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Post-quantum Cryptography
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. Most widely used public-key algorithms rely on the difficulty of one of three mathematical problems: the integer factorization problem, the discrete logarithm problem or the elliptic-curve discrete logarithm problem. All of these problems could be easily solved on a sufficiently powerful quantum computer running Shor's algorithm or possibly alternatives. As of 2024, quantum computers lack the processing power to break widely used cryptographic algorithms; however, because of the length of time required for migration to quantum-safe cryptography, cryptographers are already designing new algorithms to prepare for Y2Q or Q-Day, the day when current algorithms will be vulnerable to quantum computing atta ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cryptographic Primitive
Cryptographic primitives are well-established, low-level cryptography, cryptographic algorithms that are frequently used to build cryptographic protocols for computer security systems. These routines include, but are not limited to, one-way hash functions and cipher, encryption functions. Rationale When creating cryptosystem, cryptographic systems, system designer, designers use cryptographic primitives as their most basic building blocks. Because of this, cryptographic primitives are designed to do one very specific task in a precisely defined and highly reliable fashion. Since cryptographic primitives are used as building blocks, they must be very reliable, i.e. perform according to their specification. For example, if an encryption routine claims to be only breakable with number of computer operations, and it is broken with significantly fewer than operations, then that cryptographic primitive has failed. If a cryptographic primitive is found to fail, almost every protocol t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Grover's Algorithm
In quantum computing, Grover's algorithm, also known as the quantum search algorithm, is a quantum algorithm for unstructured search that finds with high probability the unique input to a black box function that produces a particular output value, using just O(\sqrt) evaluations of the function, where N is the size of the function's domain of a function, domain. It was devised by Lov Grover in 1996. The analogous problem in classical computation would have a query complexity O(N) (i.e., the function would have to be evaluated O(N) times: there is no better approach than trying out all input values one after the other, which, on average, takes N/2 steps). Charles H. Bennett (physicist), Charles H. Bennett, Ethan Bernstein, Gilles Brassard, and Umesh Vazirani proved that any quantum solution to the problem needs to evaluate the function \Omega(\sqrt) times, so Grover's algorithm is Asymptotically optimal algorithm, asymptotically optimal. Since classical algorithms for NP-completenes ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Merkle Signature Scheme
In hash-based cryptography, the Merkle signature scheme is a digital signature scheme based on Merkle trees (also called hash trees) and one-time signatures such as the Lamport signature scheme. It was developed by Ralph Merkle in the late 1970s and is an alternative to traditional digital signatures such as the Digital Signature Algorithm or RSA. NIST has approved specific variants of the Merkle signature scheme in 2020. An advantage of the Merkle signature scheme is that it is believed to be resistant against attacks by quantum computers. The traditional public key algorithms, such as RSA and ElGamal would become insecure if an effective quantum computer could be built (due to Shor's algorithm). The Merkle signature scheme, however, only depends on the existence of secure hash function A hash function is any Function (mathematics), function that can be used to map data (computing), data of arbitrary size to fixed-size values, though there are some hash functions t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lamport Signature
In cryptography, a Lamport signature or Lamport one-time signature scheme is a method for constructing a digital signature. Lamport signatures can be built from any cryptographically secure one-way function; usually a cryptographic hash function is used. Although the potential development of quantum computers threatens the security of many common forms of cryptography such as RSA, it is believed that Lamport signatures with large hash functions would still be secure in that event. Each Lamport key can only be used to sign a single message. However, many Lamport signatures can be handled by one Merkle hash tree, thus a single hash tree key can be used for many messages, making this a fairly efficient digital signature scheme. The Lamport signature cryptosystem was invented in 1979 and named after its inventor, Leslie Lamport. Example Alice has a 256-bit cryptographic hash function and some kind of secure random number generator. She wants to create and use a Lamport key pair ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Unbalanced Oil And Vinegar
In cryptography, the unbalanced oil and vinegar (UOV) scheme is a modified version of the oil and vinegar scheme designed by J. Patarin. Both are digital signature protocols. They are forms of multivariate cryptography. The security of this signature scheme is based on an NP-hard mathematical problem. To create and validate signatures, a minimal quadratic equation system must be solved. Solving equations with variables is NP-hard. While the problem is easy if is either much much larger or much much smaller than , importantly for cryptographic purposes, the problem is thought to be difficult in the average case when and are nearly equal, even when using a quantum computer. Multiple signature schemes have been devised based on multivariate equations with the goal of achieving quantum resistance. A significant drawback with UOV is that the key size can be large. Typically , the number of variables, is chosen to be double , the number of equations. Encoding the coefficients of a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
BLISS Signature Scheme
BLISS (short for Bimodal Lattice Signature Scheme) is a digital signature scheme proposed by Léo Ducas, Alain Durmus, Tancrède Lepoint and Vadim Lyubashevsky in their 2013 paper "Lattice Signature and Bimodal Gaussians". In cryptography, a digital signature ensures that a message is authentically from a specific person who has the private key to create such a signature, and can be verified using the corresponding public key. Current signature schemes rely either on integer factorization, discrete logarithm or elliptic curve discrete logarithm problem, all of which can be effectively attacked by a quantum computer. BLISS on the other hand, is a post-quantum algorithm, and is meant to resist quantum computer attacks. Compared to other post-quantum schemes, BLISS claims to offer better computational efficiency, smaller signature size, and higher security. presentationonce anticipated that BLISS would become a potential candidate for standardization, however it was not submitted to ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
NTRUSign
NTRUSign, also known as the NTRU Signature Algorithm, is an NTRU public-key cryptography digital signature algorithm based on the GGH signature scheme. The original version of NTRUSign was Polynomial Authentication and Signature Scheme (PASS), and was published at CrypTEC'99. The improved version of PASS was named as NTRUSign, and was presented at the rump session of Asiacrypt 2001 and published in peer-reviewed form at the RSA Conference 2003. The 2003 publication included parameter recommendations for 80-bit security. A subsequent 2005 publication revised the parameter recommendations for 80-bit security, presented parameters that gave claimed security levels of 112, 128, 160, 192 and 256 bits, and described an algorithm to derive parameter sets at any desired security level. NTRU Cryptosystems, Inc. have applied for a patent on the algorithm. NTRUSign involves mapping a message to a random point in 2''N''-dimensional space, where ''N'' is one of the NTRUSign parameters, and s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
GGH Encryption Scheme
The Goldreich–Goldwasser–Halevi (GGH) lattice-based cryptosystem is a broken asymmetric cryptosystem based on lattices. There is also a GGH signature scheme which hasn't been broken as of 2024. The Goldreich–Goldwasser–Halevi (GGH) cryptosystem makes use of the fact that the closest vector problem can be a hard problem. This system was published in 1997 by Oded Goldreich, Shafi Goldwasser, and Shai Halevi, and uses a trapdoor one-way function which relies on the difficulty of lattice reduction. The idea included in this trapdoor function is that, given any basis for a lattice, it is easy to generate a vector which is close to a lattice point, for example taking a lattice point and adding a small error vector. But to return from this erroneous vector to the original lattice point a special basis is needed. The GGH encryption scheme was cryptanalyzed (broken) in 1999 by . Nguyen and Oded Regev had cryptanalyzed the related GGH signature scheme in 2006. Operation ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
NTRU
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. NTRUEncrypt was patented, but it was placed in the public domain in 2017. NTRUSign is patented, but it can be used by software under the GPL. History The first version of the system, which was called NTRU, was developed in 1996 by mathematicians Jeffrey Hoffstein, Jill Pipher, and Joseph H. Silverman. That same year, the developers of NTRU joined with Daniel Lieman and founded the company NTRU Cryptosystems, Inc., and were given a patent on the cryptosystem. The name "NTRU", chosen for the company and soon applied to the system as well, was originally derived from the pun ''Number Theorists 'R' Us'' or, alternatively, stood for ''Number T ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ring Learning With Errors Signature
Digital signatures are a means to protect digital information from intentional modification and to authenticate the source of digital information. Public key cryptography provides a rich set of different cryptographic algorithms the create digital signatures. However, the primary public key signatures currently in use ( RSA and Elliptic Curve Signatures) will become completely insecure if scientists are ever able to build a moderately sized quantum computer. Post quantum cryptography is a class of cryptographic algorithms designed to be resistant to attack by a quantum cryptography. Several post quantum digital signature algorithms based on hard problems in lattices are being created replace the commonly used RSA and elliptic curve signatures. A subset of these lattice based scheme are based on a problem known as Ring learning with errors. Ring learning with errors based digital signatures are among the post quantum signatures with the smallest public key and signature sizes ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ring Learning With Errors Key Exchange
In cryptography, a public key exchange algorithm is a cryptographic algorithm which allows two parties to create and share a secret key, which they can use to encrypt messages between themselves. The ring learning with errors key exchange (RLWE-KEX) is one of a new class of public key exchange algorithms that are designed to be secure against an adversary that possesses a quantum computer. This is important because some public key algorithms in use today will be easily broken by a quantum computer if such computers are implemented. RLWE-KEX is one of a set of post-quantum cryptographic algorithms which are based on the difficulty of solving certain mathematical problems involving lattices. Unlike older lattice based cryptographic algorithms, the RLWE-KEX is provably reducible to a known hard problem in lattices. Background Since the 1980s the security of cryptographic key exchanges and digital signatures over the Internet has been primarily based on a small number of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ideal Lattice Cryptography
In discrete mathematics, ideal lattices are a special class of lattices and a generalization of cyclic lattices. Ideal lattices naturally occur in many parts of number theory, but also in other areas. In particular, they have a significant place in cryptography. Micciancio defined a generalization of cyclic lattices as ideal lattices. They can be used in cryptosystems to decrease by a square root the number of parameters necessary to describe a lattice, making them more efficient. Ideal lattices are a new concept, but similar lattice classes have been used for a long time. For example, cyclic lattices, a special case of ideal lattices, are used in NTRUEncrypt and NTRUSign. Ideal lattices also form the basis for quantum computer attack resistant cryptography based on the Ring Learning with Errors. These cryptosystems are provably secure under the assumption that the shortest vector problem (SVP) is hard in these ideal lattices. Introduction In general terms, ideal lattices are ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
