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The RSA numbers were generated on a computer with no network connection of any kind. The computer's hard drive was subsequently destroyed so that no record would exist, anywhere, of the solution to the factoring challenge. [6] The first RSA numbers generated, RSA-100 to RSA-500 and RSA-617, were labeled according to their number of decimal ...
The factoring challenge included a message encrypted with RSA-129. When decrypted using the factorization the message was revealed to be " The Magic Words are Squeamish Ossifrage ". In 2015, RSA-129 was factored in about one day, with the CADO-NFS open source implementation of number field sieve, using a commercial cloud computing service for ...
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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The decryption of the 1977 ciphertext involved the factoring of a 129-digit (426 bit) number, RSA-129, in order to recover the plaintext. Ron Rivest estimated in 1977 that factoring a 125-digit semiprime would require 40 quadrillion years, using the best algorithm known and the fastest computers of the day. [ 6 ]
RSA-110 is one of the RSA numbers, large semiprimes that are part of the RSA Factoring Challenge. In base 10, the number 110 is a Harshad number [ 2 ] and a self number . [ 3 ]
After a while the project attempted the RSA factoring challenge trying to factor RSA-640. After RSA-640 was factored by an outside team in November 2005, the project moved on to RSA-768. With the chance to succeed too small, it discarded the RSA challenges, was renamed to PrimeGrid, and started generating a list of the first prime numbers.
More specifically, the RSA problem is to efficiently compute P given an RSA public key (N, e) and a ciphertext C ≡ P e (mod N). The structure of the RSA public key requires that N be a large semiprime (i.e., a product of two large prime numbers), that 2 < e < N, that e be coprime to φ(N), and that 0 ≤ C < N.