Computer algebra : Primality testing and integer factorisation
نویسنده
چکیده
منابع مشابه
Computer 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 کاملPrimality Testing and Integer Factorisation
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 factorisati...
متن کاملBacktracking 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 کامل18.703 Modern Algebra, A Quick Primality Test
Prime numbers are one of the most basic objects in mathematics and one of the most basic questions is to decide which numbers are prime (a clearly related problem is to find the prime factorisation of a number). Given a number n one would like a quick way to decide if n is prime, say using a computer. Quick can be given a precise meaning. First one measures the complexity by the number of digit...
متن کاملSome Primality Testing Algorithms
We describe the primality testing algorithms in use in some popular computer algebra systems, and give some examples where they break down in practice.
متن کامل