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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.
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 ...
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 ...
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 ...
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.
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
In general terms, ideal lattices are lattices corresponding to ideals in rings of the form [] / for some irreducible polynomial of degree . [1] All of the definitions of ideal lattices from prior work are instances of the following general notion: let be a ring whose additive group is isomorphic to (i.e., it is a free -module of rank), and let be an additive isomorphism mapping to some lattice ...