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Lattice-based cryptographic constructions hold a great promise for public-key post-quantum cryptography. [38] Indeed, the main alternative forms of public-key cryptography are schemes based on the hardness of factoring and related problems and schemes based on the hardness of the discrete logarithm and related problems.
In computer science, lattice problems are a class of optimization problems related to mathematical objects called lattices.The conjectured intractability of such problems is central to the construction of secure lattice-based cryptosystems: lattice problems are an example of NP-hard problems which have been shown to be average-case hard, providing a test case for the security of cryptographic ...
These ideas can be applied to a more realistic cryptography application. Peggy wants to prove to Victor that she knows the discrete logarithm of a given value in a given group. [11] For example, given a value y, a large prime p, and a generator , she wants to prove that she knows a value x such that g x ≡ y (mod p), without revealing x.
As a general rule, for 128 bits of security in a symmetric-key–based system, one can safely use key sizes of 256 bits. The best quantum attack against arbitrary symmetric-key systems is an application of Grover's algorithm, which requires work proportional to the square root of the size of the key space. To transmit an encrypted key to a ...
The Short Integer Solution (SIS) problem is an average case problem that is used in lattice-based cryptography constructions. Lattice-based cryptography began in 1996 from a seminal work by Ajtai [ 1 ] who presented a family of one-way functions based on the SIS problem.
NTRU is an open-source public-key cryptosystem that uses lattice-based cryptography to encrypt and decrypt data. It consists of two algorithms: NTRUEncrypt, which is used for encryption, and NTRUSign, which is used for digital signatures. Unlike other popular public-key cryptosystems, it is resistant to attacks using Shor's algorithm ...
BLISS (short for Bimodal Lattice Signature Scheme) is a digital signature scheme proposed by Léo Ducas, Alain Durmus, Tancrède Lepoint and Vadim Lyubashevsky in their 2013 paper "Lattice Signature and Bimodal Gaussians".
Public-key cryptosystems use a public key for encryption and a private key for decryption. Diffie–Hellman key exchange; RSA encryption; Rabin cryptosystem; Schnorr signature; ElGamal encryption; Elliptic-curve cryptography; Lattice-based cryptography; McEliece cryptosystem; Multivariate cryptography; Isogeny-based cryptography