- 期刊
A New Modular Multiplication Method and Its Application in RSA Cryptosystem
摘要
Modular multiplication is a very important fundamental operation in exponentiation based cryptography. Any problem of security, high cost or speed of a cryptosystem is based on modular exponentiation. Modular exponentiation is realized by a series of modular multiplications. Therefore the performances of an exponentiation based cryptosystem can be increased by using a fast modular multiplication algorithm. In this paper a new modular multiplication algorithm is presented with showing the algorithm is faster than the previous algorithms. The proposed algorithm is based on the following two ideas. The remainder in regard to n can be constructed from the remainder with modulus (n+1)/2 and the remainder with modulus (n-1)/2. It often happen that (n+1)/2 and (n-1)/2 can easily be factorized, even if n is a prime number or difficult to be prime factorized. Then, the Chinese Remainder Theorem can be applied to the remainder calculation with those numbers as the modulus.
延伸閱讀
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