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公开(公告)号：US20120072975A1
公开(公告)日：2012-03-22
申请号：US13052967
申请日：2011-03-21
IPC分类号： H04L9/32
CPC分类号： G06F21/31 , G06F2221/2103 , G06F2221/2111 , G06Q20/382
摘要： An authentication system is provided. The authentication system comprises a first component configured to obtain information specific to an individual, a second component configured to dynamically formulate at least one challenge question based on the information, a third component configured to cause the at least one challenge question to be presented on a device when the device is used to perform an act that involves authentication, and a fourth component configured to judge authenticity based on an answer to the at least one challenge question.
摘要翻译： 提供了认证系统。 所述认证系统包括被配置为获得特定于个人的信息的第一组件，被配置为基于所述信息动态地制定至少一个挑战问题的第二组件，被配置为使所述至少一个挑战问题在 该设备用于执行涉及认证的动作时，以及第四组件，被配置为基于对所述至少一个挑战问题的答案来判断真实性。
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公开(公告)号：US20130064367A1
公开(公告)日：2013-03-14
申请号：US13620206
申请日：2012-09-14
申请人： Marinus Struik , Daniel R. Brown , Scott A. Vanstone , Robert P. Gallant , Adrian Antipa , Robert J. Lambert
发明人： Marinus Struik , Daniel R. Brown , Scott A. Vanstone , Robert P. Gallant , Adrian Antipa , Robert J. Lambert
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 so that v=w/z. The verification equality R=uG+vQ may then be computed as −zR+(uz mod n) G+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，代表点R的值对应于其他两个点uG和vG的和的验证是通过导出比特长度减小的整数w，z获得的，并且使得v = w / z。 然后，验证等式R = uG + vQ可以被计算为-zR +（uz mod n）G + wQ = 0，其中z和w为减少的比特长度。 这在数字签名验证中是有益的，其中可以实现增加的验证。
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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
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。
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公开(公告)号：US08788827B2
公开(公告)日：2014-07-22
申请号：US13620206
申请日：2012-09-14
申请人： Marinus Struik , Daniel R. Brown , Scott A. Vanstone , Robert P. Gallant , Adrian Antipa , Robert J. Lambert
发明人： Marinus Struik , Daniel R. Brown , Scott A. Vanstone , Robert P. Gallant , Adrian Antipa , Robert J. Lambert
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 so that v=w/z. The verification equality R=uG+vQ may then be computed as −zR+(uz mod n) G+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，代表点R的值对应于其他两个点uG和vG的和的验证是通过导出比特长度减小的整数w，z获得的，并且使得v = w / z。 然后，验证等式R = uG + vQ可以被计算为-zR +（uz mod n）G + wQ = 0，其中z和w的比特长度减小。 这在数字签名验证中是有益的，其中可以实现增加的验证。
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公开(公告)号：US09503267B2
公开(公告)日：2016-11-22
申请号：US14368737
申请日：2011-12-28
CPC分类号： H04L9/3252 , G06F21/10 , G06F21/64 , G06F21/72 , H04L9/3066
摘要： Methods, systems, and computer programs for generating a digital signature are disclosed. In some aspects, a symmetric key is accessed. The symmetric key is based on an ephemeral public key. The ephemeral public key is associated with an ephemeral private key. A ciphertext is generated based on the symmetric key and a message. An input value is obtained based on the ciphertext independent of a hash function. A digital signature is generated from the ephemeral private key, the input value, and a long term private key.
摘要翻译： 公开了用于生成数字签名的方法，系统和计算机程序。 在一些方面，访问对称密钥。 对称密钥是基于短暂的公开密钥。 短暂的公钥与短暂的私钥相关联。 基于对称密钥和消息生成密文。 基于独立于散列函数的密文获得输入值。 从临时私钥，输入值和长期私钥生成数字签名。
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公开(公告)号：US08806197B2
公开(公告)日：2014-08-12
申请号：US13478288
申请日：2012-05-23
申请人： Marinus Struik , Daniel R. Brown , Scott A. Vanstone , Robert P. Gallant , Adrian Antipa , Robert J. Lambert
发明人： Marinus Struik , Daniel R. Brown , Scott A. Vanstone , Robert P. Gallant , Adrian Antipa , Robert J. Lambert
IPC分类号： H04L29/06
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 so that v=w/z. The verification equality R=uG+vQ may then be computed as −zR+(uz mod n) G+wQ=O with z and w of reduced bit length. This is beneficial in digital signature verification where increased verification can be attained.
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公开(公告)号：US08284930B2
公开(公告)日：2012-10-09
申请号：US13177286
申请日：2011-07-06
申请人： Adrian Antipa , Yuri Poeluev
发明人： Adrian Antipa , Yuri Poeluev
CPC分类号： G06F7/725 , H04L9/3066 , H04L2209/20
摘要： In computing point multiples in elliptic curve schemes (e.g. kP and sQ) separately using, for example, Montgomery's method for the purpose of combining kP+sQ, several operations are repeated in computing kP and sQ individually, that could be executed at the same time. A simultaneous scalar multiplication method is provided that reduces the overall number of doubling and addition operations thereby providing an efficient method for multiple scalar multiplication. The elements in the pairs for P and Q method are combined into a single pair, and the bits in k and s are evaluated at each step as bit pairs. When the bits in k and s are equal, only one doubling operation and one addition operation are needed to compute the current pair, and when the bits in k and s are not equal, only one doubling operation is needed and two addition operations.
摘要翻译： 在椭圆曲线方案（例如kP和sQ）的计算点倍数中，使用例如用于组合kP + sQ的蒙哥马利方法，分别在计算kP和sQ时重复几个操作，这可以同时执行 。 提供一种同时的标量乘法方法，其减少加倍和加法运算的总数，从而提供用于多标量乘法的有效方法。 用于P和Q方法的对中的元素被组合成单个对，并且在每个步骤中以比特对来评估k和s中的比特。 当k和s中的比特相等时，只需要一个加倍运算和一个加法运算来计算当前对，当k和s中的比特不相等时，只需要一个加倍运算和两个加法运算。
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公开(公告)号：US20110261956A1
公开(公告)日：2011-10-27
申请号：US13177286
申请日：2011-07-06
申请人： Adrian Antipa , Yuri Poeluev
发明人： Adrian Antipa , Yuri Poeluev
IPC分类号： H04L9/28
CPC分类号： G06F7/725 , H04L9/3066 , H04L2209/20
摘要： In computing point multiples in elliptic curve schemes (e.g. kP and sQ) separately using, for example, Montgomery's method for the purpose of combining kP+sQ, several operations are repeated in computing kP and sQ individually, that could be executed at the same time. A simultaneous scalar multiplication method is provided that reduces the overall number of doubling and addition operations thereby providing an efficient method for multiple scalar multiplication. The elements in the pairs for P and Q method are combined into a single pair, and the bits in k and s are evaluated at each step as bit pairs. When the bits in k and s are equal, only one doubling operation and one addition operation are needed to compute the current pair, and when the bits in k and s are not equal, only one doubling operation is needed and two addition operations.
摘要翻译： 在椭圆曲线方案（例如kP和sQ）的计算点倍数中，使用例如用于组合kP + sQ的蒙哥马利方法，分别在计算kP和sQ时重复几个操作，这可以同时执行 。 提供一种同时的标量乘法方法，其减少加倍和加法运算的总数，从而提供用于多标量乘法的有效方法。 用于P和Q方法的对中的元素被组合成单个对，并且在每个步骤中以比特对来评估k和s中的比特。 当k和s中的比特相等时，只需要一个加倍运算和一个加法运算来计算当前对，当k和s中的比特不相等时，只需要一个加倍运算和两个加法运算。
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公开(公告)号：US08045705B2
公开(公告)日：2011-10-25
申请号：US11556531
申请日：2006-11-03
申请人： Adrian Antipa , Yuri Poeluev
发明人： Adrian Antipa , Yuri Poeluev
CPC分类号： G06F7/725 , H04L9/3066 , H04L2209/20
摘要： In computing point multiples in elliptic curve schemes (e.g. kP and sQ) separately using, for example, Montgomery's method for the purpose of combining kP+sQ several operations are repeated in computing kP and sQ individually, that could be executed at the same time. A simultaneous scalar multiplication method is provided that reduces the overall number of doubling and addition operations thereby providing an efficient method for multiple scalar multiplication. The elements in the pairs for P and Q method are combined into a single pair, and the bits in k and s are evaluated at each step as bit pairs. When the bits in k and s are equal, only one doubling operation and one addition operation are needed to compute the current pair, and when the bits in k and s are not equal, only one doubling operation is needed and two addition operations.
摘要翻译： 在椭圆曲线方案（例如，kP和sQ）中，使用例如蒙哥马利方法，为了组合kP + sQ而分开地计算点椭圆曲线方案（例如kP和sQ）中的多个像素，可以在同时计算kP和sQ时重复几个操作。 提供一种同时的标量乘法方法，其减少加倍和加法运算的总数，从而提供用于多标量乘法的有效方法。 用于P和Q方法的对中的元素被组合成单个对，并且在每个步骤中以比特对来评估k和s中的比特。 当k和s中的比特相等时，只需要一个加倍运算和一个加法运算来计算当前对，当k和s中的比特不相等时，只需要一个加倍运算和两个加法运算。
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公开(公告)号：US07177423B2
公开(公告)日：2007-02-13
申请号：US10863162
申请日：2004-06-09
申请人： Adrian Antipa
发明人： Adrian Antipa
IPC分类号： H04L9/00
CPC分类号： H04L9/3247 , H04L9/005 , H04L9/302 , H04L2209/12 , H04L2209/20
摘要： A method of computing an exponent of a message m in an RSA cryptosystem having a private key d, a public key e and system parameters p, q where p and q are primes and ed=1 mod (p−1) (q−1). The method comprises the steps of obtaining a value r, and exponentiating the value r to the power e to obtain an exponent re mod p, combining said exponent re with the message m to obtain a combined value re m and mod p; selecting a value s and obtaining a difference (d−s), exponentiating the combined value with said difference to obtain an intermediate exponent (rem)d−s, multiplying the intermediate exponent by a value ms to obtain a resultant value equivalent to r1−es md and multiplying the resultant value by a value corresponding to r1−es to obtain an exponent corresponding to md mod p.
摘要翻译： 一种在具有私钥d，公钥e和系统参数p，q的RSA密码系统中计算消息m的指数的方法，其中p和q是素数，并且ed = 1 mod（p-1）（q-1 ）。 该方法包括以下步骤：获得值r，并且将值r与幂e进行取幂以获得指数r∈mod mod mod p p p p p the the the the the the the the the the the the the 消息m以获得组合值r∈m和mod p; 选择值s并获得差值（ds），将所述组合值与所述差值进行指数，以获得中间指数（r m），将中间指数乘以 得到相当于r1-es的结果值的值m S，并将结果值乘以对应于r < SUP> 1-es 以获得对应于mdd mod p的指数。
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