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Lattice-based cryptography is the generic term for constructions of cryptographic primitives that involve lattices, either in the construction itself or in the security proof. Lattice-based constructions support important standards of post-quantum cryptography . [ 1 ]
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 ...
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 ...
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. NTRUSign is claimed to be faster than those algorithms at low security levels, and considerably faster at high security levels.
The NTRUEncrypt public key cryptosystem, also known as the NTRU encryption algorithm, is an NTRU lattice-based alternative to RSA and elliptic curve cryptography (ECC) and is based on the shortest vector problem in a lattice (which is not known to be breakable using quantum computers).
Lattice-based cryptography began in 1996 from a seminal work by Miklós Ajtai [1] who presented a family of one-way functions based on SIS problem. He showed that it is secure in an average case if the shortest vector problem S V P γ {\displaystyle \mathrm {SVP} _{\gamma }} (where γ = n c {\displaystyle \gamma =n^{c}} for some constant c > 0 ...
An important feature of basing cryptography on the ring learning with errors problem is the fact that the solution to the RLWE problem can be used to solve a version of the shortest vector problem (SVP) in a lattice (a polynomial-time reduction from this SVP problem to the RLWE problem has been presented [1]).
In 1999, Nguyen [1] showed that the GGH encryption scheme has a flaw in the design. He showed that every ciphertext reveals information about the plaintext and that the problem of decryption could be turned into a special closest vector problem much easier to solve than the general CVP.