Cartier Pairing Abelian Varieties Cryptographic Processing
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Solution Overview
Problem
Existing pairing-based cryptographic systems rely on Weil or Tate pairings evaluated at points on an elliptic curve, which may not provide sufficient cryptographic processing capabilities for various cryptographic protocols, limiting their effectiveness and versatility.
Innovation Solution
The use of Cartier pairings generated from two different abelian varieties and an isogeny between them for cryptographic processing, enabling the implementation of various cryptographic protocols such as identity-based encryption, digital signatures, and key agreement by leveraging the properties of Cartier pairings to sign, encrypt, and verify data.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Adaptability or versatility
If Weil or Tate pairings are used on elliptic curves, then the cryptographic system has a well-defined structure, but the cryptographic processing capabilities are limited and insufficient for various cryptographic protocols
Solution Approach 1:
The patent transitions from traditional single elliptic curve pairings to Cartier pairings involving two different abelian varieties (E and E') connected by an isogeny φ. This dimensional expansion from one curve to two varieties enables enhanced cryptographic processing capabilities while maintaining a structured mathematical framework through the isogeny relationship.
Solution Approach 2:
The invention combines two different abelian varieties E and E' with an isogeny φ to create a composite pairing structure. This composite approach integrates multiple mathematical components (two varieties plus isogeny) to achieve superior cryptographic functionality compared to single-variety pairings, resolving the contradiction between versatility and complexity.
2Reliability
If traditional pairing-based systems are used, then the implementation is relatively simple, but the security and efficiency for diverse cryptographic protocols are insufficient
Solution Approach 1:
The patent changes key parameters of the pairing system by moving from standard elliptic curve pairings to Cartier pairings on abelian varieties with isogenies. This parameter transformation includes using different variety types, introducing isogeny relationships, and operating with modified pairing structures, thereby enhancing security and efficiency for diverse cryptographic protocols.
Data Source
AI summary
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.