Computational problem possibly useful for post-quantum cryptography
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.[1] 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.[2] 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]).
^ abCite error: The named reference :0 was invoked but never defined (see the help page).
^Peikert, Chris (2014). "Lattice Cryptography for the Internet". In Mosca, Michele (ed.). Post-Quantum Cryptography. Lecture Notes in Computer Science. Vol. 8772. Springer International Publishing. pp. 197–219. CiteSeerX 10.1.1.800.4743. doi:10.1007/978-3-319-11659-4_12. ISBN 978-3-319-11658-7. S2CID 8123895.
and 22 Related for: Ring learning with errors information
In post-quantum cryptography, ringlearningwitherrors (RLWE) is a computational problem which serves as the foundation of new cryptographic algorithms...
In cryptography, learningwitherrors (LWE) is a mathematical problem that is widely used to create secure encryption algorithms. It is based on the idea...
problem known as Ringlearningwitherrors. Ringlearningwitherrors based digital signatures are among the post quantum signatures with the smallest public...
which they can use to encrypt messages between themselves. The ringlearningwitherrors key exchange (RLWE-KEX) is one of a new class of public key exchange...
for quantum computer attack resistant cryptography based on the RingLearningwithErrors. These cryptosystems are provably secure under the assumption...
reconciliation. Previous ringlearningwitherror key exchange schemes correct errors one coefficient at a time, whereas NewHope corrects errors 2 or 4 coefficients...
security of most of these schemes is based on the hardness of the (Ring) LearningWithErrors (RLWE) problem, except for the LTV and BLLN schemes that rely...
Regularized long-wave equation; see Benjamin–Bona–Mahony equation Ringlearningwitherrors Radio Limerick Weekly Echo, popular radio station broadcasting...
Deep learning is the subset of machine learning methods based on neural networks with representation learning. The adjective "deep" refers to the use of...
key-agreement algorithm for TLS that combines X25519 and NewHope, a ringlearningwitherrors primitive. Even if NewHope were to turn out to be compromised...
made ridiculous by the number of errors that were made throughout". Set in the Greek city of Ephesus, The Comedy of Errors tells the story of two sets of...
assumption of the ringlearningwitherrors (RLWE) problem, the ring variant of very promising lattice-based hard problem Learningwitherrors (LWE). Currently...
Perceptrons can be trained by a simple learning algorithm that is usually called the delta rule. It calculates the errors between calculated output and sample...
Discrimination learning is defined in psychology as the ability to respond differently to different stimuli. This type of learning is used in studies...
with the highest ring number). On most operating systems, Ring 0 is the level with the most privileges and interacts most directly with the physical hardware...
amiss. The system is based on the module learningwitherrors (M-LWE) problem, in conjunction with cyclotomic rings. Recently, there has also been a tight...
robust to errors such as an individual bit error (a 0 flips to 1 or vice versa) missed by error-correcting mechanisms. Eliminating such error-correcting...
of ringers attempt to ringwith their best striking. They are judged on their number of faults (striking errors); the band with the fewest faults wins...
of the error. Some scholars include only errors that result from a temporary failure to produce the word which the speaker intended. Such errors are sometimes...
Social learning refers to learning that is facilitated by observation of, or interaction with, another animal or its products. Social learning has been...