapping y to compute the scalar multiple of the elliptic curve point Q.

    摘要翻译： 本发明提供了一种用于加速椭圆曲线点Q（x，y）乘以标量k的方法，所述方法包括以下步骤：在有限域Fq上选择椭圆曲线，其中q是素数，使得存在 同构ψ，其中ψ（Q）=λ·Q对于椭圆曲线上的所有点Q（x，y）; 并且与映射y一起使用标量k的较小表示ki来计算椭圆曲线点Q的标量倍数。

    Method and apparatus for elliptic curve scalar multiplication
    9.
    发明授权
    Method and apparatus for elliptic curve scalar multiplication 有权
    椭圆曲线标量乘法的方法和装置

    公开(公告)号：US07412062B2

    公开(公告)日：2008-08-12

    申请号：US11687773

    申请日：2007-03-19

    申请人： Robert J. Lambert ,  Ashok Vadekar ,  Adrian Antipa

    发明人： Robert J. Lambert ,  Ashok Vadekar ,  Adrian Antipa

    IPC分类号： H04L9/00

    CPC分类号： G06F7/725 ,  G06F7/722

    摘要： The applicants have recognized an alternate method of performing modular reduction that admits precomputation. The precomputation is enabled by approximating the inverse of the truncator T, which does not depend on the scalar.The applicants have also recognized that the representation of a scalar in a τ-adic representation may be optimized for each scalar that is needed.The applicants have further recognized that a standard rounding algorithm may be used to perform reduction modulo the truncator.In general terms, there is provided a method of reducing a scalar modulo a truncator, by pre-computing an inverse of the truncator. Each scalar multiplication then utilizes the pre-computed inverse to enable computation of the scalar multiplication without requiring a division by the truncator for each scalar multiplication.

    摘要翻译： 申请人已经认识到承认预先计算的执行模块化减少的替代方法。 通过逼近截断器T的反向来实现预计算，其不依赖于标量。 申请人还认识到，可以针对所需的每个标量来优化标量的代表性。 申请人进一步认识到，可以使用标准舍入算法来执行缩减模数截断器。 一般而言，提供了一种通过预先计算截断器的倒数来减少标量模截断器的方法。 每个标量乘法然后利用预先计算的逆来实现标量乘法的计算，而不需要每个标量乘法的截断器的除法。

    Two way authentication protocol
    10.
    发明授权
    Two way authentication protocol 有权
    双向认证协议

    公开(公告)号：US06487660B1

    公开(公告)日：2002-11-26

    申请号：US09432166

    申请日：1999-11-02

    申请人： Scott Alexander Vanstone ,  Donald B. Johnson ,  Robert J. Lambert ,  Ashok Vadekar

    发明人： Scott Alexander Vanstone ,  Donald B. Johnson ,  Robert J. Lambert ,  Ashok Vadekar

    IPC分类号： G06F124

    CPC分类号： G07F7/1008 ,  G06Q20/341 ,  G06Q20/40975 ,  H04L9/0841 ,  H04L9/3066 ,  H04L9/3273

    摘要： A method of authenticating a pair of correspondents C,S to permit the exchange of information therebetween, each of the correspondents having a respective private key, e, d and a public key, Qu, and Qs derived from a generator element of a group and a respective ones of the private keys e,d, the method comprising the steps of: a first of the correspondents C generating a session value x; the first correspondent generating a private value t, a public value derived from the private value t and the generator and a shared secret value derived from the private value t and the public key Qs of the second correspondent; the second correspondent generating a challenge value y and transmitting the challenge value y to the first correspondent; the first correspondent in response thereto computing a value h by applying a function H to the challenge value y, the session value x, the public value an of the first correspondent; the first correspondent signing the value h utilizing the private key e; the first correspondent transmitting to the second correspondent the signature including the session value x, and the private value t; and the second correspondent verifying the signature utilizing the public key Qu of the first correspondent and whereby verification of the signature authenticates the first correspondent to the second correspondent.

    摘要翻译： 一种认证一对记者C，S以允许它们之间的信息交换的方法，每个通信对象具有从组的发生器元素导出的相应私钥，e，d和公钥Qu和Q，以及 相应的私钥e，d，该方法包括以下步骤：生成会话值x的通信对象C中的第一个; 生成私有值t的第一通信对象，从私有值t和生成器导出的公有值和从私有值t和第二通信对方的公钥Qs导出的共享秘密值; 第二记者产生质询值y并将询问值y发送给第一通讯员; 响应于第一记者通过将函数H应用于质询值y，会话值x，第一记者的公开值a来计算值h; 第一个记者利用私钥e签名值h; 第一记者向第二记者发送包括会话值x和私有值t的签名; 以及第二记者利用第一记者的公钥Qu验证签名，由此签名的验证对第二通信对象的第一对应者进行认证。