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公开(公告)号：US20090287756A1
公开(公告)日：2009-11-19
申请号：US12510991
申请日：2009-07-28
IPC分类号： G06F17/17
CPC分类号： G06F7/725
摘要： Systems and methods for computing modular polynomials modulo large primes are described. In one aspect, the systems and methods generate l-isogenous elliptic curves. A modular polynomial modulo a large prime p is then computed as a function of l-isogenous elliptic curves modulo p.
摘要翻译： 描述了用于计算模多项式模数大素数的系统和方法。 在一个方面，系统和方法产生l个等式的椭圆曲线。 然后，模数为大素数p的模多项式作为模p的l-均质椭圆曲线的函数被计算。
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公开(公告)号：US07382876B2
公开(公告)日：2008-06-03
申请号：US11263701
申请日：2005-11-01
IPC分类号： H04L9/28
CPC分类号： H04L9/0643 , G06F17/30949
摘要： Hash function constructions from expander graphs are described. In one aspect, an expander graph is walked to compute a hash function. The expander graph is walked using respective subsets of an input message. A label of a last vertex walked is an output of the hash function.
摘要翻译： 描述了来自扩展器图形的散列函数结构。 在一个方面，走扩展器图来计算哈希函数。 使用输入消息的相应子集来走扩展器图。 走过的最后一个顶点的标签是散列函数的输出。
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公开(公告)号：US08259932B2
公开(公告)日：2012-09-04
申请号：US12510991
申请日：2009-07-28
CPC分类号： G06F7/725
摘要： Systems and methods for computing modular polynomials modulo large primes are described. In one aspect, the systems and methods generate l-isogenous elliptic curves. A modular polynomial modulo a large prime p is then computed as a function of l-isogenous elliptic curves modulo p. In one aspect, the modular polynomial may be used in a cryptosystem.
摘要翻译： 描述了用于计算模多项式模数大素数的系统和方法。 在一个方面，系统和方法产生l个等式的椭圆曲线。 然后，模数为大素数p的模多项式作为模p的l-均质椭圆曲线的函数被计算。 在一个方面，可以在密码系统中使用模块多项式。
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公开(公告)号：US08196186B2
公开(公告)日：2012-06-05
申请号：US12123979
申请日：2008-05-20
IPC分类号： H04L29/06
CPC分类号： H04L63/062 , G06F21/335 , G06F2221/2151
摘要： An exemplary method includes receiving a request to register a peer in a peer-to-peer system; generating or selecting a transaction key for the peer; storing the transaction key in association with registration information for the peer; transmitting the transaction key to the peer and, in response to a request to perform a desired peer-to-peer transaction by another peer, generating a token, based at least in part on the transaction key. Such a token allows for secure transactions in a peer-to-peer system including remote storage of data and retrieval of remotely stored data. Other exemplary techniques are also disclosed including exemplary modules for a peer-to-peer server and peers in a peer-to-peer system.
摘要翻译： 一种示例性方法包括：在对等系统中接收注册对等体的请求; 生成或选择对等体的交易密钥; 存储与对等体的注册信息相关联的交易密钥; 将所述交易密钥发送到所述对等体，并且响应于至少部分地基于所述交易密钥来生成令牌的请求来执行所述对等交易所需的对等交易。 这样的令牌允许对等系统中的安全事务，包括远程存储数据和检索远程存储的数据。 还公开了其它示例性技术，其包括用于对等服务器和对等系统中的对等体的示例性模块。
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15.发明申请公开(公告)号：US20100082992A1
公开(公告)日：2010-04-01
申请号：US12242801
申请日：2008-09-30
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因，并将评估结果与 整数。
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公开(公告)号：US07594261B2
公开(公告)日：2009-09-22
申请号：US11053339
申请日：2005-02-08
CPC分类号： H04L9/3073 , H04L9/3247 , H04L2209/80
摘要： Systems and methods for cryptographically processing data as a function of a Cartier pairing are described. In one aspect, a Cartier pairing is generated from two different abelian varieties or abelian varieties and an isogeny between them. Data is cryptographically processed based on the Cartier pairing.
摘要翻译： 描述了用于密码处理作为卡地亚配对的函数的数据的系统和方法。 在一个方面，卡地亚配对是由两种不同的阿贝尔品种或阿贝尔品种产生的，并且它们之间具有同位素。 基于卡地亚配对对数据进行加密处理。
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17.发明授权Elliptic curve point octupling using single instruction multiple data processing 失效使用单指令多次数据处理的椭圆曲线点八倍公开(公告)号：US07680268B2
公开(公告)日：2010-03-16
申请号：US11080301
申请日：2005-03-15
申请人： Kristin E. Lauter , Denis X Charles
发明人： Kristin E. Lauter , Denis X Charles
CPC分类号： G06F7/725
摘要： Systems and methods for elliptic curve octupling using Single Instruction Multiple Data (SIMD) processing are described. In one aspect, a weighted projective point P on an elliptic curve, P having coordinates (x, y, z) is identified. Value 8P is computed from P with 12 sets of field multiplications using SIMD processing. Each set of field multiplications includes one to four respective field multiplications. Each set of field multiplications is performed in parallel according to an assigned time-step.
摘要翻译： 描述了使用单指令多数据（SIMD）处理的椭圆曲线八倍频的系统和方法。 在一个方面，识别椭圆曲线上具有坐标（x，y，z）的P的加权投影点P。 使用SIMD处理，使用12组场乘法从P计算值8P。 每组场乘法包括一到四个相应的场乘法。 根据分配的时间步长并行地执行每组场乘法。
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18.发明授权公开(公告)号：US08250367B2
公开(公告)日：2012-08-21
申请号：US12242801
申请日：2008-09-30
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。
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公开(公告)号：US20090290715A1
公开(公告)日：2009-11-26
申请号：US12123979
申请日：2008-05-20
CPC分类号： H04L63/062 , G06F21/335 , G06F2221/2151
摘要： An exemplary method includes receiving a request to register a peer in a peer-to-peer system; generating or selecting a transaction key for the peer; storing the transaction key in association with registration information for the peer; transmitting the transaction key to the peer and, in response to a request to perform a desired peer-to-peer transaction by another peer, generating a token, based at least in part on the transaction key. Such a token allows for secure transactions in a peer-to-peer system including remote storage of data and retrieval of remotely stored data. Other exemplary techniques are also disclosed including exemplary modules for a peer-to-peer server and peers in a peer-to-peer system.
摘要翻译： 一种示例性方法包括：在对等系统中接收注册对等体的请求; 生成或选择对等体的交易密钥; 存储与对等体的注册信息相关联的交易密钥; 将所述交易密钥发送到所述对等体，并且响应于至少部分地基于所述交易密钥来生成令牌的请求来执行所述对等交易所需的对等交易。 这样的令牌允许对等系统中的安全事务，包括远程存储数据和检索远程存储的数据。 还公开了其它示例性技术，其包括用于对等服务器和对等系统中的对等体的示例性模块。
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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。
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