Variable-Length Hash Signature Generation for Efficient Message Recovery
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Solution Overview
Problem
Conventional message-recoverable signature techniques face inefficiencies when dealing with messages of varying lengths, as they require fixed bit lengths for signature components, leading to suboptimal signature generation and verification processes.
Innovation Solution
A signature generation and verification system that uses hash functions with variable output bit lengths to accommodate messages of different lengths, allowing for flexible bit length management and ensuring all bits of the message can be targeted in the signature, using cyclic groups and hash functions to ensure security and accuracy.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If fixed bit length is used for signature components, then security is maintained, but efficiency deteriorates when message length varies
Solution Approach 1:
The patent makes the bit length of signature components dynamic rather than fixed. Specifically, the bit length of the first hash value is set to match the bit length of the message, allowing the signature components to adapt their size based on the actual message length. This dynamic adjustment maintains security while improving efficiency for variable-length messages.
Solution Approach 2:
The patent changes the parameter of bit length from a fixed constant to a variable that depends on the message length. By setting the bit length of the first hash value equal to the message bit length, and consequently adjusting the bit length of the signature component r, the system optimizes the balance between security and efficiency for different message sizes.
2Device complexity
If fixed bit length is used for signature components, then implementation is simplified, but adaptability to various message lengths deteriorates
Solution Approach 1:
The system dynamically adjusts the bit length of signature components based on the input message length. The first hash value's bit length is set to match the message bit length, and the signature component r's bit length is derived from this, enabling the system to adapt to various message lengths without complex preprocessing or truncation logic.
Solution Approach 2:
The patent creates a universal signature generation mechanism that can handle messages of any length by making the hash function output length variable. This single mechanism serves multiple functions: it maintains security for short messages, provides full coverage for long messages, and automatically optimizes the signature size based on the input, eliminating the need for separate handling logic for different message size categories.
3Loss of information
If all bits of the message are targeted in the signature, then completeness is improved, but computational overhead increases
Solution Approach 1:
The patent changes the parameter of hash output bit length to match the message bit length exactly. This ensures that all bits of the message are incorporated into the signature (completeness) while avoiding the computational overhead of fixed-length hashing that would process unnecessary bits. The first hash function H1 outputs a bit length equal to the message bit length, making the computation proportional to the actual input size.
Data Source
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AI summary
A signature is generated by a scheme in which x denotes a secret key of a signature generating apparatus, mrec ∈ {0, 1}M denotes a recovery message, k denotes an arbitrary value, g denotes a generator of a cyclic group G of order q, R represents gk ∈ G, H1 represents a hash function H1: {0, 1}* → {0, 1}L, H2 represents a hash function H2: {0, 1}* → {0, 1}M that has a variable output length, H3 represents a hash function H3: {0, 1}* → Zq, r = H1(R, mrec)lmrec(+)H2(R, H1(R, mrec)), where (+) represents an exclusive-OR operator, t is defined for γ, which depends on r, as t = H3(γ), s is defined as s = k-t·x ∈ Z, and a signature is σ = (r, s).