Abstract:
Modern computational tasks involving large-number processing demand not only high precision but also significant operational speed. In this context, the residue number system provides an effective approach for parallel processing of large numbers, with applications in cryptography, signal processing, and artificial neural networks. The primary task in defining such a system is determining its basis. This paper presents an algorithm for generating compact residue number system bases based on the Diemitko theorem. The proposed algorithm generates bases 15.5% faster on average than Pseudo-Mersenne-based construction and 75.7% faster than the general filtering method. Comparative analysis demonstrates that using compact bases delivers an average 12% acceleration in modular operations compared to special moduli sets.
Keywords:residue number system, high-performance computing, special sets of moduli, generation of prime numbers, cryptography.
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