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The RSA Factoring Challenge was a challenge put forward by RSA Laboratories on March 18, 1991 [1] to encourage research into computational number theory and the practical difficulty of factoring large integers and cracking RSA keys used in cryptography.
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.
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.
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.
A TI-83+ graphing calculator displaying a sine wave. The Texas Instruments signing key controversy resulted from Texas Instruments' (TI) response to a project to factorize the 512-bit RSA cryptographic keys needed to write custom firmware to TI devices.
The RSA scheme; The finite-field Diffie–Hellman key exchange; The elliptic-curve Diffie–Hellman key exchange [10] RSA can be broken if factoring large integers is computationally feasible. As far as is known, this is not possible using classical (non-quantum) computers; no classical algorithm is known that can factor integers in polynomial ...
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.