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1. 发明申请

US20070098150A1 Hash function constructions from expander graphs 失效
标题翻译：来自扩展器图的散列函数结构
公开(公告)号：US20070098150A1
公开(公告)日：2007-05-03
申请号：US11263701
申请日：2005-11-01
申请人： Kristin Lauter , Denis Charles , Eyal Goren
发明人： Kristin Lauter , Denis Charles , Eyal Goren
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。

2. 发明申请

US20060177051A1 Cryptographic applications of the Cartier pairing 有权
公开(公告)号：US20060177051A1
公开(公告)日：2006-08-10
申请号：US11053339
申请日：2005-02-08
申请人： Kristin Lauter , Denis Charles
发明人： Kristin Lauter , Denis Charles
IPC分类号： H04L9/28 , H04L9/30 , H04L9/00 , H04K1/00
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.

3. 发明申请

US20070192397A1 Cryptosystem Based on a Jacobian of a Curve 失效
标题翻译：基于雅可比曲线的加密系统
公开(公告)号：US20070192397A1
公开(公告)日：2007-08-16
申请号：US11275215
申请日：2005-12-19
申请人： Kristin Lauter , Peter Montgomery , Ramarathnam Venkatesan
发明人： Kristin Lauter , Peter Montgomery , Ramarathnam Venkatesan
IPC分类号： H04L9/28 , H04L9/00 , G06F12/14 , G06F7/38 , H04L9/32 , H04K1/00 , G06F11/30
CPC分类号： H04L9/302 , H04L9/32 , H04L2209/20 , H04L2209/30
摘要： A cryptosystem has a secret based on an order of a group of points on a Jacobian of a curve. In certain embodiments, the cryptosystem is used to generate a product identifier corresponding to a particular product. The product identifier is generated by initially receiving a value associated with a copy (or copies) of a product. The received value is padded using a recognizable pattern, and the padded value is converted to a number represented by a particular number of bits. The number is then converted to an element of the Jacobian of the curve, and the element is then raised to a particular power. The result of raising the element to the particular power is then compressed and output as the product identifier. Subsequently, the encryption process can be reversed and the decrypted value used to indicate validity and/or authenticity of the product identifier.
摘要翻译：密码系统具有基于曲线雅可比的一组点的顺序的秘密。在某些实施例中，密码系统用于生成对应于特定产品的产品标识符。产品标识符是通过初始接收与产品的副本（或副本）相关联的值来生成的。使用可识别的图案填充接收的值，并且将填充值转换为由特定位数表示的数字。然后将该数字转换为曲线的雅可比元素，然后将元素升高到特定的功率。然后将元件升高到特定功率的结果被压缩并作为产品标识符输出。随后，可以反转加密处理，并且解密的值用于指示产品标识符的有效性和/或真实性。

4. 发明申请

US20070165843A1 Trapdoor Pairings 失效
标题翻译： Trapdoor配对
公开(公告)号：US20070165843A1
公开(公告)日：2007-07-19
申请号：US11275560
申请日：2006-01-13
申请人： Kristin Lauter , Denis Charles , Anton Mityagin
发明人： Kristin Lauter , Denis Charles , Anton Mityagin
IPC分类号： H04L9/30
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。

5. 发明申请

US20070055880A1 Authenticated key exchange with derived ephemeral keys 有权
标题翻译：使用衍生的短暂密钥进行认证密钥交换
公开(公告)号：US20070055880A1
公开(公告)日：2007-03-08
申请号：US11207686
申请日：2005-08-18
申请人： Kristin Lauter , Brian LaMacchia , Anton Mityagin
发明人： Kristin Lauter , Brian LaMacchia , Anton Mityagin
IPC分类号： H04L9/00
CPC分类号： H04L9/0844 , H04L9/3066 , H04L63/06
摘要： AKE with derived ephemeral keys is described. In one aspect, a first party computes a derived ephemeral public-key based on a derived ephemeral secret key and a mathematical group. The derived ephemeral secret key is based on an ephemeral secret key and a long-term secret key. The first party generates a session key for secure exchange of information with a second party. The session key is generated using the derived ephemeral secret key and a second party derived ephemeral public-key key to demonstrate to the second party that the first party possesses the long-term secret key.
摘要翻译：描述了具有派生短暂键的AKE。一方面，第一方基于导出的临时秘密密钥和数学组来计算衍生的临时公钥。衍生的短暂秘密密钥基于短暂密钥和长期密钥。第一方生成会话密钥，用于与第二方进行安全的信息交换。会话密钥是使用派生的短暂密钥和第二方派生的短暂公钥密钥生成的，以向第二方证明第一方拥有长期秘密密钥。

6. 发明申请

US20070028106A1 Extended authenticated key exchange with key confirmation 有权
标题翻译：扩展认证密钥交换密钥确认
公开(公告)号：US20070028106A1
公开(公告)日：2007-02-01
申请号：US11190374
申请日：2005-07-26
申请人： Kristin Lauter , Anton Mityagin
发明人： Kristin Lauter , Anton Mityagin
IPC分类号： H04L9/00
CPC分类号： H04L9/3066 , H04L9/0844 , H04L9/3247
摘要： Extended authenticated key exchange with key confirmation is described. In one aspect, and before computing session keys to exchange information securely between an initiator and a responder, each party of the initiator and the responder, confirms whether the other party has received corresponding information to generate a valid session key. If either party determines that the other respective party has not received the corresponding information, the party terminates the extended authenticated key exchange with key confirmation protocol. Otherwise, when a party determines that the other party has received the corresponding information, the party generates a respective session key. In this manner, when both parties confirm that the other party has received the appropriate information for session key generation, both parties are assured that information can be exchanged between the parties securely using the session keys.
摘要翻译：描述了密钥确认的扩展认证密钥交换。在一个方面中，并且在计算会话密钥之前，安全地在发起者和应答者之间交换信息，发起者和应答者的每一方确认对方是否已经接收到相应的信息以生成有效的会话密钥。如果任一方确定其他各方尚未收到相应的信息，则该方以密钥确认协议终止扩展认证密钥交换。否则，当方确定对方已经接收到相应的信息时，该方生成相应的会话密钥。以这种方式，当双方确认对方已经接收到用于会话密钥生成的适当信息时，确保双方可以使用会话密钥安全地在各方之间交换信息。

7. 发明申请

US20060182273A1 Methods for Point Compression for Jacobians of Hyperelliptic Curves 有权
标题翻译： Jacobians的超椭圆曲线点压缩方法
公开(公告)号：US20060182273A1
公开(公告)日：2006-08-17
申请号：US11278467
申请日：2006-04-03
申请人： Kristin Lauter , Peter Montgomery
发明人： Kristin Lauter , Peter Montgomery
IPC分类号： H04L9/28
CPC分类号： G06F7/725
摘要： A cryptosystem based on a Jacobian of a hyperelliptic curve is being used. Various methods and apparati are provided for generating a compressed data format that identifies one or more points—on the Jacobian of the hyperelliptic curve, and for subsequently decompressing the compressed format data.
摘要翻译：正在使用基于超椭圆曲线雅可比的密码系统。提供了各种方法和装置，用于生成标识超椭圆曲线的雅可比的一个或多个点的压缩数据格式，并用于随后解压缩压缩格式数据。

8. 发明申请

US20050025311A1 Tate pairing techniques for use with hyperelliptic curves 有权
标题翻译：用于超椭圆曲线的Tate配对技术
公开(公告)号：US20050025311A1
公开(公告)日：2005-02-03
申请号：US10628729
申请日：2003-07-28
申请人： Anne Eisentraeger , Kristin Lauter , Peter Montgomery
发明人： Anne Eisentraeger , Kristin Lauter , Peter Montgomery
IPC分类号： H04L9/30 , H04L9/00
CPC分类号： H04L9/3073 , H04L2209/12 , H04L2209/38
摘要： Methods and apparati are provided for determining a “Squared Tate pairing” for hyperelliptic curves and using the results so support at least one cryptographic process. The improved techniques provide increased efficiency and an alternative method to the conventional method of implementing the Tate pairing for Jacobians of hyperelliptic curves. With the Squared Tate pairing for hyperelliptic curves, one may obtain a significant speed-up over a contemporary implementation of the Tate pairing for hyperelliptic curves. The Squared Tate pairing for hyperelliptic curves can be substituted for the Tate pairing for hyperelliptic curves in any applicable cryptographic application.
摘要翻译：提供了用于确定超椭圆曲线的“平方泰特配对”的方法和设备，并且使用结果支持至少一个加密过程。改进的技术提供了提高效率和替代方法来实现对于超椭圆曲线的Jacobians的Tate配对的传统方法。对于超椭圆曲线的平方泰特配对，可以比超椭圆曲线的Tate配对的当代实现获得显着的加速。在任何适用的加密应用程序中，用于超椭圆曲线的平方泰特配对可以替代超椭圆曲线的Tate配对。

9. 发明申请

US20070180012A1 Approximating Function Properties with Expander Graphs 有权
标题翻译：带扩展图的近似函数属性
公开(公告)号：US20070180012A1
公开(公告)日：2007-08-02
申请号：US11275625
申请日：2006-01-19
申请人： Kristin Lauter , Denis Charles , Eyal Goren
发明人： Kristin Lauter , Denis Charles , Eyal Goren
IPC分类号： G06F7/38
CPC分类号： G06F17/18 , G06F7/725
摘要： Function properties may be approximated using an expander graph. For example, an approximate average of a function may be determined by randomly exploring an expander graph. Values of the function are associated with vertices of the expander graph. The expander graph is randomly explored by traversing edges and encountering vertices. The exploration may comprise a crawl, a walk, and so forth. An approximate average of the function is determined based on the function values that are associated with encountered vertices.
摘要翻译：函数属性可以使用扩展器图近似。例如，函数的近似平均值可以通过随机地浏览扩展器图来确定。函数的值与扩展器图的顶点相关联。通过遍历边缘并遇到顶点来随机探索扩展器图。探索可能包括爬行，散步等等。基于与遇到的顶点相关联的函数值来确定函数的近似平均值。

10. 发明申请

US20070118746A1 Digital signature for network coding 有权
标题翻译：网络编码的数字签名
公开(公告)号：US20070118746A1
公开(公告)日：2007-05-24
申请号：US11267096
申请日：2005-11-04
申请人： Kristin Lauter , Denis Charles , Kamal Jain
发明人： Kristin Lauter , Denis Charles , Kamal Jain
IPC分类号： H04L9/00
CPC分类号： H04L9/3073 , H04L9/008 , H04L9/3247 , H04L2209/60
摘要： Digital signatures for network coding are described. In one aspect, digital signatures for network coding are described. In one aspect, segmented blocks of content for distribution are digitally signed using homomorphic digital signatures generated from an elliptic curve. A linear combination of packets comprising the digitally signed content is distributed to a destination device according to an implemented distribution scheme. The linear combination of packets includes public information when digitally signing the segmented blocks. The homomorphic digital signatures and the public information allow a device receiving one or more packets of the linear combination of packets to verify and authenticate content associated with the one of our packets independent of secure transmission of secret keys and hash digests used to digitally sign the one or more packets.
摘要翻译：描述了用于网络编码的数字签名。在一个方面，描述了用于网络编码的数字签名。在一个方面，用于分发的内容分段块使用从椭圆曲线生成的同形数字签名进行数字签名。根据实施的分配方案，将包括数字签名的内容的分组的线性组合分发到目的地设备。数字线路组合包括在分段块数字签名时的公开信息。同态数字签名和公共信息允许接收分组的线性组合的一个或多个分组的设备来验证和认证与我们的一个分组相关联的内容，独立于秘密密钥的安全传输和用于数字签名的一些散列摘要或更多数据包。

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