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1. 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。

2. 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。

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

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。

5. 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。

6. 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。

7. 发明授权

US08782400B2 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：US08782400B2
公开(公告)日：2014-07-15
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： H04L29/06 , G06F21/64
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。

8. 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。

9. 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。

10. 发明授权

US08588409B2 Custom static Diffie-Hellman groups 有权
标题翻译：自定义静态Diffie-Hellman组
公开(公告)号：US08588409B2
公开(公告)日：2013-11-19
申请号：US11272150
申请日：2005-11-14
申请人： Daniel R. L. Brown , Robert P. Gallant , Scott A. Vanstone
发明人： Daniel R. L. Brown , Robert P. Gallant , Scott A. Vanstone
IPC分类号： G06F21/00
CPC分类号： G06F7/72 , G06F7/724 , G06F7/725 , G06F2207/7204 , H04L9/002 , H04L9/0841 , H04L9/3066 , H04L2209/26
摘要： Methods for choosing groups for a static Diffie-Hellman key agreement protocol to inhibit active attacks by an adversary are provided. In mod p groups, an even h is chosen of value approximately ( 9/16)(log2n)2, values r and n are determined using sieving and primality testing on r and n, and a value t is found to compute p=tn+1 wherein p is prime. In elliptic curve groups defined over a binary filed, a random curve is chosen, the number of points on the curve is counted and this number is checked for value of 2n wherein n is prime and n−1 meets preferred criteria. In elliptic curve groups defined over a prime field of order q, a value n=hr+1 is computed, wherein n is prime and n−1 meets preferred criteria, and a complex multiplication method is applied on n to produce a value q and an elliptic curve E defined over q and having an order n.
摘要翻译：提供了用于选择静态Diffie-Hellman密钥协商协议以抑制对手的主动攻击的组的方法。在mod p组中，偶数h被选择为大约（9/16）（log2n）2的值，使用r和n上的筛选和原色度测试来确定值r和n，并且发现值t计算p = tn +1，其中p是素数。在二进制字段中定义的椭圆曲线组中，选择随机曲线，对曲线上的点数进行计数，并检查2n的值，其中n是素数，n-1符合优选标准。在序列q的质场上定义的椭圆曲线组中，计算值n = hr + 1，其中n是素数，n-1满足优选标准，并且在n上应用复数乘法以产生值q和在q上定义并具有n阶的椭圆曲线E.

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