Logical candidates for residue number system (RNS) implementations are applications which require very high data rates and are numerically intensive. The quadratic residue number system (QRNS) is specifically designed for fast complex arithmetic. In a previous paper by Dubois and Venetsanopoulos the use of Eisenstein complex numbers was proposed for the implementation of a radix-3 fast Fourier ...

This thesis investigates architectures for high speed signal convolution using residue number system techniques. The focus is on VLSI implementations, a choice that gives two parameters by which judge different architectures: speed and hardware size. Although the focus is on the standard residue number system, the same concepts can be directly applied to quadratic residue number system architec...

Graph Theory has been realized as one of the most useful branches of Mathematics of recent origin, finding widest applications in all most all branches of sciences, social sciences, and engineering and computer science. Nathanson[8] was the pioneer in introducing the concepts of NumberTheory, particularly, the “Theory of congruences” i n Graph Theory, thus paving way for the emergence of a new ...

Tidal energy is the most foreseeable form of renewable energy. Tidal energy can be harnessed by tidal barrage, tidal fence and tidal current technologies. Present efforts are focused on diffuser augmented tidal turbines that exploit the kinetic energy of the tidal currents. The power output by a tidal turbine is directly proportional to the cube of velocity of incoming fluid flow. Thus, even a ...

such that N is a solution to s of the congruences. (It is, of course, clear that no Ar can be a solution to more than s of the congruences (1).) Examples : On the one extreme there is the Sieve of Eratosthenes for finding all primes p in the range A = B12 ^ p < B, where ti = m, — 1 for all i. (Here to, are all the primes < Bl .) On the other extreme there is the Chinese remainder type of proble...

It has been known for some time that solving x2 = a (modn) is as difficult as factoring n, at least in the sense that the two problems are random polynomial time equivalent. By contrast, solving a bivariate quadratic congruence x2 ky2 = m (mod n) can usually be done in random polynomial time even if the factorization of n is unknown. This was first proved by Pollard and Schnorr in 1985 under th...

Deniable encryption, introduced in 1997 by Canetti, Dwork, Naor, and Ostrovsky, guarantees that the sender or the receiver of a secret message is able to “fake” the message encrypted in a specific ciphertext in the presence of a coercing adversary, without the adversary detecting that he was not given the real message. To date, constructions are only known either for weakened variants with sepa...