Signature Verification System Reducing Group Elements
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Solution Overview
Problem
Existing group structure preserving signature systems face security uncertainties in practical implementations, particularly with random oracle-based methods, and are inefficient in computation and security for symmetric bilinear mapping.
Innovation Solution
A signature verification system using two verification equations with a signature comprising four group elements (w, s, t, r) that ensures security even with symmetric bilinear mapping, reducing computational complexity and signature length compared to existing methods.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If the system uses seven group elements for signature to ensure security against chosen message attacks, then security is improved, but signature length and computational complexity increase
Solution Approach 1:
The patent extracts and eliminates redundant group elements from the signature structure. By removing unnecessary elements while retaining the core security mechanisms, the signature is reduced from seven group elements to four group elements (a, b, c, d), thereby reducing signature length and verification computational complexity while maintaining security against chosen message attacks
Solution Approach 2:
The patent changes the parameters of the signature structure by modifying the verification equations and the composition of signature elements. The new verification equations use bilinear pairings in a different configuration, allowing the signature to be composed of fewer group elements while preserving the security properties against chosen message attacks
2Device complexity
If the system uses asymmetric bilinear mapping groups to reduce signature elements, then signature length is reduced, but security is compromised in symmetric bilinear mapping groups
Solution Approach 1:
The patent creates a universal signature scheme that works securely in both symmetric and asymmetric bilinear mapping groups. By designing verification equations that are agnostic to the specific type of bilinear mapping, the system achieves multi-functionality and can be deployed in diverse cryptographic settings without compromising security or requiring separate implementations
3Ease of manufacture
If the system uses random oracle-based methods to simplify the signature structure, then ease of implementation is improved, but security in practical implementations becomes unclear
Solution Approach 1:
The patent replaces the idealized random oracle model with concrete, implementable cryptographic primitives based on standard bilinear pairing assumptions. This substitution provides practical security guarantees without requiring the unrealistic assumption of random oracles, making the system both implementable and secure in real-world deployments
Data Source
AI summary
A group structure preserving signature system that can be applied to groups based on symmetric bilinear mapping, that reduces the signature length, and that enables efficient computation of verification equations is provided. At least, information indicating p, G1, G2, GT, e, g1, and g2, information needed to obtain e(hu, hv), and data that includes gs, hs, gt, ht, {g1, h1}, . . . , {gK, hK} are held as a public key vk, and data that includes vk, γs, δs, γt, δt, δu, δv, {γ1, δ1}, . . . , {γK, δK} are held as a secret key sk. A signature device selects ζ and ρ at random from integers between 0 and p−1, both inclusive, obtains w, s, t, and r, and generates, as a signature σ, data that includes w, s, t, and r. A verification device verifies the signature σ by using two verification equations.