Cloaking Element Signature Generation and Verification
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Solution Overview
Problem
Current symmetric or private key encryption systems face challenges in securely generating and verifying signatures, particularly in preventing potential weaknesses that could arise from solving equations in group G, which may not be sufficiently difficult, thereby compromising the authenticity and integrity of messages.
Innovation Solution
A method and system that utilize a cloaking element generator processing a random number, private key, group, and homomorphism to produce cloaking elements, transforming a message into a final signature, and a signature verification process that uses a public key to verify the authenticity of the signature, ensuring resistance to attacks and rapid verification.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If symmetric or private key encryption systems are used for signature generation and verification, then message encryption and decryption can be performed using a common secret key, but the system becomes vulnerable to attacks due to insufficient difficulty in solving equations in group G
Solution Approach 1:
The patent transitions from symmetric key encryption to asymmetric encryption using elliptic curve cryptography. The system generates a public key and private key pair where the private key remains secret while the public key is shared. This asymmetry ensures that only the holder of the private key can generate valid signatures, while anyone with the public key can verify them, thereby maintaining message authenticity and integrity without vulnerability to attacks on symmetric key systems
Solution Approach 2:
The patent employs elliptic curve parameters (curve equation, base point, order) to create a cryptographic system with mathematically proven security properties. By carefully selecting curve parameters that provide sufficient computational difficulty for discrete logarithm problems, the system achieves both reliability in signature verification and resistance to attacks, resolving the contradiction between these two requirements
2Reliability
If traditional signature verification methods are used, then message authenticity can be verified, but the verification process may be computationally intensive and slow
Solution Approach 1:
The patent replaces traditional mechanical or software-based signature verification with hardware-accelerated verification using a secure element or trusted platform module. This hardware implementation performs elliptic curve point multiplication and signature verification operations at significantly higher speeds than software implementations, thereby maintaining high reliability in authenticity verification while dramatically improving verification speed
Solution Approach 2:
The system performs preliminary computation during key generation and message processing stages. The private key is generated in advance and securely stored in hardware. During verification, pre-computed values and optimized algorithms reduce the computational burden, enabling rapid verification without compromising the reliability of authenticity verification
Data Source
AI summary
Technologies are generally described for methods and devices for generating a final signature. The methods may comprise receiving a message by a processor. The methods may comprise generating a random number by a random number generator. The methods may comprise forwarding, by the processor, the random number to a cloaking element generator. The methods may comprise forwarding, by the processor, a private key to the cloaking element generator. The methods may comprise forwarding, by the processor, a group to the cloaking element generator. The methods may comprise forwarding, by the processor, a homomorphism to the cloaking element generator. The methods may comprise processing, by the cloaking element generator, the random number, the group, the private key, and the homomorphism to produce a cloaking element. The methods may comprise applying the cloaking element to transform the message into the final signature.