Modified SM2 Elliptic Curve Signature Algorithm for Partial Message Recovery

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Solution Overview

Problem

The SM2 Elliptic Curve Signature Algorithm lacks partial message recovery and has a larger signature size compared to traditional cryptographic strengths, which limits its efficiency in authentication and data integrity.

Innovation Solution

A modified SM2 Elliptic Curve Signature Algorithm is developed, which partitions messages into two portions, generates an ephemeral key, computes an encryption key based on the ephemeral and public keys, encrypts the first portion, computes a hash value, and outputs an enciphered message including the signature key and the second portion, allowing for partial message recovery and reducing signature size by 50%.

Engineering Contradictions & Design Principles

VSEngineering Contradiction Analysis

1Reliability

If the SM2 Elliptic Curve Signature Algorithm is used, then digital signature authentication is provided, but the signature size is larger compared to traditional cryptographic strengths

Engineering Contradiction:

ImproveauthenticationVSAvoidsignature size

Core Design Contradiction:

ReliabilityVSLength of stationary object

Solution Approach 1:

The patent extracts and recovers part of the original message from the signature itself during verification. By incorporating message recovery techniques, the signature structure is optimized to embed recoverable message portions, reducing the overall signature size while maintaining authentication reliability.

Inventive Principle:

Principle #2Taking out (Extraction)

Solution Approach 2:

The patent modifies the signature algorithm parameters and structure to achieve more efficient encoding. By changing how signature components are generated and verified, the solution reduces signature size while preserving the cryptographic strength and authentication capability of the SM2 algorithm.

Inventive Principle:

Principle #35Parameter changes

2Reliability

If the SM2 Elliptic Curve Signature Algorithm is used, then digital signature authentication is provided, but partial message recovery is not available

Engineering Contradiction:

ImproveauthenticationVSAvoidmessage recovery

Core Design Contradiction:

ReliabilityVSLoss of information

Solution Approach 1:

The patent implements message recovery by extracting and recovering portions of the original message directly from the signature data during the verification process. This allows the recipient to retrieve part of the signed message without requiring separate transmission, reducing redundancy and improving efficiency.

Inventive Principle:

Principle #2Taking out (Extraction)

Solution Approach 2:

The patent merges the signature generation and message recovery functions into a unified process. The signature structure is designed to simultaneously provide authentication and embed recoverable message components, combining multiple functions into a single cryptographic operation.

Inventive Principle:

Principle #5Merging (Combining)

Data Source

PatentUS8971528B2Modified elliptic curve signature algorithm for message recovery

Publication Date: 2015.03.03 MALIKIE INNOVATIONS LTD

AI summary

A modified Chinese State Encryption Management Bureau's SM2 Elliptic Curve Signature Algorithm that offers partial message recovery and lowers the signature size for a given cryptographic strength. The modified SM2 Elliptic Curve Signature Algorithm includes a signature and verification algorithm that modifies a signature generation primitive to compute a key derived from the ephemeral signing key, and a multiple of the signer's public key.