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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.
In cryptography, security level is a measure of the strength that a cryptographic primitive — such as a cipher or hash function — achieves. Security level is usually expressed as a number of "bits of security" (also security strength), [1] where n-bit security means that the attacker would have to perform 2 n operations to break it, [2] but other methods have been proposed that more ...
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 ...
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.
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.
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.
Finding modular multiplicative inverses also has practical applications in the field of cryptography, e.g. public-key cryptography and the RSA algorithm. [ 3 ] [ 4 ] [ 5 ] A benefit for the computer implementation of these applications is that there exists a very fast algorithm (the extended Euclidean algorithm ) that can be used for the ...
The difficulty of computing φ(n) without knowing the factorization of n is thus the difficulty of computing d: this is known as the RSA problem which can be solved by factoring n. The owner of the private key knows the factorization, since an RSA private key is constructed by choosing n as the product of two (randomly chosen) large primes p and q.