METHOD FOR ACCELERATING THE COMPUTATIONAL IMPLEMENTATION OF MULTIPLICATIVE OPERATIONS IN MODULAR ARITHMETIC
Keywords:
modular multiplication, Montgomery method, segmented multiplication, modular arithmetic, computational optimizationAbstract
This paper explores methods for improving the efficiency of implementing modular arithmetic operations, which are fundamental to public-key cryptographic systems. The research is motivated by the growing importance of information security and the increasing use of low-bit microcontrollers in real-time applications. The paper focuses on accelerating modular multiplication and squaring operations through optimized algorithms tailored for processors with limited bit capacity. The proposed methods leverage Montgomery reduction and segmented multiplication with dynamic operand adjustment, aiming to significantly improve computational speed while maintaining cryptographic robustness.
References
Handbook of Applied Cryptography. A. Menezes, P. van Oorschot, S. Vanstone.
Montgomery, P. L. (1985). Modular multiplication without trial division. Mathematics of Computation.
Barrett, P. (1986). Implementing the Rivest Shamir and Adleman public key encryption algorithm on a standard digital signal processor.
RSA Laboratories. (2023). PKCS standards and cryptographic benchmarks.
NIST Special Publication 800-56B: Recommendations for Pair-Wise Key Establishment Schemes.
IEEE Standard Specifications for Public-Key Cryptography.
Koc, C. K. (1995). High-speed RSA implementation.
Gura, N., Patel, A., Wander, A., Eberle, H., & Shantz, S. C. (2004). Comparing elliptic curve cryptography and RSA on 8-bit CPUs.
National Institute of Standards and Technology (NIST). (2023). Cryptographic Algorithm Validation Program.
OpenSSL Cryptographic Library Documentation.
