GMR (cryptography)

In cryptography, GMR is a digital signature algorithm named after its inventors Shafi Goldwasser, Silvio Micali and Ron Rivest.

As with RSA the security of the system is related to the difficulty of factoring very large numbers. But, in contrast to RSA, GMR is secure against adaptive chosen-message attacks, which is the currently accepted security definition for signature schemes— even when an attacker receives signatures for messages of his choice, this does not allow them to forge a signature for a single additional message.

External links[edit]

Goldwasser, Shafi; Micali, Silvio; Rivest, Ronald L. (April 1988). "A Digital Signature Scheme Secure Against Adaptive Chosen-Message Attacks" (PDF). SIAM Journal on Computing. 17 (2): 281–308. doi:10.1137/0217017. S2CID 1715998. Retrieved 26 October 2022.

Public-key cryptography

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
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