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公开(公告)号：US07639799B2
公开(公告)日：2009-12-29
申请号：US11011289
申请日：2004-12-14
CPC分类号： H04L9/3073 , H04L9/3247
摘要： Systems and methods for cryptographically processing data as a function of a Cassels-Tate pairing are described. In one aspect, a Shafarevich-Tate group is generated from a cohomology group. A Cassels-Tate pairing is determined as a function of elements of the Shafarevich-Tate group. Data is then cryptographically processed as a function of the Cassels-Tate pairing.
摘要翻译： 描述了用于密码处理作为Cassels-Tate配对的函数的数据的系统和方法。 在一个方面，Shafarevich-Tate组由同源组组成。 Cassels-Tate配对是根据Shafarevich-Tate组的要素确定的。 然后将数据作为Cassels-Tate配对的函数进行加密处理。
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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：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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6.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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