logarithm logb a is a number x such that bx = a. Analogously, in any group G, powers bk can be defined for all integers k, and the discrete logarithm...

elliptic-curve-based protocols, the base assumption is that finding the discrete logarithm of a random elliptic curve element with respect to a publicly known...

example, the complex logarithm is the multi-valued inverse of the complex exponential function. Similarly, the discrete logarithm is the multi-valued inverse...

multiple similar algorithms for solving the factoring problem, the discrete logarithm problem, and the period-finding problem. "Shor's algorithm" usually...

Discrete logarithm records are the best results achieved to date in solving the discrete logarithm problem, which is the problem of finding solutions x...

of the discrete logarithms of an + 1, called Zech's logarithms, for n = 0, ..., q − 2 (it is convenient to define the discrete logarithm of zero as being...

find a given only g, p and ga mod p. Such a problem is called the discrete logarithm problem. The computation of ga mod p is known as modular exponentiation...

of a certain problem in G {\displaystyle G} related to computing discrete logarithms. The algorithm can be described as first performing a Diffie–Hellman...

computing the discrete logarithm. Currently there are several popular groups for which no algorithm to calculate the underlying discrete logarithm in polynomial...

algorithm is a probabilistic algorithm for computing discrete logarithms. Dedicated to the discrete logarithm in ( Z / q Z ) ∗ {\displaystyle (\mathbb {Z} /q\mathbb...

integer factorization, discrete logarithm, and elliptic curve discrete logarithm. DL/ECKAS-DH1 and DL/ECKAS-DH2 (Discrete Logarithm/Elliptic Curve Key Agreement...

and its logarithm can be computed with probability 1/poly(n) in polynomial time. Then loggx ≡ loggxgB - B (mod |G|) and the discrete logarithm is self-reducible...

mathematics which have discrete versions, such as discrete calculus, discrete Fourier transforms, discrete geometry, discrete logarithms, discrete differential...

lambda algorithm, see Naming below) is an algorithm for solving the discrete logarithm problem. The algorithm was introduced in 1978 by the number theorist...

algorithm for computing the discrete logarithm or order of an element in a finite abelian group by Daniel Shanks. The discrete log problem is of fundamental...

ciphers are based on the difficulty of factoring integers or the discrete logarithm problem, both of which can be solved by Shor's algorithm. In particular...

problems are intractable, such as the integer factorization or the discrete logarithm problems, so there are deep connections with abstract mathematics...

problem. The CDH assumption involves the problem of computing the discrete logarithm in cyclic groups. The CDH problem illustrates the attack of an eavesdropper...

Binary logarithm Bode plot Henry Briggs Bygrave slide rule Cologarithm Common logarithm Complex logarithm Discrete logarithm Discrete logarithm records...

for very large integers. On the other hand, computing the modular discrete logarithm – that is, finding the exponent e when given b, c, and m – is believed...

the first whose security is based on the intractability of certain discrete logarithm problems. It is efficient and generates short signatures. It was covered...

having selected it), unless that party can solve the elliptic curve discrete logarithm problem. Bob's private key is similarly secure. No party other than...

computational Diffie–Hellman problem. Two variants of IES are specified: Discrete Logarithm Integrated Encryption Scheme (DLIES) and Elliptic Curve Integrated...

is computationally inexpensive, whereas the inverse operation, the discrete logarithm, is computationally expensive. More precisely, if g is a primitive...

based on the mathematical concept of modular exponentiation and the discrete logarithm problem. In a public-key cryptosystem, two keys are generated: data...

problems: the integer factorization problem, the discrete logarithm problem or the elliptic-curve discrete logarithm problem. All of these problems could be easily...

computational hardness assumption about a certain problem involving discrete logarithms in cyclic groups. It is used as the basis to prove the security of...

v t e Public-key cryptography Algorithms Theory Discrete logarithm cryptography Elliptic-curve cryptography Hash-based cryptography Non-commutative cryptography...

v t e Public-key cryptography Algorithms Theory Discrete logarithm cryptography Elliptic-curve cryptography Hash-based cryptography Non-commutative cryptography...

Cryptosystem and A Signature Scheme Based on Discrete Logarithms" proposed the design of the ElGamal discrete log cryptosystem and of the ElGamal signature...