Diffie-Hellman (disambiguation)

Diffie-Hellman (DH) refers to one of the following.

Assumptions in a cyclic group $\mathbb{G}=⟨g⟩$:

• Computational Diffie-Hellman (CDH) — given $(g,g^a,g^b)$, compute $g^{ab}$.
• Decisional Diffie-Hellman (DDH) — distinguish $(g,g^a,g^b,g^{ab})$ from $(g,g^a,g^b,g^c)$.
• Discrete logarithm (DLOG) — given $(g,g^a)$, compute $a$.

Assumptions in bilinear groups:

• co-CDH — CDH across the two source groups of an asymmetric pairing.
• Bilinear Diffie-Hellman (BDH, DBDH) — computational and decisional problems in the target group.
• $q$-Strong Diffie-Hellman ($q$-SDH) — given $(g,g^{\tau },\dots ,g^{{\tau }^q})$, output $(c,g^{1/(\tau +c)})$.

Other:

• Supersingular Isogeny Diffie-Hellman (SIDH) — an isogeny-based assumption, broken by a classical polynomial-time key-recovery attack — CD22.
• Key exchange — the Diffie-Hellman key exchange protocol — DH76.