Highly Parallel Modular Multiplier for Elliptic Curve Cryptography in Residue Number System

Improved Sum of Residues Modular Multiplication Algorithm

“…Calculation of α has been discussed in [12,20]. It is shown that choosing proper constants q and ∆ and enforcing boundary condition of (12), α can be calculated using (13).…”

“…The factor (κ) is a function of γ i , not a constant. Therefore the value of V -which is actually the output of SOR algorithm introduced in [19,20] -is not presenting the true reduction of Z p . In fact:…”

“…Modular reduction based on the sum of residues (SOR) algorithm was first presented by Phillips et al [19] in 2010. The SOR algorithm hardware implementation was proposed later in [20]. A disadvantage of the SOR algorithm is that unlike the Montgomery reduction method, the output is an unknown and variable factor of the "X mod p" value.…”

“…A disadvantage of the SOR algorithm is that unlike the Montgomery reduction method, the output is an unknown and variable factor of the "X mod p" value. Although this algorithm offers a high level of parallelism in calculations, the proposed implementation in [20] is considerably big in area.…”

“…In this paper, we do an improvement to the sum of residues algorithm by introducing the correction factor κ to obtain a precise result. Using an efficient moduli set, we also propose a new design to improve the area in comparison to [20]. The timing of our design is improved compared to RNS Montgomery reduction as well.…”