The RSA cryptosystem is one of the widely used public key systems. The security of it is based on the intractability of factoring a large composite integer into two component primes, which is referred to as the RSA assumption. So far, the Quadratic Sieve (QS) is the fastest and general-purpose method for factoring composite numbers having less than about 110 digits. In this paper, we present ou...

1. Proof. (a) Let x ∈ [0, 1] and δ > 0, we want to show that there exist n such that nλ mod 1 ∈ (x−δ, x+δ), for which it suffices to show that there exists n0 and y ∈ (−δ, δ) such that n0λ ≡ y (mod 1). Then take n to be an appropriate multiple of n0. To prove the reduced proposition, choose m such that 10−m < δ. Note that there exist n1 < n2 such that (n1λ mod 1) and (n2λ mod 1) have the same f...

This paper describes the audio-visual database collected at AT&T Labs{Research for the study of bimodal speech recognition. To date, this database consists of two multiple speaker parts, namely isolated confusable words and connected letters, thus allowing the study of some popular and relatively simple speaker independent audio-visual recognition tasks. In addition, a single speaker connected ...

In this paper, the authors propose an algorithm to find all the minimal signed digit (MSD) representations of a constant and present an algorithm to synthesize digital filters based on the MSD representation. The hardware complexity of a digital signal processing system is dependent on the number system used for the implementation. Although the canonical signed digit (CSD) representation is wid...

Fairly complicated data structures, other than a string of binary digits, as chromosome representations of genetic algorithms (GAs) have been tried, and published, by various researchers. How to choose an appropriate representation for a GA problem is not only necessary, but also a critical step. Once the genome 1 is not a string of binary digits, the recombination operators have to be re-defin...

A multi-layer neural network with multiple hidden layers was trained as an autoencoder using steepest descent, scaled conjugate gradient and alopex algorithms. These algorithms were used in different combinations with steepest descent and alopex used as pretraining algorithms followed by training using scaled conjugate gradient. All the algorithms were also used to train the autoencoders withou...

The process of transcribing a language represented in its spatial form graphical characters into symbolic representation is called handwriting recognition. Each script has collection or letters, often known as symbols, that all share the same fundamental shapes. Handwriting analysis aims to correctly identify input images before being analysed by various automated systems. Recent research image...