A fast residue arithmetic circuit using a complement of modulus in a signed-digit (SD) number representation is proposed. For a large modulus M with a length of (p+1)-bit used as a keg in RSA public-keg crypto-system, a complement of M, M=2{sup}p-M, with the p-digit SD number representation is used to calculate the modular operations. Thus, a modular addition can be implemented by using two SD adders, one for SD addition and another for the modular operation with the complement M. A modular multiplication is performed by repeating the modular shift and the modular addition operations in a radix-two SD number representation. By using a booth recording method, the speed of a modular multiplication becomes twice as fast as. The circuit design and simulation results by VHDL show that high speed RSA public-keg encryption processor can be implemented by applying the presented residue arithmetic circuit.
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