A polynomial, A(z), can be represented by a polynomial residue system and, given enough independent residues, the polynomial can be reconstituted from its residues by the Chinese remainder theorem (CRT). A special case occurs when the discrete Fourier transform and its inverse realise the residue evaluations and CRT respectively, in which case the residue system is realised by the action of a m...

Based on the Chinese Remainder Theorem (CRT), Quisquater and Couvreur proposed an RSA variant, RSA-CRT, to speed up RSA decryption. Then, Wiener suggested another RSA variant, Rebalanced RSA-CRT, to further accelerate RSA-CRT decryption by shifting decryption cost to encryption cost. However, such an approach makes RSA encryption very timeconsuming because the public exponent e in Rebalanced RS...

Location perception has become a quality in mobile systems, where a wide range of set of rulesand applications require dataof the placeof the contributingnodes. In lackof a priori trustworthy nodes the discovery and confirmationof fellow citizen positions becomes mainly challenging in the occurrenceof adversaries directing at injuring the system. In this paper, we reportthis exposedissue by sug...

The efficiency of decryption process of Multi prime RSA, in which the modulus contains more than two primes, can be speeded up using Chinese remainder theorem (CRT). On the other hand, to achieve the same level of security in terms integer factorization problem the length of RSA modulus must be larger than the traditional RSA case. In [9], authors studied the RSA public key cryptosystem in a sp...

A novel quantum group signature scheme is proposed based on Chinese Remainder Theorem (CRT), in order to improve the security of quantum signature. The generation and verification of the signature can be successfully conducted only if all the participants cooperate with each other and with the message owner's and the arbitrator's help. The quantum parallel algorithm is applied to efficiently co...

In communication systems corruption of data and hacking of data is unavoidable. These are the major problems we are facing in communication system. This paper presents an enhanced multiple error detection and correction scheme based on the Redundant Residue Number System (RRNS). RRNS is often used in parallel processing environments because of its ability to increase the robustness of informati...

We present the algorithm to multiply univariate polynomials with integer coefficients efficiently using the Number Theoretic transform (NTT) on Graphics Processing Units (GPU). The same approach can be used to multiply large integers encoded as polynomials. Our algorithm exploits fused multiply-add capabilities of the graphics hardware. NTT multiplications are executed in parallel for a set of ...

Embedded devices performing RSA signatures are subject to Fault Attacks, particularly when the Chinese Remainder Theorem is used. In most cases, the modular exponentiation and the Garner recombination algorithms are targeted. To thwart Fault Attacks, we propose a new generic method of computing modular exponentiation and we prove its security in a realistic fault model. By construction, our pro...

RSA is a well-known algorithm that is used in various cryptographic systems like smart cards and e-commerce applications. This article presents practical attacks on implementations of RSA that use the Chinese Remainder Theorem (CRT). The attacks have been performed by inducing faults into a cryptographic device through optical and electromagnetic injections. We show optical attacks using fibre-...