Learn More
The paper describes a new RNS modular inversion algorithm based on the extended Euclidean algorithm and the plus-minus trick. In our algorithm, comparisons over large RNS values are replaced by cheap computations modulo 4. Comparisons to an RNS version based on Fermat’s little theorem were carried out. The number of elementary modular operations is(More)
The paper describes a new RNS modular multiplication algorithm for efficient implementations of ECC over FP . Thanks to the proposition of RNS-friendly Mersenne-like primes, the proposed RNS algorithm requires 2 times less moduli than the state-of-art ones, leading to 4 times less precomputations and about 2 times less operations. FPGA implementations of(More)
The paper describes a new RNS (residue number system) modular multiplication algorithm, for finite field arithmetic over FP , based on a reduced number of moduli in base extensions with only 3n/2moduli instead of 2n for standard ones. Our algorithm reduces both the number of elementary modular multiplications (EMMs) and the number of stored precomputations(More)
We propose an hybrid representation of large integers, or prime field elements, combining both positional and residue number systems (RNS). Our hybrid position-residues (HPR) number system mixes a high-radix positional representation and digits represented in RNS. RNS offers an important source of parallelism for addition, subtraction and multiplication(More)
  • 1