Signature Generation Segmentation for Verification Accuracy
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Solution Overview
Problem
Inappropriate signature verification errors occur in existing digital signature schemes, particularly when the difference between the largest and smallest values of elements in the signature exceeds the modulo q, leading to information loss and incorrect verification.
Innovation Solution
A signature generation and verification apparatus that generates signature data by calculating elements s and t such that s=sl+sh×q and t=tl+th×q, allowing proper decryption without performing the mod q operation, ensuring accurate verification even when the difference exceeds q.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Loss of substance
If the mod q operation is performed on signature elements, then the signature data size is reduced, but information loss occurs leading to verification errors
Solution Approach 1:
The signature element s is segmented into two parts: s = sl + sh × q, where sl is the lower part (0 ≤ sl < q) and sh is the higher part. This segmentation allows the signature to be represented with reduced data size (storing only sl) while preserving verification accuracy by using sh to compensate for the modular reduction during verification.
Solution Approach 2:
The invention extends the signature representation from a single modular value to a two-dimensional structure (sl, sh) where sl represents the value modulo q and sh represents the quotient. This dimensional change allows the system to avoid information loss by distributing information across two components rather than compressing it into a single modular value.
2Adaptability or versatility
If the difference between largest and smallest signature elements exceeds q, then the signature range increases, but information loss occurs during mod q operation
Solution Approach 1:
By segmenting the signature element s into sl (remainder) and sh (quotient) where s = sl + sh × q, the invention handles arbitrary range values without information loss. The segment sl captures the modular information (0 ≤ sl < q) while sh captures the magnitude information, together preserving the complete signature value regardless of how large the difference between maximum and minimum elements is.
3Productivity
If modular arithmetic is used for high-speed processing, then computation speed increases, but verification errors occur when signature range exceeds modulo
Solution Approach 1:
The segmentation s = sl + sh × q enables the system to use efficient modular arithmetic for computing sl while separately tracking sh to maintain accuracy. During verification, the relationship s = sl + sh × q is used to reconstruct the original signature value, ensuring accurate verification even when the signature range exceeds the modulo q, thus maintaining both high processing speed and verification reliability.
Solution Approach 2:
The quotient sh acts as an intermediary that bridges the gap between modular arithmetic and full-precision verification. By introducing sh as an additional component, the system can perform fast modular operations on sl while using sh to restore the complete value for accurate verification, thus mediating between speed and accuracy requirements.
Data Source
AI summary
A signature generation apparatus and a signature verification apparatus preventing an occurrence of an inappropriate signature verification error. The signature generation apparatus (110) including a signature generation unit (114) calculating signature vector (s, t) for a message m using a private key, and generating signature data S indicating polynomials sl and sh specifying the polynomial s and a polynomial th which is a quotient when the polynomial t is divided by q.