Probabilistic algorithm for testing primality pdf

For many applications a randomized algorithm is the fastest algorithm available, or the simp Abstract - Cited by 36 self - Add to MetaCart Randomized algorithms, once viewed as a tool in computational number theory, have by now found widespread application. For many applications a randomized algorithm is the fastest algorithm available, or the simplest, or both.

A randomized algorithm is an algorithm that uses random numbers to influence the choices it makes in the course of its computation. Thus its behavior typically quantified as running time or quality of output varies from. Rivest , We present a digital signature scheme based on the computational diculty of integer factorization. The scheme possesses the novel property of being robust against an adaptive chosen-message attack: an adversary who receives signatures for messages of his choice where each message may be chosen in a Abstract - Cited by 40 self - Add to MetaCart We present a digital signature scheme based on the computational diculty of integer factorization.

The scheme possesses the novel property of being robust against an adaptive chosen-message attack: an adversary who receives signatures for messages of his choice where each message may be chosen in a way that depends on the signatures of previously chosen messages can not later forge the signature of even a single additional message. This may be somewhat surprising, since the properties of having forgery being equivalent to factoring and being invulnerable to an adaptive chosen-message attack were considered in the folklore to be contradictory.

The new scheme is potentially practical: signing and verifying signatures are reasonably fast, and signatures are compact.

Citation Context We present three alternative simple constructions of small probability spaces on n bits for which any k bits are almost independent. Abstract - Cited by 40 self - Add to MetaCart We present three alternative simple constructions of small probability spaces on n bits for which any k bits are almost independent. An additional advantage of our constructions is their simplicity. The NP-completeness column: an ongoing guide by David S. This is the nineteenth edition of a usually quarterly column that covers new developments in the theory of NP-completeness.

The presentation is modeled on that used by M. Abstract - Cited by 0 self - Add to MetaCart This is the nineteenth edition of a usually quarterly column that covers new developments in the theory of NP-completeness. The theorem states that, if p is prime, then where.

In such situations, a is referred to as a Fermat liar. As suggested earlier, we can minimize this probability by repeating the process k times and selecting k witnesses. This allows us to improve the probability of correctly determining the primality of p by performing k iterations, in which the probability of error becomes vanishingly small for large values of k.

Nonetheless, being probabilistic in nature, this algorithm is inherently nondeterministic , which is really just a fancy way of saying we can get different results on different runs for the same input. Only within the last decade has a deterministic, polynomial-time algorithm for testing primality been developed. In , the AKS primality test was discovered, moving primality into the P complexity class. Try busting that out at an interview. For the mathematically inclined of which I do not consider myself , primality presents some interesting uses and even more interesting problems.

In terms of on-the-hoof interview answers, variations on the Newton-Raphson method convergent scaled binary-chop — square of double versus square of half are occasionally given. Your email address will not be published. Has PDF. Publication Type. More Filters. Computation of prime numbers by using a probabilistic algorithm. The algorithm is then compiled and run on the Pascal programming language. If the algorithm determines … Expand.

Primality Testing — A Deterministic Algorithm. Primality Testing and Factoring. Computer Science, Mathematics. Realistic Analysis of Some Randomized Algorithms. A New Probabilistic Primality Test. In this paper, a new general probabilistic primality test is presented. The estimated efficiency of the test turns out to be inferior to that of the Miller—Rabin test.

However, some heuristic … Expand. Realistic analysis of some randomized algorithms. Prime numbers are extremely useful, and are an essential input to many algorithms in large part due to the algebraic structure of arithmetic modulo a prime.

In everyday life, perhaps the most … Expand.