Zero-Knowledge Proof One-Way Function for Digital Signature Compression
Find Innovative SolutionsGenerate Solutions
Solution Overview
Problem
Zero-knowledge proof-based digital signatures using block ciphers result in large signature sizes due to increased nonlinear operations, leading to high network transmission costs and vulnerability to algebraic attacks.
Innovation Solution
A calculating method employing a zero-knowledge proof-friendly one-way function that reduces signature size by using an augmented matrix and substitution-box operations, configuring the matrices with random values and circular shifts, and minimizing the number of nonlinear operations through polynomial operations on a finite field.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If block cipher operations are used to ensure safety against algebraic attacks, then security is improved, but signature size becomes very large
Solution Approach 1:
The patent extracts only the essential nonlinear operations needed for security from the full block cipher, using a minimized set of S-box operations rather than complete block cipher rounds. This extraction approach maintains algebraic attack resistance while removing redundant operations that inflate signature size.
Solution Approach 2:
The patent changes the parameters of the one-way function by using a customizable number of S-box operations (k times) rather than fixed block cipher rounds. This allows optimization of the balance between security strength and signature size by adjusting the parameter k based on specific security requirements.
2Reliability
If the number of nonlinear operations is increased to ensure safety, then security is improved, but network transmission costs increase
Solution Approach 1:
The patent extracts only the necessary nonlinear operations from traditional block ciphers, using a minimized sequence of S-box operations. This extraction reduces the total number of nonlinear operations while maintaining security, thereby reducing signature size and network transmission costs.
Solution Approach 2:
The patent allows dynamic adjustment of the number of S-box operation iterations (k times) to optimize the trade-off between security strength and transmission cost. By parameterizing the security level, users can choose minimal configurations that satisfy security requirements without excessive transmission overhead.
3Reliability
If standard block cipher operations are used, then cryptographic security is achieved, but signature size becomes large
Solution Approach 1:
The patent extracts the essential cryptographic functionality from standard block ciphers by using a simplified sequence of matrix operations and S-box applications. This extraction maintains cryptographic security properties while eliminating the bulk operations that cause large signature sizes.
Solution Approach 2:
The patent replaces traditional mechanical block cipher operations with an optimized sequence of matrix multiplications and S-box operations. This substitution uses more efficient mathematical operations that achieve the same cryptographic purpose with fewer steps, reducing signature size.
Data Source
Figure 1
Figure 2
Figure 3
AI summary
An example embodiment provides a calculating method using a zero-knowledge proof-friendly one-way function, performed by a computing device, the calculating method including: calculating a first intermediate bit stream by inputting an input bit stream of a one-way function to an augmented matrix, calculating a second intermediate bit stream by dividing the first intermediate bit stream into a predetermined number of bit streams and inputting each of the predetermined number of divided bit streams to a substitution-box (S-box), and outputting an output bit stream of the one-way function by inputting the second intermediate bit stream to a reduced matrix.