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Lattice-based constructions support important standards of post-quantum cryptography. [1] Unlike more widely used and known public-key schemes such as the RSA , Diffie-Hellman or elliptic-curve cryptosystems — which could, theoretically, be defeated using Shor's algorithm on a quantum computer — some lattice-based constructions appear to be ...
The standard X9.98 standardizes lattice-based public-key cryptography, especially NTRUEncrypt, as part of the X9 standards for the financial services industry. [ 13 ] The PQCRYPTO project of the European Commission is considering standardization of the provably secure Stehle–Steinfeld version of NTRU.
IEEE P1363 is an Institute of Electrical and Electronics Engineers (IEEE) standardization project for public-key cryptography. It includes specifications for: Traditional public-key cryptography (IEEE Std 1363-2000 and 1363a-2004) Lattice-based public-key cryptography (IEEE Std 1363.1-2008) Password-based public-key cryptography (IEEE Std 1363. ...
Post-quantum cryptography (PQC), sometimes referred to as quantum-proof, quantum-safe, or quantum-resistant, is the development of cryptographic algorithms (usually public-key algorithms) that are currently thought to be secure against a cryptanalytic attack by a quantum computer.
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 ...
Craig Gentry, using lattice-based cryptography, described the first plausible construction for a fully homomorphic encryption scheme in 2009. [9] Gentry's scheme supports both addition and multiplication operations on ciphertexts, from which it is possible to construct circuits for performing arbitrary computation.
The lattice reduction attack is one of the best known and one of the most practical methods to break the NTRUEncrypt. In a way it can be compared to the factorization of the modulus in RSA. The most used algorithm for the lattice reduction attack is the Lenstra-Lenstra-Lovász algorithm.
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.