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1. 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。

2. 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。

3. 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.

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. 发明申请

US20090100267A1 Signatures with confidential message recovery 有权
标题翻译：签名与保密信息恢复
公开(公告)号：US20090100267A1
公开(公告)日：2009-04-16
申请号：US12230799
申请日：2008-09-04
申请人： Daniel R. Brown , Matthew J. Campagna , Marinus Struik , Scott A. Vanstone
发明人： Daniel R. Brown , Matthew J. Campagna , Marinus Struik , Scott A. Vanstone
IPC分类号： H04L9/06 , H04L9/30
CPC分类号： H04L9/3066 , H04L9/3242 , H04L9/3252
摘要： A portion of the signed message in an ECPVS is kept truly confidential by dividing the message being signed into at least three parts, wherein one portion is visible, another portion is recoverable by any entity and carries the necessary redundancy for verification, and at least one additional portion is kept confidential. The additional portion is kept confidential by encrypting such portion using a key generated from information specific to that verifying entity. In this way, any entity with access to the signer's public key can verify the signature by checking for a specific characteristic, such as a certain amount of redundancy in the one recovered portion, but cannot recover the confidential portion, only the specific entity can do so. Message recovery is also provided in an elliptic curve signature using a modification of the well analyzed ECDSA signing equation instead of, e.g. the Schnorr equation used in traditional PV signature schemes.
摘要翻译：通过将被签名的消息划分成至少三个部分，其中一个部分是可见的，另一个部分可被任何实体恢复并且携带必要的冗余以用于验证，并且至少一个额外的部分保密。通过使用由该验证实体特有的信息生成的密钥加密这样的部分来将附加部分保密。以这种方式，任何访问签名者公钥的实体都可以通过检查一个特定的特征来验证签名，例如一个恢复的部分中的一定数量的冗余，但是不能恢复机密部分，只有特定的实体可以做所以。消息恢复还以椭圆曲线签名提供，使用经分析良好的ECDSA签名方案的修改，而不是例如。传统光伏签名方案中使用的Schnorr方程。

9. 发明授权

US09455832B2 Signatures with confidential message recovery 有权
公开(公告)号：US09455832B2
公开(公告)日：2016-09-27
申请号：US12230799
申请日：2008-09-04
申请人： Daniel R. Brown , Matthew J. Campagna , Marinus Struik , Scott A. Vanstone
发明人： Daniel R. Brown , Matthew J. Campagna , Marinus Struik , Scott A. Vanstone
IPC分类号： H04L9/30 , H04L9/32
CPC分类号： H04L9/3066 , H04L9/3242 , H04L9/3252
摘要： A portion of the signed message in an ECPVS is kept truly confidential by dividing the message being signed into at least three parts, wherein one portion is visible, another portion is recoverable by any entity and carries the necessary redundancy for verification, and at least one additional portion is kept confidential. The additional portion is kept confidential by encrypting such portion using a key generated from information specific to that verifying entity. In this way, any entity with access to the signer's public key can verify the signature by checking for a specific characteristic, such as a certain amount of redundancy in the one recovered portion, but cannot recover the confidential portion, only the specific entity can do so. Message recovery is also provided in an elliptic curve signature using a modification of the well analyzed ECDSA signing equation instead of, e.g. the Schnorr equation used in traditional PV signature schemes.

10. 发明授权

US08634559B2 Aggregate signature schemes 有权
标题翻译：总体签名方案
公开(公告)号：US08634559B2
公开(公告)日：2014-01-21
申请号：US13461586
申请日：2012-05-01
申请人： Daniel R. Brown , Scott A. Vanstone
发明人： Daniel R. Brown , Scott A. Vanstone
IPC分类号： H04K1/00 , G05B11/01 , G08C19/12
CPC分类号： H04L9/3066 , H04L9/3252 , H04L2209/805
摘要： An authenticated RFID system is provided that uses elliptic curve cryptography (ECC) to reduce the signature size and read/write times when compared to traditional public key implementations such as RSA. Either ECDSA or ECPVS can be used to reduce the signature size and ECPVS can be used to hide a portion of the RFID tag that contains sensitive product identifying information. As a result, smaller tags can be used or multiple signatures can be written at different stages in a manufacturing or supply chain. A key management system is used to distribute the verification keys and aggregate signature schemes are also provided for adding multiple signatures to the RFID tags, for example in a supply chain.
摘要翻译：提供了一种经过认证的RFID系统，与传统的公共密钥实现（如RSA）相比，使用椭圆曲线密码术（ECC）来减少签名大小和读/写时间。 ECDSA或ECPVS可以用于减小签名大小，并且ECPVS可用于隐藏包含敏感产品标识信息的RFID标签的一部分。因此，可以使用较小的标签，或者可以在制造或供应链中的不同阶段写入多个签名。密钥管理系统用于分发验证密钥，并且聚合签名方案也被提供用于向RFID标签添加多个签名，例如在供应链中。

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