Cassels-Tate Pairing Cryptographic Processing

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Solution Overview

Problem

Existing pairing-based cryptographic systems rely on Weil or Tate pairings evaluated at points on elliptic curves or abelian varieties, which limits their security and versatility in cryptographic processing.

Innovation Solution

The use of Cassels-Tate pairings on a Shafarevich-Tate group provides an alternative cryptographic processing method, generating a bilinear, anti-symmetric pairing that enhances security through the hardness of discrete log problems within the Shafarevich-Tate group, enabling applications in various cryptographic protocols.

Engineering Contradictions & Design Principles

VSEngineering Contradiction Analysis

1Reliability

If Weil or Tate pairings are used for cryptographic processing, then existing cryptographic systems can be implemented, but security and versatility are limited

Engineering Contradiction:

ImprovesecurityVSAvoidversatility

Core Design Contradiction:

ReliabilityVSAdaptability or versatility

Solution Approach 1:

The patent changes the fundamental parameter of the pairing type from Weil/Tate pairings to Cassels-Tate pairings on Shafarevich-Tate groups. This parameter change enables new cryptographic applications while maintaining security through the hardness of discrete log problems in the Shafarevich-Tate group context.

Inventive Principle:

Principle #35Parameter changes

Solution Approach 2:

The patent moves from pairings on elliptic curves/abelian varieties to pairings on Shafarevich-Tate groups, representing a dimensional shift in the mathematical structure. This allows cryptographic protocols to operate in a new mathematical dimension with enhanced security properties.

Inventive Principle:

Principle #17Another dimension (Dimensionality change)

2Reliability

If Cassels-Tate pairings on Shafarevich-Tate groups are used, then security through discrete log hardness is enhanced, but computational complexity increases

Engineering Contradiction:

ImprovesecurityVSAvoidcomputational complexity

Core Design Contradiction:

ReliabilityVSDevice complexity

Solution Approach 1:

The patent uses the Shafarevich-Tate group as an intermediary mathematical structure that bridges the gap between cryptographic security requirements and computational feasibility. The group structure provides a framework where discrete log hardness can be leveraged while organizing computations in a manageable way.

Inventive Principle:

Principle #24Intermediary (Mediator)

Solution Approach 2:

The patent replaces traditional pairing-based cryptographic mechanisms with Cassels-Tate pairings on Shafarevich-Tate groups, substituting the mathematical framework to achieve security through discrete log hardness while managing computational complexity through the group's structural properties.

Inventive Principle:

Principle #28Mechanics substitution (Replace mechanical system)

Data Source

PatentUS7639799B2Cryptographically processing data based on a Cassels-Tate pairing

Publication Date: 2009.12.29 MICROSOFT TECHNOLOGY LICENSING LLC

AI summary

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.