Primality Testing and Integer Factorisation
نویسنده
چکیده
The problem of finding the prime factors of large composite numbers has always been of mathematical interest. With the advent of public key cryptosystems it is also of practical importance, because the security of some of these cryptosystems, such as the Rivest-Shamir-Adelman (RSA) system, depends on the difficulty of factoring the public keys. In recent years the best known integer factorisation algorithms have improved greatly, to the point where it is now easy to factor a 60-decimal digit number, and possible to factor numbers larger than 120 decimal digits, given the availability of enough computing power. We describe several recent algorithms for primality testing and factorisation, give examples of their use and outline some applications.
منابع مشابه
Backtracking Based Integer Factorisation, Primality Testing and Square Root Calculation
Breaking a big integer into two factors is a famous problem in the field of Mathematics and Cryptography for years. Many crypto-systems use such a big number as their key or part of a key with the assumption it is too big that the fastest factorisation algorithms running on the fastest computers would take impractically long period of time to factorise. Hence, many efforts have been provided to...
متن کاملComputer algebra — a beginners course using SAGE Universität Hannover , WS 2012
1 Integer arithmetic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 2 Divisibility . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 3 Modular arithmetic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 4 The RSA cryptosystem . . . . . . . . . . . . . . . . . . . . . . . . . . 7 5 Primality testing . . . . . . . . . . . . . . . . . . . . . . . . . . . ....
متن کاملApplied Number Theory
A prime number is an integer bigger than l that has no factor except l and itself . A number that is not prime is called composite. The primality testing problem is to decide whether a given integer is prime or composite. It is considered to be well solved, in contrast to ine factoring problem, which asks for the factorization of a given integer into prime factors. As an example of what can be ...
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