The residue number system (RNS) is a method for representing an integer x as n-tuple of its residues with respect to given set moduli. In RNS, addition, subtraction, and multiplication can be carried out by independent operations each modulus. Therefore, n-fold speedup achieved parallel processing. main disadvantage RNS that we cannot efficiently compare the magnitude two integers or determine ...

Nowadays RSA using Chinese Remainder Theorem (CRT) is widely used in practical applications. However there is a very powerful attack against it with a fault injection during one of its exponentiations. Many countermeasures were proposed but almost all of them are proven to be insecure. In 2005, two new countermeasures were proposed. However they still have a weakness. The final signature is sto...

In this paper we investigate the question whether a perfect matching can be isolated by a weighting scheme using Chinese Remainder Theorem (short: CRT). We give a systematical analysis to a method based on CRT suggested by Agrawal in a CCC’03-paper for testing perfect matchings. We show that this desired test-procedure is based on a deterministic weighting scheme which can be generalized in a n...

This paper analyzes a key recovery method for RSA signature generation or decryption implementations using the Chinese Remainder Theorem (CRT) speed up. The CRT-based RSA implementation is common in both low computing power devices and high speed cryptographic acceleration cards. This recovery method is designed to work in conjunction with a side-channel attack where the CRT exponents are disco...

We propose a simple, full-range carrier frequency offset (CFO) algorithm for coherent optical orthogonal frequency division multiplexing (CO-OFDM) systems. By applying the Chinese remainder theorem (CRT) to training symbol of single frequency, the proposed CFO algorithm has wide range with shorter training symbol. We numerically and experimentally demonstrate the performance of CRT-based algori...

Because the t-out-of-n oblivious transfer (OT) protocol can guarantee the privacy of both participants, i.e., the sender and the receiver, it has been used extensively in the study of cryptography. Recently, Chang and Lee presented a robust t-out-of-n OT protocol based on the Chinese remainder theorem (CRT). In this paper, we use the Aryabhata remainder theorem (ART) to achieve the functionalit...

The Rivest–Shamir–Adleman (RSA) cryptosystem is currently the most influential and commonly used algorithm in public-key cryptography. Whether security of RSA equivalent to intractability integer factorization problem an interesting issue mathematics Coron May solved above fundamental proved polynomial-time equivalence computing secret key factoring. They demonstrated that modulus N=pq can be f...