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    Accelerated Verification of Digital Signatures and Public Keys
    2.
    发明申请
    Accelerated Verification of Digital Signatures and Public Keys 审中-公开
    加速验证数字签名和公钥

    公开(公告)号：US20140344579A1

    公开(公告)日：2014-11-20

    申请号：US14318313

    申请日：2014-06-27

    申请人： Certicom Corp.

    发明人： Marinus STRUIK ,  Daniel Richard L. BROWN ,  Scott Alexander VANSTONE ,  Robert Philip GALLANT ,  Adrian ANTIPA ,  Robert John LAMBERT

    IPC分类号： H04L9/30 ,  H04L9/32

    CPC分类号： H04L9/3066 ,  G06F7/725 ,  H04L9/30 ,  H04L9/3252

    摘要： Accelerated computation of combinations of group operations in a finite field is provided by arranging for at least one of the operands to have a relatively small bit length. In a elliptic curve group, verification that a value representative of a point R corresponds the sum of two other points uG and vG is obtained by deriving integers w,z of reduced bit length and that v=w/z. The verification equality R=uG+vQ may then be computed as −zR+(uz mod n)+wQ=O with z and w of reduced bit length This is beneficial in digital signature verification where increased verification can be attained.

    摘要翻译： 通过将至少一个操作数布置成具有相对较小的比特长度来提供有限域中的组操作的组合的加速计算。 在椭圆曲线组中，验证表示点R的值对应于两个其他点uG和vG的和是通过导出减小位长度的整数w，z以及v = w / z获得的。 然后，验证等式R = uG + vQ可以被计算为-zR +（uz mod n）+ wQ = 0，其中z和w为减少的比特长度这对于可以获得增加的验证的数字签名验证是有益的。

    Challenge-Response Authentication Using a Masked Response Value
    4.
    发明申请
    Challenge-Response Authentication Using a Masked Response Value 审中-公开
    使用掩蔽响应值进行挑战响应验证

    公开(公告)号：US20160261417A1

    公开(公告)日：2016-09-08

    申请号：US15158035

    申请日：2016-05-18

    申请人： Certicom Corp.

    发明人： Robert John LAMBERT

    IPC分类号： H04L9/32

    CPC分类号： H04L9/3271 ,  H04L9/3236 ,  H04L2209/04 ,  H04W12/06

    摘要： Challenge-response authentication protocols are disclosed herein, including systems and methods for a first device to authenticate a second device. In one embodiment, the following operations are performed by the first device: (a) sending to the second device: (i) a challenge value corresponding to an expected response value known by the first device, and (ii) a hiding value; (b) receiving from the second device a masked response value; (c) obtaining an expected masked response value from the expected response value and the hiding value; and (d) determining whether the expected masked response value matches the masked response value received from the second device. The operations from the perspective of the second device are also disclosed, which in some embodiments include computing the masked response value using the challenge value, the hiding value, and secret information known to the second device.

    摘要翻译： 本文公开了挑战响应认证协议，包括用于第一设备认证第二设备的系统和方法。 在一个实施例中，以下操作由第一设备执行：（a）向第二设备发送：（i）对应于由第一设备已知的预期响应值的挑战值，以及（ii）隐藏值; （b）从第二设备接收被屏蔽的响应值; （c）从预期响应值和隐藏值获得预期屏蔽响应值; 以及（d）确定预期的屏蔽响应值是否与从第二设备接收到的屏蔽的响应值相匹配。 还公开了从第二设备的角度的操作，在一些实施例中，这些操作包括使用挑战值，隐藏值和第二设备已知的秘密信息来计算被屏蔽的响应值。

    HYBRID SIGNATURE SCHEME
    5.
    发明申请
    HYBRID SIGNATURE SCHEME 审中-公开
    混合签名方案

    公开(公告)号：US20140298033A1

    公开(公告)日：2014-10-02

    申请号：US14307299

    申请日：2014-06-17

    申请人： Certicom Corp. ,  Pitney Bowes Inc.

    发明人： Scott Alexander VANSTONE ,  Robert Philip GALLANT ,  Robert John LAMBERT ,  Leon A. PINTSOV ,  Frederick W. RYAN, JR. ,  Ari SINGER

    IPC分类号： H04L9/32

    CPC分类号： H04L9/3247 ,  H04L9/3252

    摘要： A signature scheme is provided in which a message is divided in to a first portion which is hidden and is recovered during verification, and a second portion which is visible and is required as input to the verification algorithm. A first signature component is generated by encrypting the first portion alone. An intermediate component is formed by combining the first component and the visible portion and cryptographically hashing them. A second signature component is then formed using the intermediate component and the signature comprises the first and second components with the visible portion. A verification of the signature combines a first component derived only from the hidden portion of the message with the visible portion and produces a hash of the combination. The computed hash is used together with publicly available information to generate a bit string corresponding to the hidden portion.

    摘要翻译： 提供一种签名方案，其中消息被分成隐藏的第一部分，并且在验证期间被恢复，并且第二部分是可见的并且被要求作为验证算法的输入。 通过单独加密第一部分来产生第一签名组件。 通过组合第一组件和可见部分并对其进行密码散列来形成中间组件。 然后使用中间部件形成第二签名部件，并且签名包括具有可见部分的第一和第二部件。 签名的验证将仅从消息的隐藏部分导出的第一组件与可见部分组合，并产生组合的散列。 所计算的散列与公开可用的信息一起使用以产生对应于隐藏部分的位串。

    METHOD TO CALCULATE SQUARE ROOTS FOR ELLIPTIC CURVE CRYPTOGRAPHY
    7.
    发明申请
    METHOD TO CALCULATE SQUARE ROOTS FOR ELLIPTIC CURVE CRYPTOGRAPHY 有权
    用于计算椭圆曲线图的平方根的方法

    公开(公告)号：US20140369492A1

    公开(公告)日：2014-12-18

    申请号：US13920426

    申请日：2013-06-18

    申请人： Certicom Corp.

    发明人： Robert John LAMBERT

    IPC分类号： H04L9/06

    CPC分类号： H04L9/3066 ,  G06F7/72 ,  G06F7/725

    摘要： A method is presented to compute square roots of finite field elements from the prime finite field of characteristic p over which points lie on a defined elliptic curve. Specifically, while performing point decompression of points that lie on a standardized elliptic curve over a prime finite field of characteristic 2224−296+1, the present method utilizes short Lucas sub-sequences to optimize the implementation of a modified version of Mueller's square root algorithm, to find the square root modulo of a prime number. The resulting method is at least twice as fast as standard methods employed for square root computations performed on elliptic curves.

    摘要翻译： 提出了一种从特征p的主有限域计算有限域元素的平方根的方法，其中点位于定义的椭圆曲线上。 具体来说，当在特征2224-296 + 1的主要有限域上执行位于标准化椭圆曲线上的点的点解压缩时，本方法利用短Lucas子序列来优化Mueller平方根算法的修改版本的实现 ，找到素数的平方根模。 所得到的方法至少是用于在椭圆曲线上进行的平方根计算的标准方法的两倍。