High Dynamic Range RNS Bases for Modular Multiplication
Modular multiplication is the most important part of public key
cryptography algorithm like RSA and elliptic curve cryptography.
Residue Number System is an efficient way to speed up these
applications because of its carry free nature. Efficiency of
modular multiplication in RNS is depending on effective
selection of RNS bases. In this work efficient design of RNS
bases are reported where comparing to the state-of-the-art, the
proposed RNS bases has enjoyed more efficient arithmetic
operation and residue/binary to binary/residue conversion.
Therefore modular multiplication in RNS is implemented with
more speed. Comparison with the best work in literature shows
that noticeable improvement in speed has achieved by the
proposed RNS bases.
Keywords: Montgomery Modular Multiplication, Residue Number System (RNS), modular arithmetic, Elliptic curve cryptography (ECC)
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