The Decision Linear assumption is a mathematical assumption used in elliptic curve cryptography

Elliptic curve cryptography

Elliptic curve cryptography is an approach to public-key cryptography based on the algebraic structure of elliptic curves over finite fields. The use of elliptic curves in cryptography was suggested independently by Neal Koblitz and Victor S...

. In particular, the DLIN assumption is useful in settings where the decisional Diffie–Hellman assumption does not hold (as is often the case in pairing-based cryptography

Pairing-based cryptography

Pairing-based cryptography is the use of a pairing between elements of two cryptographic groups to a third group to construct cryptographic systems. If the same group is used for the first two groups, the pairing is called symmetric and is a mapping from two elements of one group to an element from...

). The Decision Linear assumption was introduced by Boneh, Boyen, and Shacham .

Informally the DLIN assumption states that given , with random group elements and random exponents, it is hard to distinguish (for random ) from (for independently random ).