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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 ]
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 ...
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 (where = for some constant >) is hard in a worst-case scenario. Average case problems are the problems that are hard to ...
Kyber is a key encapsulation mechanism (KEM) designed to be resistant to cryptanalytic attacks with future powerful quantum computers.It is used to establish a shared secret between two communicating parties without an attacker in the transmission system being able to decrypt it.
On the other hand, contrary to the most of public key cryptography, lattice-based cryptography allows security against subexponential quantum attacks. Most of the cryptosystems based on general lattices rely on the average-case hardness of the Learning with errors (LWE). Their scheme is based on a structured variant of LWE, that they call Ideal ...
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).
An early successful application of the LLL algorithm was its use by Andrew Odlyzko and Herman te Riele in disproving Mertens conjecture. [5]The LLL algorithm has found numerous other applications in MIMO detection algorithms [6] and cryptanalysis of public-key encryption schemes: knapsack cryptosystems, RSA with particular settings, NTRUEncrypt, and so forth.
The standard IEEE Std 1363.1, issued in 2008, standardizes lattice-based public-key cryptography, especially NTRUEncrypt. [ 12 ] The standard X9.98 standardizes lattice-based public-key cryptography, especially NTRUEncrypt, as part of the X9 standards for the financial services industry.
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