An improved Chen's parity detection technique for the twomoduli set
ABSTRACT This paper improved Chen's residue number system (RNS) parity detection technique such that the original twomoduli set {2(h)  1, 2(h) + 1} is extended to {2p  1, 2p + 1}, where h and p are positive integers. Given an RNS number X = (x(1), x(2)) based on the extended twomoduli set, it is found that the parity of X is (p mod 2) . y(0) circle plus y(1) if x1 >= x(2), where y(1)y(0) denotes the binary representation of x(1) + x(2) mod 4. On the contrary, if x(1) < x(2), the parity of X is (p mod 2) . y(0) circle plus (y(0) circle plus y(1)) over bar. Obviously, our parity technique, compared with Lu and Chiang's, can discover the parity of an RNS number without the table lookup and fractional number approaches.
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Article: a full RNS implementation of RSA
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ABSTRACT: We present the first implementation of RSA in the residue number system (RNS) which does not require any conversion, either from radix to RNS beforehand or RNS to radix afterward. Our solution is based on an optimized RNS version of Montgomery multiplication. Thanks to the RNS, the proposed algorithms are highly parallelizable and seem then well suited to hardware implementations. We give the computational procedure both parties must follow in order to recover the correct result at the end of the transaction (encryption or signature).IEEE Transactions on Computers 07/2004; DOI:10.1109/TC.2004.2 · 1.47 Impact Factor 
Article: Efficient Implementations of the Chinese Remainder Theorem for Sign Detection and Residue Decoding
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ABSTRACT: Two conversion techniques based on the Chinese remainder theorem are developed for use in residue number systems. The new implementations are fast and simple mainly because adders modulo a large and arbitrary integer M are effectively replaced by binary adders and possibly a lookup table of small address space. Although different in form, both techniques share the same principle that an appropriate representation of the summands must be employed in order to evaluate a sum modulo M efficiently. The first technique reduces the sum modulo M in the conversion formula to a sum modulo 2 through the use of fractional representation, which also exposes the sign bit of numbers. Thus, this technique is particularly useful for sign detection and for any operation requiring a comparison with a binary fraction of M. The other technique is preferable for the full conversion from residues to unsigned or 2's complement integers. By expressing the summands in terms of quotients and remainders with respect to a properly chosen divisor, the second technique systematically replaces the sum modulo M by two binary sums, one accumulating the quotients modulo a power of 2 and the other accumulating the remainders the ordinary way. A final recombination step is required but is easily implemented with a small lookup table and binary adders.IEEE Transactions on Computers 08/1985; DOI:10.1109/TC.1985.1676602 · 1.47 Impact Factor