Big-Digits Representation and Its Application in Cryptography

The efficiency of number theory based cryptosystems correlatesdirectly to the efficiency of large integer multiplication operation. in this paper,we propose a hybrid of karatsuba-classical multiplication algorithm that is based on a look-up table of big-digits representation. the big-digits representation is a more compact representation compared to the binary representation. therefore,by using the big-digits representation,the number of sub-multiplication operations in a multiplication algorithm will reduce significantly. the results of this study show that the proposed multiplication algorithm,which is based on the big-digits representation,is faster than the classical,karatsuba and the hybrid of karatsuba- classical multiplication algorithms in range of the public-key cryptography implementation.