Decision Linear assumption

The Decision Linear (DLIN) assumption is a mathematical assumption used in elliptic curve cryptography^[1]. 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). The Decision Linear assumption was introduced by Boneh, Boyen, and Shacham ^[2].

Informally the DLIN assumption states that given ${\displaystyle (f, \, g, \, f^x, \, g^y)}$, with ${\displaystyle f, \, g}$ random group elements and ${\displaystyle x, \, y}$ random exponents, it is hard to distinguish ${\displaystyle (h, \, h^{x+y})}$ (for random ${\displaystyle h}$) from ${\displaystyle (h, \, h')}$ (for independently random ${\displaystyle h, \, h'}$).

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