The sub-group hiding assumption is a computational hardness assumption used in
elliptic curve cryptography
Elliptic-curve cryptography (ECC) is an approach to public-key cryptography based on the algebraic structure of elliptic curves over finite fields. ECC allows smaller keys compared to non-EC cryptography (based on plain Galois fields) to provide e ...
and
pairing-based cryptography Pairing-based cryptography is the use of a pairing between elements of two cryptographic groups to a third group with a mapping e :G_1 \times G_2 \to G_T to construct or analyze cryptographic systems.
Definition
The following definition is commonly ...
.
It was first introduced in
[Dan Boneh, Eu-Jin Goh, Kobbi Nissim: Evaluating 2-DNF Formulas on Ciphertexts. TCC 2005: 325–341] to build a
2-DNF homomorphic encryption
Homomorphic encryption is a form of encryption that permits users to perform computations on its encrypted data without first decrypting it. These resulting computations are left in an encrypted form which, when decrypted, result in an identical ...
scheme.
See also
*
Non-interactive zero-knowledge proof
Non-interactive zero-knowledge proofs are zero-knowledge proofs where information between a prover and a verifier can be authenticated by the prover, without revealing any of the specific information beyond the validity of the transaction itself. T ...
References
Computational hardness assumptions
Elliptic curve cryptography
Pairing-based cryptography
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