Implementation of Modular Exponentiation Using Montgomery Algorithms
نویسنده
چکیده
Several algorithms for Public Key Cryptography (PKC), such as RSA, Diffie-Hellman, and Elliptic Curve Cryptography are used for secure communications. These algorithms require modular exponentiation as their basic operation. Modular exponentiation implies repeated modular multiplication which is computationally very costly as the large operands are used. Therefore computation time is very large. This computation time can be reduced by Montgomery multiplication algorithm. Montgomery multiplication algorithm involves three basic phases 1. Conversion of operands from integer domain to Montgomery domain. 2. Multiplication of operands. 3. Conversion of operands back from Montgomery domain to integer domain. A architecture designed to implement Montgomery Modular exponentiation using right to left exponentiation approach, which allows the parallel execution of modular operations “square and multiplications”. The implementation of Montgomery modular exponentiation is achieved on Spartan3E, virtex4 and virtex6 series of FPGAs for 4, 8, 16 and 32 bits
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