Attribute based addition outperforms Kogge-Stone binary adders for a wide range of m when w is small. Attribute addition outperformed RNS addition for all values of m where 128≤m≤32,768 bits for all machine word sizes w where 4≤w≤128 bits. Results show that addition is done faster in our proposed representation when compared with binary and residue number system (RNS) based additions. Extensive numerical simulations were done to verify the performance of the new number representation. Algorithms are also developed for converting binary numbers to attribute representation, and vice versa. Algorithms are proposed for this new representation to implement arithmetic operations such as two’s complement, addition/subtraction, comparison, sign detection and modular reduction. We propose a novel and efficient attribute-based large integer representation scheme suitable for large integers commonly used in cryptography such as the five NIST primes and the Pierpont primes used in supersingular isogeny Diffie-Hellman (SIDH) for post-quantum cryptography. Higher levels of security require larger key sizes and this becomes a limiting factor in GF(p) using large integers because of the carry propagation problem. Addition is an essential operation in all cryptographic algorithms.
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