Decision Linear assumption

The Decision Linear (DLIN) assumption is a computational hardness assumption used in elliptic curve cryptography. 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.^[1]

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

References

↑ Dan Boneh, Xavier Boyen, Hovav Shacham: Short Group Signatures. CRYPTO 2004: 41–55

Public-key cryptography

Algorithms

Integer Factorization	Benaloh Blum–Goldwasser Cayley–Purser Damgård–Jurik GMR Goldwasser–Micali Paillier Rabin RSA Okamoto–Uchiyama Schmidt–Samoa

Discrete logarithm	Cramer–Shoup DH DSA ECDH ECDSA EdDSA EKE ElGamal signature scheme MQV Schnorr SPEKE SRP STS

Others	AE CEILIDH EPOC HFE IES Lamport McEliece Merkle–Hellman Naccache–Stern Naccache–Stern knapsack cryptosystem NTRUEncrypt NTRUSign Three-pass protocol XTR

Theory

Standardization

Topics

Cryptography

History of cryptography Cryptanalysis Outline of cryptography

Symmetric-key algorithm Block cipher Stream cipher Public-key cryptography Cryptographic hash function Message authentication code Random numbers Steganography

Portal

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