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公开(公告)号：US07729494B2
公开(公告)日：2010-06-01
申请号：US11942618
申请日：2007-11-19
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。
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公开(公告)号：US07440569B2
公开(公告)日：2008-10-21
申请号：US10628729
申请日：2003-07-28
IPC分类号： 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 to 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，并使用结果来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。
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公开(公告)号：US07298839B2
公开(公告)日：2007-11-20
申请号：US10626948
申请日：2003-07-25
IPC分类号： H04L9/30
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。
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公开(公告)号：US07730315B2
公开(公告)日：2010-06-01
申请号：US11275215
申请日：2005-12-19
IPC分类号： H04L9/00
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。
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公开(公告)号：US07469048B2
公开(公告)日：2008-12-23
申请号：US11277604
申请日：2006-03-27
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，用于生成识别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。
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公开(公告)号：US07236589B2
公开(公告)日：2007-06-26
申请号：US11278467
申请日：2006-04-03
CPC分类号： G06F7/725
摘要： A cryptosystem based on a Jacobian of a hyperelliptic curve is being used. Various methods and apparatus 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，用于产生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。
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公开(公告)号：US07043015B2
公开(公告)日：2006-05-09
申请号：US10285198
申请日：2002-10-31
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，用于生成识别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。
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8.发明申请公开(公告)号：US20080137839A1
公开(公告)日：2008-06-12
申请号：US11942618
申请日：2007-11-19
IPC分类号： H04L9/28
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。
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公开(公告)号：US07020776B2
公开(公告)日：2006-03-28
申请号：US09886147
申请日：2001-06-20
IPC分类号： H04L9/00
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。
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公开(公告)号：US07769167B2
公开(公告)日：2010-08-03
申请号：US10627281
申请日：2003-07-25
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。
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