ECDSA Signature Component Information Embedding
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Solution Overview
Problem
Existing cryptographic algorithms like DSA and RSA require larger cryptographic values for similar security levels, leading to increased storage, transmission, and computational demands, whereas elliptic curve cryptography (ECC) aims to address this with smaller values, but there is a need for efficient methods to incorporate additional information into ECC-based protocols without compromising security.
Innovation Solution
The proposed framework for generating ECDSA signatures incorporates information into the signature components by iteratively selecting a private key and computing signature components until the desired information is embedded, using elliptic curve domain parameters and a cryptographic hash function, allowing for reduced message size and computational efficiency.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If traditional cryptographic algorithms like DSA and RSA are used, then security level is maintained, but cryptographic value size increases leading to larger storage and transmission requirements
Solution Approach 1:
The patent changes the cryptographic algorithm parameters from traditional DSA/RSA to elliptic curve cryptography (ECC), which uses different mathematical foundations (elliptic curve discrete logarithm problem) to achieve the same security level with smaller key sizes. For example, a 160-bit ECC key provides equivalent security to a 1024-bit RSA key, directly resolving the contradiction between security level and cryptographic value size.
2Adaptability or versatility
If additional information is incorporated into ECDSA signature components, then information embedding capability improves, but signature generation complexity increases
Solution Approach 1:
The patent merges multiple functions into the ECDSA signature generation process: instead of separately generating a signature and then embedding additional information, the method combines these operations by incorporating the additional information directly into the signature component calculation. This is achieved by modifying the signature equation to include the additional information as an input parameter, thereby achieving both signature generation and information embedding in a single integrated process.
Solution Approach 2:
The patent applies preliminary action by pre-processing the additional information before it is incorporated into the signature generation. The method prepares the additional information in advance (such as converting it to the appropriate format or combining it with the message hash) so that it can be seamlessly integrated into the ECDSA algorithm without requiring complex post-processing or iterative adjustments during the signing operation.
Data Source
AI summary
During generation of a signature on a message to create a signed message, a signer determines one of the signature components such that particular information can be extracted from the signature component. The particular information may be related to one or more of the signer and the message to be signed. After receiving a signed message purported to be signed by the signer, a verifier can extract the particular information from the signature component.