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The RSA Factoring Challenge was a challenge put forward by RSA Laboratories on March 18, 1991 [1] ... The problem is to find these two primes, given only n.
Breaking RSA may be as difficult as factoring, D. Brown, 2005. This unrefereed preprint purports that solving the RSA problem using a Straight line program is as difficult as factoring provided e has a small factor. Breaking RSA Generically is Equivalent to Factoring, D. Aggarwal and U. Maurer, 2008.
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.
The first RSA numbers generated, from RSA-100 to RSA-500, were labeled according to their number of decimal digits. Later, beginning with RSA-576, binary digits are counted instead. An exception to this is RSA-617, which was created before the change in the numbering scheme.
The security of RSA relies on the practical difficulty of factoring the product of two large prime numbers, the "factoring problem". Breaking RSA encryption is known as the RSA problem. Whether it is as difficult as the factoring problem is an open question. [3] There are no published methods to defeat the system if a large enough key is used.
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).
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Important special cases include the Quadratic residuosity problem and the Decisional composite residuosity problem. As in the case of RSA, this problem (and its special cases) are conjectured to be hard, but become easy given the factorization of . Some cryptosystems that rely on the hardness of residuousity problems include: