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In post-quantum cryptography, ring learning with errors (RLWE) is a computational problem which serves as the foundation of new cryptographic algorithms, such as NewHope, designed to protect against cryptanalysis by quantum computers and also to provide the basis for homomorphic encryption. Public-key cryptography relies on construction of mathematical problems that are believed to be hard to solve if no further information is available, but are easy to solve if some information used in the problem construction is known. Some problems of this sort that are currently used in cryptography are at risk of attack if sufficiently large quantum computers can ever be built, so resistant problems are sought. Homomorphic encryption is a form of encryption that allows computation on ciphertext, such

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rdfs:label	Ring learning with errors (en) Обучение с ошибками в кольце (ru)
rdfs:comment	In post-quantum cryptography, ring learning with errors (RLWE) is a computational problem which serves as the foundation of new cryptographic algorithms, such as NewHope, designed to protect against cryptanalysis by quantum computers and also to provide the basis for homomorphic encryption. Public-key cryptography relies on construction of mathematical problems that are believed to be hard to solve if no further information is available, but are easy to solve if some information used in the problem construction is known. Some problems of this sort that are currently used in cryptography are at risk of attack if sufficiently large quantum computers can ever be built, so resistant problems are sought. Homomorphic encryption is a form of encryption that allows computation on ciphertext, such (en) Обучение с ошибками в кольце (англ. Ring learning with errors, RLWE) — это вычислительная задача, которая была сформулирована как вариант более общей задачи обучения с ошибками (с англ. LWE), с целью использовать преимущество дополнительной алгебраической структуры (т.е. кольца многочленов) из теории решёток, что дало возможность повысить и расширить возможности шифрования тех криптографических приложений, которые ранее основывались на LWE. Задача RLWE стала основой новых криптографических алгоритмов, предназначенных для защиты данных от криптоанализа квантовыми компьютерами, а также важным применением для построения схем гомоморфного шифрования. По причине того, что предполагаемая трудность решения задачи RLWE очень высока даже на квантовом компьютере, криптография на её основе может стат (ru)
dcterms:subject	Cryptography Computational hardness assumptions Computational problems Lattice-based cryptography Post-quantum cryptography
Wikipage page ID	45588368 (xsd:integer)
Wikipage revision ID	1103527916 (xsd:integer)
Link from a Wikipage to another Wikipage	Algorithm Cyclotomic polynomial Uniform norm Integer factorization Quotient ring Cryptography Gaussian function NP-hard Cryptanalysis Computational hardness assumptions Computational problem Feige–Fiat–Shamir identification scheme Key size Post-quantum cryptography Public-key cryptography Irreducible polynomial Learning with errors Finite field Discrete logarithm Computational problems Homomorphic encryption Lattice-based cryptography Post-quantum cryptography Polynomial ring RSA (cryptosystem) Shortest vector problem NewHope Polynomials Bits of security Quantum computers
sameAs	Ring learning with errors Ring learning with errors Ring learning with errors Ring learning with errors Ring learning with errors
dbp:wikiPageUsesTemplate	dbt:Failed_verification dbt:Main dbt:Reflist dbt:Short_description dbt:Technical dbt:Computational_hardness_assumptions
has abstract	In post-quantum cryptography, ring learning with errors (RLWE) is a computational problem which serves as the foundation of new cryptographic algorithms, such as NewHope, designed to protect against cryptanalysis by quantum computers and also to provide the basis for homomorphic encryption. Public-key cryptography relies on construction of mathematical problems that are believed to be hard to solve if no further information is available, but are easy to solve if some information used in the problem construction is known. Some problems of this sort that are currently used in cryptography are at risk of attack if sufficiently large quantum computers can ever be built, so resistant problems are sought. Homomorphic encryption is a form of encryption that allows computation on ciphertext, such as arithmetic on numeric values stored in an encrypted database. RLWE is more properly called learning with errors over rings and is simply the larger learning with errors (LWE) problem specialized to polynomial rings over finite fields. Because of the presumed difficulty of solving the RLWE problem even on a quantum computer, RLWE based cryptography may form the fundamental base for public-key cryptography in the future just as the integer factorization and discrete logarithm problem have served as the base for public key cryptography since the early 1980s. 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 the NP-hard shortest vector problem (SVP) in a lattice (a polynomial-time reduction from the SVP problem to the RLWE problem has been presented). (en) Обучение с ошибками в кольце (англ. Ring learning with errors, RLWE) — это вычислительная задача, которая была сформулирована как вариант более общей задачи обучения с ошибками (с англ. LWE), с целью использовать преимущество дополнительной алгебраической структуры (т.е. кольца многочленов) из теории решёток, что дало возможность повысить и расширить возможности шифрования тех криптографических приложений, которые ранее основывались на LWE. Задача RLWE стала основой новых криптографических алгоритмов, предназначенных для защиты данных от криптоанализа квантовыми компьютерами, а также важным применением для построения схем гомоморфного шифрования. По причине того, что предполагаемая трудность решения задачи RLWE очень высока даже на квантовом компьютере, криптография на её основе может стать основополагающей криптографией с открытым ключом в будущем, так же как и задачи целочисленной факторизации и дискретного логарифмирования послужили основой для криптографии с открытым ключом в начале 1980-х годов. Следует отметить, что RLWE может быть аппроксимирована задачей нахождения кратчайшего вектора на идеальных решётках, которые представляют собой математически структурированные решётки, соответствующие идеалам в кольце. (ru)
prov:wasDerivedFrom	wikipedia-en:Ring_learning_with_errors?oldid=1103527916&ns=0
page length (characters) of wiki page	20213 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Ring_learning_with_errors
is Link from a Wikipage to another Wikipage of	Oded Regev (computer scientist) Post-quantum cryptography Lattice-based cryptography RLWE HEAAN Ring Learning with Errors Homomorphic encryption CECPQ1 NewHope Ring learning with errors key exchange Ring learning with errors signature Ring-LWE
is Wikipage redirect of	Ring Learning with Errors Ring-LWE
is Wikipage disambiguates of	RLWE
is foaf:primaryTopic of	wikipedia-en:Ring_learning_with_errors

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