What is discrete logarithm problem in cryptography?
Discrete logarithms are logarithms defined with regard to multiplicative cyclic groups. The discrete logarithm problem is defined as: given a group G, a generator g of the group and an element h of G, to find the discrete logarithm to the base g of h in the group G. Discrete logarithm problem is not always hard.
What encryption uses discrete logarithms?
ElGamal encryption
Popular choices for the group G in discrete logarithm cryptography (DLC) are the cyclic groups (Zp)× (e.g. ElGamal encryption, Diffie–Hellman key exchange, and the Digital Signature Algorithm) and cyclic subgroups of elliptic curves over finite fields (see Elliptic curve cryptography).
What is the use of discrete logarithm?
The term “discrete logarithm” is most commonly used in cryptography, although the term “generalized multiplicative order” is sometimes used as well (Schneier 1996, p. 501). In number theory, the term “index” is generally used instead (Gauss 1801; Nagell 1951, p.
What is the importance of discrete logarithms?
Aside from the intrinsic interest that the problem of computing discrete logarithms has, it is of considerable importance in cryptography. An efficient algorithm for discrete logarithms would make several authentication and key-exchange systems insecure.
What is the use of Discrete logarithm?
Is RSA based on Discrete logarithm?
RSA labs makes a similar statement: The discrete logarithm problem bears the same relation to these systems as factoring does to the RSA system: the security of these systems rests on the assumption that discrete logarithms are difficult to compute.
What is factorization problem in cryptography?
Prime Factorization (or integer factorization) is a commonly used mathematical problem often used to secure public-key encryption systems. A common practice is to use very large semi-primes (that is, the result of the multiplication of two prime numbers) as the number securing the encryption.
What is weak key cryptography?
In cryptography, a weak key is a key, which, used with a specific cipher, makes the cipher behave in some undesirable way. Nevertheless, it is considered desirable for a cipher to have no weak keys. A cipher with no weak keys is said to have a flat, or linear, key space.