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41. 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。

42. 发明授权

US07996677B2 Digitally certified stationery 有权
标题翻译：数码认证文具
公开(公告)号：US07996677B2
公开(公告)日：2011-08-09
申请号：US11567707
申请日：2006-12-06
申请人： Denis X. Charles , Kamal Jain , Kristin E. Lauter
发明人： Denis X. Charles , Kamal Jain , Kristin E. Lauter
IPC分类号： H04L9/32
CPC分类号： G06F21/64 , G06F21/6272
摘要： Systems and methods for digitally certified stationery are described. In one aspect, a stationery granting authority (SGA) receives a request from a user to generate a document. If the user is authorized for the requested document, the SGA generates a certificate with credentialing information from data in the request. The SGA generates a first digital signature from some of the credentialing information. The SGA communicates the certificate to the user for editing and distribution as the document. A recipient of the document determines whether the document is “official” by contacting a specified service to provide certain information from the document. The verification service computes a second digital signature from the provided information for comparison to the first digital signature. If there is a match, the service notifies the recipient that the document is valid/official. Otherwise, the recipient is notified that the document is not valid.
摘要翻译：描述了数字认证的文具的系统和方法。一方面，文具授予机构（SGA）从用户接收生成文档的请求。如果用户被授权请求的文档，则SGA将从请求中的数据生成具有凭据信息的证书。 SGA从一些凭证信息生成第一个数字签名。 SGA将证书通信给用户进行编辑和分发作为文档。文档的收件人通过联系指定的服务来确定文档是否“正式”，以从文档中提供某些信息。验证服务根据所提供的信息计算第二数字签名，以便与第一数字签名进行比较。如果有匹配，则该服务通知收件人该文档是有效/正式的。否则，通知收件人该文档无效。

43. 发明授权

US07769167B2 Weil and Tate pairing techniques using parabolas 有权
标题翻译： Weil和Tate配对技术使用抛物线
公开(公告)号：US07769167B2
公开(公告)日：2010-08-03
申请号：US10627281
申请日：2003-07-25
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： H04L9/30
CPC分类号： G06F7/725 , H04L9/3073
摘要： Methods and apparati are provided for use in cryptographically processing information based on elliptic and other like curves. The methods and apparati allow pairings, such as, for example, Weil pairings, Tate Pairings, Squared Weil pairings, Squared Tate pairings, and/or other like pairings to be determined based on algorithms that utilize a parabola. The methods and apparati represent an improvement over conventional algorithms since they tend to me more computationally efficient.
摘要翻译：提供了基于椭圆和其他类似曲线的密码处理信息的方法和装置。方法和设备允许基于使用抛物线的算法确定配对，例如Weil配对，Tate Pairings，Squared Weil配对，Squared Tate配对和/或其他类似配对。这些方法和设计代表了对传统算法的改进，因为它们对我来说更有计算效率。

44. 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。

45. 发明申请

US20090290705A1 Algorithms for generating parameters for genus 2 hyperelliptic curve cryptography 有权
标题翻译：用于生成第2类超椭圆曲线密码学参数的算法
公开(公告)号：US20090290705A1
公开(公告)日：2009-11-26
申请号：US12125834
申请日：2008-05-22
申请人： Kristin E. Lauter , Ning Shang
发明人： Kristin E. Lauter , Ning Shang
IPC分类号： H04L9/06
CPC分类号： G06F7/725
摘要： An exemplary method includes defining a CM field, representing coefficients of a Frobenius element of a hyperelliptic curve over a prime field as non-linear polynomials that are functions of an integer x and selecting a value for x whereby the product of the Frobenius element and its complex conjugate is a prime number. Such a method may further include determining the order of the Jacobian of the hyperelliptic curve, for example, where the order is an almost prime number. Various other methods, devices, systems, etc., are also disclosed, which may be optionally used for cryptography.
摘要翻译：示例性方法包括定义CM场，其表示在主场上的超椭圆曲线的Frobenius元素的系数作为作为整数x的函数的非线性多项式，并且选择x的值，由此产生Frobenius元素及其复共轭是素数。这种方法还可以包括确定超椭圆曲线的雅可比的顺序，例如，其中顺序是几乎素数。还公开了各种其他方法，设备，系统等，其可以可选地用于密码学。

46. 发明申请

US20080301815A1 Detecting Unauthorized Changes to Printed Documents 审中-公开
标题翻译：检测未经授权的打印文档更改
公开(公告)号：US20080301815A1
公开(公告)日：2008-12-04
申请号：US11756599
申请日：2007-05-31
申请人： Kristin E. Lauter , Denis X. Charles , Kamal Jain
发明人： Kristin E. Lauter , Denis X. Charles , Kamal Jain
IPC分类号： G06F7/04
CPC分类号： G03G21/04 , H04N1/32144 , H04N2201/3235 , H04N2201/3236 , H04N2201/327 , H04N2201/3271
摘要： Systems and methods to detect unauthorized changes to a printed document are described. In one aspect, a digital signature of original content associated with electronic document is embedded into the original content to create a content signed document. The systems and methods use the embedded digital signature to automatically determine whether text-based content associated with a printout of the content signed document was changed from the original content associated with the electronic document.
摘要翻译：描述了检测未经授权的更改打印文档的系统和方法。一方面，将与电子文档相关联的原始内容的数字签名嵌入到原始内容中以创建内容签名文档。系统和方法使用嵌入式数字签名来自动确定与内容签名文档的打印输出相关联的基于文本的内容是否从与电子文档相关联的原始内容中改变。

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