Discrete logarithm records

Discrete logarithm records are the best results achieved to date in solving the discrete logarithm problem, which is the problem of finding solutions ${\displaystyle x}$ to the equation ${\displaystyle g^{x}=h}$ given elements ${\displaystyle g}$ and ${\displaystyle h}$ of a finite cyclic group ${\displaystyle G}$. The difficulty of this problem is the basis for the security of several cryptographic systems, including Diffie–Hellman key agreement, ElGamal encryption, the ElGamal signature scheme, the Digital Signature Algorithm, and the elliptic curve cryptography analogues of these. Common choices for ${\displaystyle G}$ used in these algorithms include the multiplicative group of integers modulo ${\displaystyle p}$, the multiplicative group of a finite field, and the group of points on an elliptic curve over a finite field.