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1. 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。

2. 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.

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。

5. 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。

6. 发明申请

US20110268270A1 Method of Public Key Generation 有权
标题翻译：公钥生成方法
公开(公告)号：US20110268270A1
公开(公告)日：2011-11-03
申请号：US13181184
申请日：2011-07-12
申请人： Scott A. Vanstone , Ashok Vadekar , Robert J. Lambert , Robert P. Gallant , Daniel R. Brown , Alfred Menezes
发明人： Scott A. Vanstone , Ashok Vadekar , Robert J. Lambert , Robert P. Gallant , Daniel R. Brown , Alfred Menezes
IPC分类号： H04L9/00 , G06F7/58
CPC分类号： H04L9/0869 , H04L2209/26 , H04L2209/46
摘要： A potential bias in the generation of a private key is avoided by selecting the key and comparing it against the system parameters. If a predetermined condition is attained it is accepted. If not it is rejected and a new key is generated.
摘要翻译：通过选择密钥并将其与系统参数进行比较来避免私钥生成中的潜在偏差。如果达到预定条件，则被接受。如果不是，则被拒绝并生成新的密钥。

7. 发明授权

US07372961B2 Method of public key generation 有权
标题翻译：公钥生成方法
公开(公告)号：US07372961B2
公开(公告)日：2008-05-13
申请号：US10025924
申请日：2001-12-26
申请人： Scott A. Vanstone , Ashok Vadekar , Robert J. Lambert , Robert P. Gallant , Daniel R. Brown , Alfred Menezes
发明人： Scott A. Vanstone , Ashok Vadekar , Robert J. Lambert , Robert P. Gallant , Daniel R. Brown , Alfred Menezes
IPC分类号： H04L9/08 , G06F7/58
CPC分类号： H04L9/0869 , H04L2209/26 , H04L2209/46
摘要： A potential bias in the generation or a private key is avoided by selecting the key and comparing it against the system parameters. If a predetermined condition is attained it is accepted. If not it is rejected and a new key is generated.
摘要翻译：通过选择密钥并将其与系统参数进行比较来避免生成中的潜在偏差或私钥。如果达到预定条件，则被接受。如果不是，则被拒绝并生成新的密钥。

8. 发明授权

US06430690B1 Secure one-way authentication communication system 有权
标题翻译：安全单向认证通信系统
公开(公告)号：US06430690B1
公开(公告)日：2002-08-06
申请号：US09628045
申请日：2000-07-28
申请人： Scott A. Vanstone , Ashok V. Vadekar , Robert J. Lambert , Robert P. Gallant
发明人： Scott A. Vanstone , Ashok V. Vadekar , Robert J. Lambert , Robert P. Gallant
IPC分类号： G06F124
CPC分类号： G07F7/1008 , G06Q20/341 , G06Q20/40975 , H04L9/3263 , H04L9/3271 , H04L9/3273
摘要： A protocol for authenticating at least one of a pair of first and second correspondents C and T in a data communication system, the method comprising the steps or storing a public key in the first correspondent C; computing a shared secret by the second correspondent T incorporating the public key C; storing the shared secret in the first correspondent C: the second correspondent T generating a challenge value a; the first correspondent C transmitting to the second correspondent T information including the stored public key C; the second correspondent T computing a test shared secret from the received public key C; the first and second correspondents computing response signals using the challenge value z and the shared secret in a one-way function fr; and the first correspondent C transmitting the computed response signal to the second correspondent T whereby the second correspondent verifies the first correspondent.
摘要翻译：一种用于在数据通信系统中验证一对第一和第二通信对象C和T中的至少一个的协议，所述方法包括以下步骤或在第一对应C中存储公共密钥; 由包含公共密钥C的第二记者T计算共享秘密; 将共享秘密存储在第一通信对象C中：生成询问值a的第二通信对象T; 第一通讯员C发送到包括存储的公开密钥C的第二通讯员T信息; 第二通讯员T从所接收的公钥C计算测试共享秘密; 第一和第二记者使用挑战值z和单向函数fr中的共享秘密来计算响应信号; 并且第一通信对象C将计算出的响应信号发送到第二通信对象T，由此第二对方验证第一通信对方。

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. 发明授权

US06337909B1 Generation of session keys for El Gamal-like protocols from low hamming weight integers 失效
标题翻译：从低汉明重量整数生成El Gamal样协议的会话密钥
公开(公告)号：US06337909B1
公开(公告)日：2002-01-08
申请号：US08948796
申请日：1997-10-10
申请人： Scott A. Vanstone , Donald B. Johnson , Robert J. Lambert , Ronald C. Mullin
发明人： Scott A. Vanstone , Donald B. Johnson , Robert J. Lambert , Ronald C. Mullin
IPC分类号： H04L928
CPC分类号： H04L9/3013 , G06F7/725 , H04L9/3066
摘要： The public key, either short term “session” key or long term key, is generated by combining a pair of components. A first component is obtained by utilizing an integer with a relatively low Hamming weight as an exponent to facilitate exponentiation. The second component is a precomputed secret value that is of the form resulting from the exponentiation of the generator of the group element by an integer that has the requisite Hamming weight. The two components are combined to provide the public key and the two exponents combined to provide the corresponding private key.
摘要翻译：通过组合一对组件来生成公钥，短期“会话”密钥或长期密钥。通过利用具有相对较低的汉明重量的整数作为指数来获得第一分量以促成取幂。第二个组件是预先计算的秘密值，其形式是由组元素的生成器乘以具有所需汉明权重的整数而产生的。组合两个组件以提供公钥和两个指数组合以提供相应的私钥。

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