NTRU Cryptosystem Using Power-of-2 Modulus for High-Speed Decryption
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Solution Overview
Problem
The NTRU cryptosystem experiences decryption failures, and the NTRUEncrypt scheme, while reducing this probability, still faces slower processing speeds and occasional decryption failures in encrypted communication systems.
Innovation Solution
A new NTRU cryptosystem configuration is introduced, using parameters p=3 and q=2^k, where all coefficients in the polynomials f, g, and r indicate either 0 or 1, and the ideal q is expressed as q=(2^k)*R, enabling high-speed processing and preventing decryption failures by ensuring all coefficients in p·r×g+f×m range from 0 to (q−1).
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If the NTRUEncrypt scheme is used to reduce decryption failure probability, then decryption reliability is improved, but processing speed deteriorates
Solution Approach 1:
The patent changes the parameter q from a general prime number (as in NTRUEncrypt) to a power of 2 (q=2^k). This parameter change enables the use of bitwise operations instead of general modular arithmetic, significantly improving processing speed while maintaining decryption reliability through the chosen parameters (p=3, q=2^k, and specific relationships between df, dg, and d).
Solution Approach 2:
The patent substitutes general modular arithmetic operations with bitwise operations (AND, OR, XOR, NOT) and shift operations. This substitution leverages the hardware-optimized nature of bitwise operations, achieving high-speed processing comparable to or exceeding traditional cryptographic systems while maintaining security.
2Productivity
If the NTRU cryptosystem is used for high-speed processing, then processing speed is improved, but decryption failures occur
Solution Approach 1:
The patent selects specific parameter relationships where q=2^k and p=3 are relatively prime, and establishes constraints on df, dg, and d such that df + min(dg, d) ≤ d. These parameter changes ensure that the decryption process always succeeds while maintaining high processing speed through efficient polynomial operations.
Solution Approach 2:
The patent designs the parameter relationships in advance to prevent decryption failures before they can occur. By ensuring that the sum of the number of non-zero coefficients in f and g does not exceed the number of non-zero coefficients in h, the system preemptively guarantees successful decryption without requiring error correction mechanisms.
3Reliability
If remainder operation in modulo q is performed with q being a prime number other than 2, then security is maintained, but processing speed deteriorates
Solution Approach 1:
The patent replaces general modular arithmetic (which is computationally intensive) with bitwise operations and shift operations that are natively supported by modern processors. By setting q=2^k, the modulo operation becomes equivalent to masking the lower k bits, which can be executed in a single CPU instruction, achieving speed comparable to or exceeding traditional cryptographic operations.
Solution Approach 2:
The patent changes q from a general prime number to a power of 2, fundamentally altering the arithmetic operations required. This parameter change enables the use of efficient bitwise operations while maintaining security through the properties of polynomial rings and the specific relationships between parameters p, q, df, dg, and d.
Data Source
AI summary
An encrypted communication system, capable of performing processing with the speed higher than the conventionally achieved speed, includes an encryption device and a decryption device sharing parameters that satisfy p=3 and q=2^k (k: an integer of 2 or greater). The decryption device generates a public key and a private key using the parameters, the encryption device encrypts a plain text using the public key, and then, the decryption device decrypts the encrypted text using its own private key.