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

Algorithms

Integer factorization	Benaloh Blum–Goldwasser Cayley–Purser Damgård–Jurik GMR Goldwasser–Micali Naccache–Stern Paillier Rabin RSA Okamoto–Uchiyama Schmidt–Samoa
Discrete logarithm	BLS Cramer–Shoup DH DSA ECDH X25519 X448 ECDSA EdDSA Ed25519 Ed448 ECMQV EKE ElGamal signature scheme MQV Schnorr SPEKE SRP STS
Lattice/SVP/CVP/LWE/SIS	BLISS Kyber NewHope NTRUEncrypt NTRUSign RLWE-KEX RLWE-SIG
Others	AE CEILIDH EPOC HFE IES Lamport McEliece Merkle–Hellman Naccache–Stern knapsack cryptosystem Three-pass protocol XTR

Theory

Standardization

Topics

v t e Cryptography
General	History of cryptography Outline of cryptography Cryptographic protocol Authentication protocol Cryptographic primitive Cryptanalysis Cryptocurrency Cryptosystem Cryptographic nonce Cryptovirology Hash function Cryptographic hash function Key derivation function Digital signature Kleptography Key (cryptography) Key exchange Key generator Key schedule Key stretching Keygen Cryptojacking malware Ransomware Random number generation Cryptographically secure pseudorandom number generator (CSPRNG) Pseudorandom noise (PRN) Secure channel Insecure channel Subliminal channel Encryption Decryption End-to-end encryption Harvest now, decrypt later Information-theoretic security Plaintext Codetext Ciphertext Shared secret Trapdoor function Trusted timestamping Key-based routing Onion routing Garlic routing Kademlia Mix network
Mathematics	Cryptographic hash function Block cipher Stream cipher Symmetric-key algorithm Authenticated encryption Public-key cryptography Quantum key distribution Quantum cryptography Post-quantum cryptography Message authentication code Random numbers Steganography
Category

v t e 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

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