Sub-group hiding

The sub-group hiding assumption is a computational hardness assumption used in elliptic curve cryptography and pairing-based cryptography.

It was first introduced in[1] to build a 2-DNF homomorphic encryption scheme.

References

Dan Boneh, Eu-Jin Goh, Kobbi Nissim: Evaluating 2-DNF Formulas on Ciphertexts. TCC 2005: 325–341

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Computational hardness assumptions
Number theoretic	Integer factorization Phi-hiding RSA problem Strong RSA Quadratic residuosity Decisional composite residuosity Higher residuosity
Group theoretic	Discrete logarithm Diffie-Hellman Decisional Diffie–Hellman Computational Diffie–Hellman
Pairings	External Diffie–Hellman Sub-group hiding Decision linear
Lattices	Shortest vector problem (gap) Closest vector problem (gap) Learning with errors Ring learning with errors Short integer solution
Non-cryptographic	Exponential time hypothesis Unique games conjecture Planted clique conjecture