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1. 发明授权

US08300807B2 Computing isogenies between genus-2 curves for cryptography 有权
标题翻译：计算加密的第2类曲线之间的等值线
公开(公告)号：US08300807B2
公开(公告)日：2012-10-30
申请号：US12350222
申请日：2009-01-07
申请人： Reinier M. Broker , Kristin E. Lauter , David Gruenewald
发明人： Reinier M. Broker , Kristin E. Lauter , David Gruenewald
IPC分类号： H04L9/00
CPC分类号： H04L9/3006
摘要： This cryptographic curve generation technique provides a faster way of constructing a genus 2 curve. The technique provides a procedure to compute isogenies between genus 2 curves over finite fields. Instead of looping over possible roots, as is typically done when solving Igusa class polynomials, the technique only finds one root and then applies the isogenies to find the others. The technique computes a set of polynomials that define all isogenies. To do this, for a given root of an Igusa class polynomial over a finite field, the technique computes a value of a small modular function ƒ. To the value of this function ƒ, the technique applies an isogeny to find an isogenous ƒ-value. The technique then transforms the ƒ-value back into an Igusa value. Once the Igusa class polynomials are solved they can be used to generate a genus 2 curve which can be used in cryptographic applications.
摘要翻译：这种加密曲线生成技术提供了构建第2类曲线的更快速的方法。该技术提供了一种在有限域上计算第2类曲线之间的等值线的过程。而不是循环可能的根，如通常在解决Igusa类多项式时完成的，该技术只找到一个根，然后应用等基因来找到其他根。该技术计算一组定义所有等代的多项式。为了做到这一点，对于有限域上的Igusa类多项式的给定根，该技术计算小的模块函数ƒ的值。对于此函数ƒ的值，该技术应用等值线来找到一个均匀的ƒ值。然后，该技术将ƒ值转换为Igusa值。一旦解决了Igusa类多项式，就可以使用它们来生成可用于密码应用的第2类曲线。

2. 发明申请

US20100172491A1 Computing Isogenies Between Genus-2 Curves for Cryptography 有权
标题翻译：计算密码学二级曲线之间的等代
公开(公告)号：US20100172491A1
公开(公告)日：2010-07-08
申请号：US12350222
申请日：2009-01-07
申请人： Reinier M. Broker , Kristin E. Lauter , David Gruenewald
发明人： Reinier M. Broker , Kristin E. Lauter , David Gruenewald
IPC分类号： H04L9/28
CPC分类号： H04L9/3006
摘要： This cryptographic curve generation technique provides a faster way of constructing a genus 2 curve. The technique provides a procedure to compute isogenies between genus 2 curves over finite fields. Instead of looping over possible roots, as is typically done when solving Igusa class polynomials, the technique only finds one root and then applies the isogenies to find the others. The technique computes a set of polynomials that define all isogenies. To do this, for a given root of an Igusa class polynomial over a finite field, the technique computes a value of a small modular function ƒ. To the value of this function ƒ, the technique applies an isogeny to find an isogenous ƒ-value. The technique then transforms the ƒ-value back into an Igusa value. Once the Igusa class polynomials are solved they can be used to generate a genus 2 curve which can be used in cryptographic applications.
摘要翻译：这种加密曲线生成技术提供了构建第2类曲线的更快速的方法。该技术提供了一种在有限域上计算第2类曲线之间的等值线的过程。而不是循环可能的根，如通常在解决Igusa类多项式时完成的，该技术只找到一个根，然后应用等基因来找到其他根。该技术计算一组定义所有等代的多项式。为了做到这一点，对于有限域上的Igusa类多项式的给定根，该技术计算小的模块函数ƒ的值。对于此函数ƒ的值，该技术应用等值线来找到一个均匀的ƒ值。然后，该技术将ƒ值转换为Igusa值。一旦解决了Igusa类多项式，就可以使用它们来生成可用于密码应用的第2类曲线。

3. 发明申请

US20100082992A1 Cryptographic Applications of Efficiently Evaluating Large Degree Isogenies 有权
标题翻译：有效评估大型同位素的密码学应用
公开(公告)号：US20100082992A1
公开(公告)日：2010-04-01
申请号：US12242801
申请日：2008-09-30
申请人： Reinier M. Broker , Denis X. Charles , Kristin E. Lauter
发明人： Reinier M. Broker , Denis X. Charles , Kristin E. Lauter
IPC分类号： H04L9/30 , H04L9/06
CPC分类号： H04L9/3073 , H04L9/3247 , H04L2209/60 , H04L2209/80
摘要： Techniques are disclosed for representing and evaluating large prime degree isogenies for use in cryptographic signature and encryption schemes. An isogeny of prime degree 1 may be represented as an ideal in the form (1, A*alpha+B), where 1 comprises the degree of a prime number, the prime number is split into integers a and b, and alpha is a known endomorphism. For a given degree 1, integers a and b define a unique isogeny, allowing the isogeny to be stored with 3 log(1) bits of information. Techniques are also disclosed to evaluate the isogeny at a given point by decomposing the isogeny into an integer and a plurality of smaller degree isogenies, evaluating the smaller degree isogenies at the point with traditional means, and multiplying the results of the evaluations together and with the integer.
摘要翻译：公开了用于表示和评估用于加密签名和加密方案的大质量等值基因的技术。素数1的均匀性可以表示为形式（1，A *α+ B）的理想，其中1包含质数的程度，素数被分解为整数a和b，而α是已知的同态对于给定的程度1，整数a和b定义了一个独特的等同原子，允许使用3个（1）位信息存储等值原理。还公开了通过将均质分解成整数和多个较小程度的同基物质来评估给定点的同位素的技术，以传统方法评估较小程度的同基因，并将评估结果与整数。

4. 发明授权

US08250367B2 Cryptographic applications of efficiently evaluating large degree isogenies 有权
标题翻译：有效评估大规模同位素的密码学应用
公开(公告)号：US08250367B2
公开(公告)日：2012-08-21
申请号：US12242801
申请日：2008-09-30
申请人： Reinier M. Broker , Denis X Charles , Kristin E. Lauter
发明人： Reinier M. Broker , Denis X Charles , Kristin E. Lauter
IPC分类号： H04L9/30
CPC分类号： H04L9/3073 , H04L9/3247 , H04L2209/60 , H04L2209/80
摘要： Techniques are disclosed for representing and evaluating large prime degree isogenies for use in cryptographic signature and encryption schemes. An isogeny of prime degree 1 may be represented as an ideal in the form (1, A*alpha+B), where 1 comprises the degree of a prime number, the prime number is split into integers a and b, and alpha is a known endomorphism. For a given degree 1, integers a and b define a unique isogeny, allowing the isogeny to be stored with 3 log(1) bits of information. Techniques are also disclosed to evaluate the isogeny at a given point by decomposing the isogeny into an integer and a plurality of smaller degree isogenies, evaluating the smaller degree isogenies at the point with traditional means, and multiplying the results of the evaluations together and with the integer.
摘要翻译：公开了用于表示和评估用于加密签名和加密方案的大质量等值基因的技术。素数1的均匀性可以表示为形式（1，A *α+ B）的理想，其中1包含质数的程度，素数被分解为整数a和b，而α是已知的同态对于给定的程度1，整数a和b定义了一个独特的等同原子，允许使用3个（1）位信息存储等值原理。还公开了通过将均质分解成整数和多个较小程度的同基物质来评估给定点的同位素的技术，以传统方法评估较小程度的同基性，并将评估结果与整数。

5. 发明授权

US08180047B2 Trapdoor pairings 失效
标题翻译： Trapdoor配对
公开(公告)号：US08180047B2
公开(公告)日：2012-05-15
申请号：US11275560
申请日：2006-01-13
申请人： Kristin E. Lauter , Denis Charles , Anton Mityagin
发明人： Kristin E. Lauter , Denis Charles , Anton Mityagin
IPC分类号： H04L9/00
CPC分类号： H04L9/3073
摘要： Systems and methods are described for trapdoor pairing. In one implementation, a trapdoor pairing is a cryptographic primitive generated by determining a bilinear pairing between an elliptic curve group and another group and selecting a parameter of the bilinear pairing, such as a group order or an isogeny between curves, to be a key for generating and evaluating the bilinear pairing. Trapdoor pairing allows construction of a group in which the Decisional Diffie-Hellman (DDH) problem is computationally infeasible given only the description of the group, but is easy given the secret key. Exemplary trapdoor pairing constructions have general applicability to cryptography and also lend themselves more specifically to certain special practical implementations, such as public key cryptography and certificate authority infrastructures.
摘要翻译：描述了用于陷门配对的系统和方法。在一个实现中，陷门配对是通过确定椭圆曲线组和另一组之间的双线性配对并且选择双线性配对的参数（诸如曲线之间的组次序或等值线）来生成的密码原语作为关键生成和评估双线性配对。陷阱配对允许建立一个组，其中决策Diffie-Hellman（DDH）问题在计算上是不可行的，只给出该组的描述，但是很容易给出秘密密钥。示例性的门锁配对结构具有对密码学的一般适用性，并且还更具体地涉及某些特殊的实际实现，例如公共密钥加密和证书颁发机构的基础设施。

6. 发明申请

US20110145198A1 Contextual and Semantic Differential Backup 有权
标题翻译：语境和语义差异备份
公开(公告)号：US20110145198A1
公开(公告)日：2011-06-16
申请号：US12639430
申请日：2009-12-16
申请人： Mathew J. Dickson , Samuel J. McKelvie , David A. Nichols , John D. Mehr , Kristin E. Lauter , Elissa E.S. Murphy
发明人： Mathew J. Dickson , Samuel J. McKelvie , David A. Nichols , John D. Mehr , Kristin E. Lauter , Elissa E.S. Murphy
IPC分类号： G06F17/30
CPC分类号： G06F17/3023
摘要： A backup system that utilizes contextual and semantic concepts is described. The backup system provides for the ability to create a version changes log for listing and tracking all the changes in the different versions of the file. The version changes log creates a contextual description around the changes, deletions and additions. The semantic concept log is created from the version changes log to create a log of all of the semantic concepts associated with each change. A visualization builder then creates visualizations that can be used by the user to search for changes, deletions and additions whether in a text file or an image file.
摘要翻译：描述了利用上下文和语义概念的备份系统。备份系统提供创建版本更改日志的功能，以列出和跟踪文件不同版本中的所有更改。版本更改日志创建一个关于更改，删除和添加的上下文描述。语义概念日志是从版本更改日志创建的，以创建与每个更改相关联的所有语义概念的日志。然后，可视化构建器创建可视化，用户可以使用这些可视化来搜索文本文件或图像文件中的更改，删除和添加。

7. 发明授权

US07907726B2 Pseudorandom number generation with expander graphs 有权
标题翻译：具有扩展器图的伪随机数生成
公开(公告)号：US07907726B2
公开(公告)日：2011-03-15
申请号：US11275629
申请日：2006-01-19
申请人： Kristin E. Lauter , Denis X Charles , Eyal Zvi Goren
发明人： Kristin E. Lauter , Denis X Charles , Eyal Zvi Goren
IPC分类号： G06F7/58
CPC分类号： G06F7/582 , H04L9/0662
摘要： Pseudorandom numbers may be generated from input seeds using expander graphs. Expander graphs are a collection of vertices that are interconnected via edges. Generally, a walk around an expander graph is determined responsive to an input seed, and a pseudorandom number is produced based on vertex names. Specifically, a next edge, which is one of multiple edges emanating from a current vertex, is selected responsive to an extracted seed chunk. The next edge is traversed to reach a next vertex. The name of the next vertex is ascertained and used as a portion of the pseudorandom number being produced by the walk around the expander graph.
摘要翻译：可以使用扩展器图从输入种子生成伪随机数。扩展器图是通过边缘互连的顶点的集合。通常，响应于输入种子确定围绕扩展器图形的步行，并且基于顶点名称产生伪随机数。具体地，响应于提取的种子块选择作为从当前顶点发出的多个边缘之一的下一个边缘。遍历下一个边以到达下一个顶点。确定下一个顶点的名称，并将其用作由扩展器图形围绕生成的伪随机数的一部分。

8. 发明授权

US07885406B2 Computing endomorphism rings of Abelian surfaces over finite fields 失效
标题翻译：计算有限域中阿贝尔面的同态环
公开(公告)号：US07885406B2
公开(公告)日：2011-02-08
申请号：US11548016
申请日：2006-10-10
申请人： Kristin E. Lauter , David Freeman
发明人： Kristin E. Lauter , David Freeman
IPC分类号： H04L9/00
CPC分类号： G06F7/724
摘要： Computing endomorphism rings of Abelian surfaces over finite fields is described. In one aspect, an endomorphism ring of an Abelian surface over a finite field is probabilistically computed. A genus-two curve is generated based on the probabilistically determined endomorphism ring. The genus-2 curve is used for encryption and decryption operations and a cryptosystem.
摘要翻译：描述了在有限域上计算阿贝利面的同态环。在一个方面，概率地计算有限域上的阿贝尔表面的同态环。基于概率确定的同胚环产生属二曲线。第2类曲线用于加密和解密操作以及密码系统。

9. 发明授权

US07729494B2 Squared Weil and Tate pairing techniques for use with elliptic curves 有权
标题翻译：用于椭圆曲线的平方魏和泰特配对技术
公开(公告)号：US07729494B2
公开(公告)日：2010-06-01
申请号：US11942618
申请日：2007-11-19
申请人： Anne Kirsten Eisentraeger , Kristin E. Lauter , Peter L. Montgomery
发明人： Anne Kirsten Eisentraeger , Kristin E. Lauter , Peter L. Montgomery
IPC分类号： H04K1/00
CPC分类号： G06F7/725 , H04L9/3073 , H04L9/3247 , H04L2209/38 , H04L2209/80
摘要： Methods and apparati are provided for use in determining “Squared Weil pairings” and/or “Squared Tate Pairing” based on an elliptic curve, for example, and which are then used to support cryptographic processing of selected information. Significant improvements are provided in computing efficiency over the conventional implementation of the Weil and Tate pairings. The resulting Squared Weil and/or Tate pairings can be substituted for conventional Weil or Tate pairings in a variety of applications.
摘要翻译：提供了方法和装置，用于例如基于椭圆曲线确定“平方魏配对”和/或“平方ate对配对”，然后用于支持所选信息的加密处理。与传统的Weil和Tate配对相比，计算效率得到了显着改善。所得到的平方魏和/或泰特对可以替代常规的Weil或Tate配对在各种应用中。

10. 发明申请

US20090290714A1 Protocol for Verifying Integrity of Remote Data 审中-公开
标题翻译：验证远程数据完整性的协议
公开(公告)号：US20090290714A1
公开(公告)日：2009-11-26
申请号：US12123688
申请日：2008-05-20
申请人： Denis X. Charles , Kristin E. Lauter , Anton Mityagin
发明人： Denis X. Charles , Kristin E. Lauter , Anton Mityagin
IPC分类号： H04L9/08
CPC分类号： H04L63/123 , G06F21/645 , H04L9/3242 , H04L9/3271 , H04L67/104
摘要： An exemplary method for verifying the integrity of remotely stored data includes providing a key; providing a fingerprint, the fingerprint generated using the key in a keyed cryptographic hash function as applied to data of known integrity; sending the key to a remote storage location that stores a copy of the data of known integrity; receiving a fingerprint from the remote storage location, the fingerprint generated using the key in a keyed cryptographic hash function as applied to the remotely stored copy of the data; and verifying the integrity of the remotely stored copy of the data based at least in part on comparing the provided fingerprint to the received fingerprint. Other exemplary methods, systems, etc., are also disclosed.
摘要翻译：用于验证远程存储数据的完整性的示例性方法包括提供密钥; 提供指纹，使用密钥在密钥加密散列函数中生成的指纹，以应用于已知完整性的数据; 将密钥发送到存储已知完整性数据的副本的远程存储位置; 从所述远程存储位置接收指纹，使用所述密钥在密钥密码散列函数中生成的指纹应用于远程存储的数据副本; 以及至少部分地基于将所提供的指纹与所接收的指纹进行比较来验证远程存储的数据副本的完整性。还公开了其它示例性方法，系统等。

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