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1. 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.

2. 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。

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。

6. 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。

7. 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。

8. 发明申请

US20120314855A1 Trapdoor One-Way Functions on Elliptic Curves and Their Application to Shorter Signatures and Asymmetric Encryption 有权
标题翻译：椭圆曲线上的Trapdoor单向函数及其对较短签名和不对称加密的应用
公开(公告)号：US20120314855A1
公开(公告)日：2012-12-13
申请号：US13495307
申请日：2012-06-13
申请人： Daniel R.L Brown , Robert P. Gallant , Scott A. Vanstone , Marinus Struik
发明人： Daniel R.L Brown , Robert P. Gallant , Scott A. Vanstone , Marinus Struik
IPC分类号： H04L9/28
CPC分类号： H04L63/0823 , G06F21/64 , H04L9/3066 , H04L9/3252
摘要： A new trapdoor one-way function is provided. In a general sense, some quadratic algebraic integer z is used. One then finds a curve E and a rational map defining [z] on E. The rational map [z] is the trapdoor one-way function. A judicious selection of z will ensure that [z] can be efficiently computed, that it is difficult to invert, that determination of [z] from the rational functions defined by [z] is difficult, and knowledge of z allows one to invert [z] on a certain set of elliptic curve points.
摘要翻译：提供了一个新的陷门单向功能。在一般意义上，使用一些二次代数整数z。然后找到曲线E和在E上定义[z]的有理图。有理图[z]是陷门单向函数。 z的明智选择将确保可以有效地计算[z]，难以反转，[z]定义的[z]的确定是困难的，而z的知识允许反转[ z]在一组椭圆曲线点上。

9. 发明申请

US20110060909A1 TRAPDOOR ONE-WAY FUNCTIONS ON ELLIPTIC CURVES AND THEIR APPLICATION TO SHORTER SIGNATURES AND ASYMMETRIC ENCRYPTION 有权
标题翻译：椭圆曲线上的TRAPDOOR单向函数及其应用于短信签名和不对称加密
公开(公告)号：US20110060909A1
公开(公告)日：2011-03-10
申请号：US12945234
申请日：2010-11-12
申请人： Daniel R.L. Brown , Robert P. Gallant , Scott A. Vanstone , Marinus Struik
发明人： Daniel R.L. Brown , Robert P. Gallant , Scott A. Vanstone , Marinus Struik
IPC分类号： H04L9/32 , H04L9/30
CPC分类号： H04L63/0823 , G06F21/64 , H04L9/3066 , H04L9/3252
摘要： The present invention provides a new trapdoor one-way function. In a general sense, some quadratic algebraic integer z is used. One then finds a curve E and a rational map defining [z] on E. The rational map [z] is the trapdoor one-way function. A judicious selection of z will ensure that [z] can be efficiently computed, that it is difficult to invert, that determination of [z] from the rational functions defined by [z] is difficult, and knowledge of z allows one to invert [z] on a certain set of elliptic curve points. Every rational map is a composition of a translation and an endomorphism. The most secure part of the rational map is the endomorphism as the translation is easy to invert. If the problem of inverting the endomorphism and thus [z] is as hard as the discrete logarithm problem in E, then the size of the cryptographic group can be smaller than the group used for RSA trapdoor one-way functions.
摘要翻译：本发明提供了一种新的陷门单向功能。在一般意义上，使用一些二次代数整数z。然后找到曲线E和在E上定义[z]的有理图。有理图[z]是陷门单向函数。 z的明智选择将确保可以有效地计算[z]，难以反转，[z]定义的[z]的确定是困难的，而z的知识允许反转[ z]在一组椭圆曲线点上。每一个合理的地图都是一个翻译和一个同化的组合。理性地图中最安全的部分是翻译易翻译的同化。如果反转内生的问题，因此[z]与E中的离散对数问题一样困难，则密码组的大小可以小于用于RSA陷门单向函数的组的大小。

10. 发明授权

US07844051B2 Trapdoor one-way functions on elliptic curves and their application to shorter signatures and asymmetric encryption 有权
标题翻译：椭圆曲线上的Trapdoor单向函数及其对较短签名和非对称加密的应用
公开(公告)号：US07844051B2
公开(公告)日：2010-11-30
申请号：US11272152
申请日：2005-11-14
申请人： Daniel R. L. Brown , Robert P. Gallant , Scott A. Vanstone , Marinus Struik
发明人： Daniel R. L. Brown , Robert P. Gallant , Scott A. Vanstone , Marinus Struik
IPC分类号： H04L9/30
CPC分类号： H04L63/0823 , G06F21/64 , H04L9/3066 , H04L9/3252
摘要： The present invention provides a new trapdoor one-way function. In a general sense, some quadratic algebraic integer z is used. One then finds a curve E and a rational map defining [z] on E. The rational map [z] is the trapdoor one-way function. A judicious selection of z will ensure that [z] can be efficiently computed, that it is difficult to invert, that determination of [z] from the rational functions defined by [z] is difficult, and knowledge of z allows one to invert [z] on a certain set of elliptic curve points. Every rational map is a composition of a translation and an endomorphism. The most secure part of the rational map is the endomorphism as the translation is easy to invert. If the problem of inverting the endomorphism and thus [z] is as hard as the discrete logarithm problem in E, then the size of the cryptographic group can be smaller than the group used for RSA trapdoor one-way functions.
摘要翻译：本发明提供了一种新的陷门单向功能。在一般意义上，使用一些二次代数整数z。然后找到曲线E和在E上定义[z]的有理图。有理图[z]是陷门单向函数。 z的明智选择将确保可以有效地计算[z]，难以反转，[z]定义的[z]的确定是困难的，而z的知识允许反转[ z]在一组椭圆曲线点上。每一个合理的地图都是一个翻译和一个同化的组合。理性地图中最安全的部分是翻译易翻译的同化。如果反转内生的问题，因此[z]与E中的离散对数问题一样困难，则密码组的大小可以小于用于RSA陷门单向函数的组的大小。

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