Message Mapping for Short Ciphertexts and Signatures
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Solution Overview
Problem
Existing cryptographic schemes produce ciphertexts and signatures that are excessively long, leading to bandwidth inefficiencies and energy consumption issues, particularly in wireless transmissions, while maintaining the need for provable security based on factoring hardness.
Innovation Solution
The implementation of a method that maps encoded messages into a subset of numbers modulo N, allowing for shorter ciphertexts and signatures through the use of quasi-permutations, specifically the π and θ mappings, which compress and decompress bit strings and numbers efficiently, while maintaining security based on factoring a larger modulus.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If conventional encryption schemes are used to ensure security, then security is maintained, but ciphertext size becomes excessively long
Solution Approach 1:
The patent changes the parameter space from all integers modulo N to a restricted subset B of quadratic residues. By mapping messages to this specialized subset and using modular square roots, the system achieves shorter ciphertexts (about 2/3 log2 N bits) while maintaining security based on the hardness of factoring N.
Solution Approach 2:
The patent extracts only the necessary information from the full message space by mapping messages to a subset B of quadratic residues. This extraction allows the system to work with a smaller effective space, reducing ciphertext length while preserving the essential security properties through the factoring hardness assumption.
2Reliability
If conventional signature schemes are used to ensure authenticity, then security is maintained, but signature size becomes excessively long
Solution Approach 1:
The patent applies the same parameter change strategy to signatures by mapping messages to quadratic residues and using modular square roots. This produces shorter signatures (about 2/3 log2 N bits) that remain secure based on the factoring hardness assumption, just as with encryption.
3Reliability
If larger modulus N is used to maintain security, then security is improved, but computational complexity increases
Solution Approach 1:
The patent changes the operational parameters to work within the subset B of quadratic residues, which allows the system to use smaller effective working sizes (about 2/3 log2 N bits) while maintaining security based on factoring the larger modulus N. This reduces the constant factors in computational operations.
4Reliability
If message encoding adds padding and random bits to prevent inversion, then security is improved, but message size increases
Solution Approach 1:
Instead of adding padding and random bits to expand the message space, the patent changes the parameter space to a restricted subset B of quadratic residues. This allows the system to work with smaller effective message representations while maintaining security through the factoring hardness assumption and the properties of modular square roots.
Data Source
AI summary
According to some embodiments of the invention, a message is processed before encryption so that the encryption method generates a short ciphertext. The message processing can be viewed as a mapping (610) that maps the message into another message that generates the short ciphertext. The mapping is reversible at least if the (possibly encoded) message (H(M)) is in a restricted set, e.g. a set [0,h″] of short messages. In some embodiments of the present invention, short signatures are provided by mapping the signature into a short signature. The mapping (810) is reversible at least if the original message (H(M)) used to generate the signature is short. Signcryption, aggregate signature, and ring signature outputs are also shortened.