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  2. RSA problem - Wikipedia

    en.wikipedia.org/wiki/RSA_problem

    The most efficient method known to solve the RSA problem is by first factoring the modulus N, a task believed to be impractical if N is sufficiently large (see integer factorization). The RSA key setup routine already turns the public exponent e , with this prime factorization, into the private exponent d , and so exactly the same algorithm ...

  3. RSA (cryptosystem) - Wikipedia

    en.wikipedia.org/wiki/RSA_(cryptosystem)

    The RSA problem is defined as the task of taking e th roots modulo a composite n: recovering a value m such that c ≡ m e (mod n), where (n, e) is an RSA public key, and c is an RSA ciphertext. Currently the most promising approach to solving the RSA problem is to factor the modulus n .

  4. Modular exponentiation - Wikipedia

    en.wikipedia.org/wiki/Modular_exponentiation

    It is useful in computer science, especially in the field of public-key cryptography, where it is used in both Diffie–Hellman key exchange and RSA public/private keys. Modular exponentiation is the remainder when an integer b (the base) is raised to the power e (the exponent), and divided by a positive integer m (the modulus); that is, c = b ...

  5. RSA numbers - Wikipedia

    en.wikipedia.org/wiki/RSA_numbers

    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.

  6. RSA Factoring Challenge - Wikipedia

    en.wikipedia.org/wiki/RSA_Factoring_Challenge

    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.

  7. Wiener's attack - Wikipedia

    en.wikipedia.org/wiki/Wiener's_attack

    In the RSA cryptosystem, Bob might tend to use a small value of d, rather than a large random number to improve the RSA decryption performance. However, Wiener's attack shows that choosing a small value for d will result in an insecure system in which an attacker can recover all secret information, i.e., break the RSA system.

  8. Shamir's secret sharing - Wikipedia

    en.wikipedia.org/wiki/Shamir's_secret_sharing

    Shamir's secret sharing (SSS) is an efficient secret sharing algorithm for distributing private information (the "secret") among a group. The secret cannot be revealed unless a quorum of the group acts together to pool their knowledge.

  9. Computational hardness assumption - Wikipedia

    en.wikipedia.org/wiki/Computational_hardness...

    Given a composite number , exponent and number := (), the RSA problem is to find . The problem is conjectured to be hard, but becomes easy given the factorization of n {\displaystyle n} . In the RSA cryptosystem , ( n , e ) {\displaystyle (n,e)} is the public key , c {\displaystyle c} is the encryption of message m {\displaystyle m} , and the ...