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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 .
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.
A deterministic encryption scheme (as opposed to a probabilistic encryption scheme) is a cryptosystem which always produces the same ciphertext for a given plaintext and key, even over separate executions of the encryption algorithm.
In cryptography, ciphertext or cyphertext is the result of encryption performed on plaintext using an algorithm, called a cipher. [1] Ciphertext is also known as encrypted or encoded information because it contains a form of the original plaintext that is unreadable by a human or computer without the proper cipher to decrypt it.
RSA (Rivest–Shamir–Adleman) is a public-key cryptosystem, one of the oldest widely used for secure data transmission. The initialism "RSA" comes from the surnames of Ron Rivest , Adi Shamir and Leonard Adleman , who publicly described the algorithm in 1977.
For example, in RSA blinding involves computing the blinding operation E(x) = (xr) e mod N, where r is a random integer between 1 and N and relatively prime to N (i.e. gcd(r, N) = 1), x is the plaintext, e is the public RSA exponent and N is the RSA modulus.
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 ]
In cryptography, key size or key length refers to the number of bits in a key used by a cryptographic algorithm (such as a cipher).. Key length defines the upper-bound on an algorithm's security (i.e. a logarithmic measure of the fastest known attack against an algorithm), because the security of all algorithms can be violated by brute-force attacks.