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Coppersmith's attack describes a class of cryptographic attacks on the public-key cryptosystem RSA based on the Coppersmith method.Particular applications of the Coppersmith method for attacking RSA include cases when the public exponent e is small or when partial knowledge of a prime factor of the secret key is available.
Mask generation functions were first proposed as part of the specification for padding in the RSA-OAEP algorithm. The OAEP algorithm required a cryptographic hash function that could generate an output equal in size to a "data block" whose length was proportional to arbitrarily sized input message. [1]
The method uses the Lenstra–Lenstra–Lovász lattice basis reduction algorithm (LLL) to find a polynomial that has the same zeroes as the target polynomial but smaller coefficients. In cryptography, the Coppersmith method is mainly used in attacks on RSA when parts of the secret key are known and forms a base for Coppersmith's attack.
Comparison of implementations of message authentication code (MAC) algorithms. A MAC is a short piece of information used to authenticate a message—in other words, to confirm that the message came from the stated sender (its authenticity) and has not been changed in transit (its integrity).
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.
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.
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 minimum number of the group's members act together to pool their knowledge.
For example, given b = 5, e = 3 and m = 13, dividing 5 3 = 125 by 13 leaves a remainder of c = 8. Modular exponentiation can be performed with a negative exponent e by finding the modular multiplicative inverse d of b modulo m using the extended Euclidean algorithm .