b^{k}} can be defined for all integers k {\displaystyle k} , and the discrete logarithm log b ⁡ ( a ) {\displaystyle \log _{b}(a)} is an integer k {\displaystyle...

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

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...

increases the difficulty for an adversary attempting to compute the discrete logarithm and compromise the shared secret. These two values are chosen in this...

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...

(1985). "A Public-Key Cryptosystem and a Signature Scheme Based on Discrete Logarithms" (PDF). IEEE Transactions on Information Theory. 31 (4): 469–472...

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

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

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 inverse operation, the discrete logarithm. This has been used in various cryptographic protocols, see Discrete logarithm for details. When the nonzero...

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...

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

then the problem of solving discrete logarithm modulo p is in P. Therefore, for cryptosystems based on discrete logarithm, such as DSA, it is required...

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

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...

based on the mathematical concept of modular exponentiation and the discrete logarithm problem. In a public-key cryptosystem, a pair of private and public...

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

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

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...

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

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...

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

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

computer science. The framework captures problems such as factoring, discrete logarithm, graph isomorphism, and the shortest vector problem. This makes it...

based on the hardness of the discrete logarithm and related problems. However, both factoring and the discrete logarithm problem are known to be solvable...

Emmanuel Thomé, and Paul Zimmermann announced the computation of a discrete logarithm modulo the 240-digit (795 bit) prime RSA-240 + 49204 (the first safe...

algorithms, notably Shor's algorithm for factoring and computing the discrete logarithm, the quantum phase estimation algorithm for estimating the eigenvalues...

digital signature scheme which is based on the difficulty of computing discrete logarithms. It was described by Taher Elgamal in 1985. The ElGamal signature...

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