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1. 发明申请

US20070064932A1 Accelerated verification of digital signatures and public keys 有权
标题翻译：加快验证数字签名和公钥
公开(公告)号：US20070064932A1
公开(公告)日：2007-03-22
申请号：US11333296
申请日：2006-01-18
申请人： Marinus Struik , Daniel Brown , Scott Vanstone , Robert Gallant , Adrian Antipa , Robert Lambert
发明人： Marinus Struik , Daniel Brown , Scott Vanstone , Robert Gallant , Adrian Antipa , Robert Lambert
IPC分类号： H04L9/30
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。

2. 发明授权

US06782100B1 Accelerated finite field operations on an elliptic curve 有权
标题翻译：加速椭圆曲线上的有限域运算
公开(公告)号：US06782100B1
公开(公告)日：2004-08-24
申请号：US09677785
申请日：2000-10-02
申请人： Scott Vanstone , Ronald Mullin , Adrian Antipa , Robert Gallant
发明人： Scott Vanstone , Ronald Mullin , Adrian Antipa , Robert Gallant
IPC分类号： H04L930
CPC分类号： G06F7/725 , H04L9/3066 , H04L9/3252
摘要： A method for multiplication of a point P on elliptic curve E by a value k in order to derive a point kP comprises the steps of representing the number k as vector of binary digits stored in a register and forming a sequence of point pairs (P1, P2) wherein the point pairs differed most by P and wherein the successive series of point pairs are selected either by computing (2mP,(2m+1)P) from (mP,(m+1)P) or ((2m+1)P,(2m+2)P) from (mP,(m+1)P). The computations may be performed without using the y-coordinate of the points during the computation while allowing the y-coordinate to be extracted at the end of the computations, thus, avoiding the use of inversion operations during the computation and therefore, speeding up the cryptographic processor functions. A method is also disclosed for accelerating signature verification between two parties.
摘要翻译：用于将椭圆曲线E上的点P乘以值k以便导出点kP的方法包括将数字k表示为存储在寄存器中的二进制数字的向量的步骤，并形成点对序列（P1， P2），其中点对最差为P，并且其中通过从（mP，（m + 1）P）或（（2m + 1）P）计算（2mP，（2m + 1）P））P，（2m + 2）P）（mP，（m + 1）P）。可以在计算期间不使用点的y坐标来执行计算，同时允许在计算结束时提取y坐标，从而避免在计算期间使用反转操作，因此加速加密处理器功能。还公开了一种加速双方签名验证的方法。

3. 发明申请

US20130064367A1 ACCELERATED VERIFICATION OF DIGITAL SIGNATURES AND PUBLIC KEYS 有权
标题翻译：数字签名和公钥的加速验证
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
IPC分类号： H04L9/00 , H04L9/28
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。

4. 发明授权

US08788827B2 Accelerated verification of digital signatures and public keys 有权
标题翻译：加快验证数字签名和公钥
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
IPC分类号： H04L29/06 , H04L9/30
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。

5. 发明授权

US08806197B2 Accelerated verification of digital signatures and public keys 有权
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.

6. 发明申请

US20120230494A1 Accelerated Verification of Digital Signatures and Public Keys 有权
标题翻译：加速验证数字签名和公钥
公开(公告)号：US20120230494A1
公开(公告)日：2012-09-13
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： H04L9/08
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。

7. 发明授权

US08204232B2 Accelerated verification of digital signatures and public keys 有权
标题翻译：加快验证数字签名和公钥
公开(公告)号：US08204232B2
公开(公告)日：2012-06-19
申请号：US11333296
申请日：2006-01-18
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： H04L9/08
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。

8. 发明申请

US20070217601A1 METHOD AND APPARATUS FOR ELLIPTIC CURVE SCALAR MULTIPLICATION 有权
标题翻译：用于ELLIPTIC CURVE SCALAR MULTIPLICATION的方法和装置
公开(公告)号：US20070217601A1
公开(公告)日：2007-09-20
申请号：US11687773
申请日：2007-03-19
申请人： Robert Lambert , Ashok Vadekar , Adrian Antipa
发明人： Robert Lambert , Ashok Vadekar , Adrian Antipa
IPC分类号： H04L9/28
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。

9. 发明授权

US07412062B2 Method and apparatus for elliptic curve scalar multiplication 有权
标题翻译：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。

10. 发明申请

US20120072975A1 Circumstantial Authentication 审中-公开
标题翻译：环境认证
公开(公告)号：US20120072975A1
公开(公告)日：2012-03-22
申请号：US13052967
申请日：2011-03-21
申请人： Christopher Labrador , Adrian Antipa , Russ F. Marsden
发明人： Christopher Labrador , Adrian Antipa , Russ F. Marsden
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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