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Integer factorization is the process of determining which prime numbers divide a given positive integer.Doing this quickly has applications in cryptography.The difficulty depends on both the size and form of the number and its prime factors; it is currently very difficult to factorize large semiprimes (and, indeed, most numbers that have no small factors).
A general-purpose factoring algorithm, also known as a Category 2, Second Category, or Kraitchik family algorithm, [10] has a running time which depends solely on the size of the integer to be factored. This is the type of algorithm used to factor RSA numbers. Most general-purpose factoring algorithms are based on the congruence of squares method.
Occasionally it may cause the algorithm to fail by introducing a repeated factor, for instance when is a square. But it then suffices to go back to the previous gcd term, where gcd ( z , n ) = 1 {\displaystyle \gcd(z,n)=1} , and use the regular ρ algorithm from there.
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The factoring challenge was intended to track the cutting edge in integer factorization. A primary application is for choosing the key length of the RSA public-key encryption scheme. Progress in this challenge should give an insight into which key sizes are still safe and for how long. As RSA Laboratories is a provider of RSA-based products ...
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