NTRUSign

NTRUSign, also known as the NTRU Signature Algorithm, is a public key cryptography digital signature algorithm based on the GGH signature scheme. It was first presented at the rump session of Asiacrypt 2001 and published in peer-reviewed form at the RSA Conference 2003. The 2003 publication included parameter recommendations for 80-bit security. A subsequent 2005 publication revised the parameter recommendations for 80-bit security, presented parameters that gave claimed security levels of 112, 128, 160, 192 and 256 bits, and described an algorithm to derive parameter sets at any desired security level. NTRU Cryptosystems, Inc. have applied for a patent on the algorithm.

NTRUSign involves mapping a message to a random point in 2N-dimensional space, where N is one of the NTRUSign parameters, and solving the closest vector problem in a lattice closely related to the NTRUEncrypt lattice. This lattice has the property that a private 2N-dimensional basis for the lattice can be described with 2 vectors, each with N coefficients, and a public basis can be described with a single N-dimensional vector. This enables public keys to be represented in O(N) space, rather than O(N²) as is the case with other lattice-based signature schemes. Operations take O(N²) time, as opposed to O(N³) for elliptic curve cryptography and RSA private key operations. NTRUSign is therefore claimed to be faster than those algorithms at low security levels, and considerably faster at high security levels.

NTRUSign is under consideration for standardization by the IEEE P1363 working group.

Security

NTRUSign is not a zero-knowledge signature scheme and a transcript of signatures leaks information about the private key, as first observed by Gentry and Szydlo.^[1] Nguyen and Regev demonstrated in 2006 that for the original unperturbed NTRUSign parameter sets an attacker can recover the private key with as few as 400 signatures.^[2]

The current proposals use perturbations to increase the transcript length required to recover the private key: the signer displaces the point representing the message by a small secret amount before the signature itself is calculated. NTRU claimed that at least 2³⁰ signatures are needed, and probably considerably more, before a transcript of perturbed signatures enabled any useful attack. In 2012 an attack on the scheme with perturbations was presented that required a few thousand signatures for standard security parameters.^[3]

External links

References

↑ http://www.szydlo.com/ntru-revised-full02.pdf
↑ P. Nguyen and O. Regev, "Learning a Parallelepiped: Cryptanalysis of GGH and NTRU Signatures", available from ftp://ftp.di.ens.fr/pub/users/pnguyen/FullLEARNING.pdf
↑ Ducas, Léo; Nguyen, Phong (2012). "Learning a Zonotope and More: Cryptanalysis of NTRUSign Countermeasures" (PDF). ASIACRYPT 2012. LNCS. Springer. pp. 433–450. doi:10.1007/978-3-642-34961-4_27. Retrieved 2013-03-07.

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

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

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