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Post-quantum
In cryptography, post-quantum cryptography (sometimes referred to as quantum-proof, quantum-safe or quantum-resistant) refers to cryptographic algorithms (usually public-key algorithms) that are thought to be secure against a cryptanalytic attack by a quantum computer. The problem with currently popular algorithms is that their security relies on one of three hard 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. Even though current quantum computers lack processing power to break any real cryptographic algorithm, many cryptographers are designing new algorithms to prepare for a time when quantum computing becomes a threat. This work has gained greater attention from academics and industry through the PQCrypto conference series since 2006 and more recently by several workshops on ... [...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 publi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Learning With Errors
Learning with errors (LWE) is the computational problem of inferring a linear n-ary function f over a finite ring from given samples y_i = f(\mathbf_i) some of which may be erroneous. The LWE problem is conjectured to be hard to solve, and thus to be useful in cryptography. More precisely, the LWE problem is defined as follows. Let \mathbb_q denote the ring of integers modulo q and let \mathbb_q^n denote the set of n- vectors over \mathbb_q . There exists a certain unknown linear function f:\mathbb_q^n \rightarrow \mathbb_q, and the input to the LWE problem is a sample of pairs (\mathbf,y), where \mathbf\in \mathbb_q^n and y \in \mathbb_q, so that with high probability y=f(\mathbf). Furthermore, the deviation from the equality is according to some known noise model. The problem calls for finding the function f, or some close approximation thereof, with high probability. The LWE problem was introduced by Oded Regev in 2005 (who won the 2018 Gödel Prize for this work), it is a g ... [...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] |
Quantum Computing
Quantum computing is a type of computation whose operations can harness the phenomena of quantum mechanics, such as superposition, interference, and entanglement. Devices that perform quantum computations are known as quantum computers. Though current quantum computers may be too small to outperform usual (classical) computers for practical applications, larger realizations are believed to be capable of solving certain computational problems, such as integer factorization (which underlies RSA encryption), substantially faster than classical computers. The study of quantum computing is a subfield of quantum information science. There are several models of quantum computation with the most widely used being quantum circuits. Other models include the quantum Turing machine, quantum annealing, and adiabatic quantum computation. Most models are based on the quantum bit, or "qubit", which is somewhat analogous to the bit in classical computation. A qubit can be in a 1 or 0 quantum s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cryptography
Cryptography, or cryptology (from grc, , translit=kryptós "hidden, secret"; and ''graphein'', "to write", or ''-logia'', "study", respectively), is the practice and study of techniques for secure communication in the presence of adversarial behavior. More generally, cryptography is about constructing and analyzing protocols that prevent third parties or the public from reading private messages. Modern cryptography exists at the intersection of the disciplines of mathematics, computer science, information security, electrical engineering, digital signal processing, physics, and others. Core concepts related to information security ( data confidentiality, data integrity, authentication, and non-repudiation) are also central to cryptography. Practical applications of cryptography include electronic commerce, chip-based payment cards, digital currencies, computer passwords, and military communications. Cryptography prior to the modern age was effectively synonymo ... [...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 all ... [...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. Vadim Lyubashevsky.Lattice-Based Identification Schemes Secure Under Active Attacks In ''Proceedings of the Practice and theory in public key cryptography , 11th international conference on Public key cryptography'', 2008. 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 b ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Grover's Algorithm
In quantum computing, Grover's algorithm, also known as the quantum search algorithm, refers to 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. It was devised by Lov Grover in 1996. The analogous problem in classical computation cannot be solved in fewer than O(N) evaluations (because, on average, one has to check half of the domain to get a 50% chance of finding the right input). 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. Since classical algorithms for NP-complete problems require exponentially many steps, and Grover's algorithm provides at most a quadratic speedup over the classical solution for un ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Shor's Algorithm
Shor's algorithm is a quantum algorithm, quantum computer algorithm for finding the prime factors of an integer. It was developed in 1994 by the American mathematician Peter Shor. On a quantum computer, to factor an integer N , Shor's algorithm runs in polynomial time, meaning the time taken is polynomial in \log N , the size of the integer given as input. Specifically, it takes quantum logic gate, quantum gates of order O \! \left((\log N)^ (\log \log N) (\log \log \log N) \right) using fast multiplication, or even O \! \left((\log N)^ (\log \log N) \right) utilizing the asymptotically fastest multiplication algorithm currently known due to Harvey and Van Der Hoven, thus demonstrating that the integer factorization problem can be efficiently solved on a quantum computer and is consequently in the complexity class BQP. This is almost exponentially faster than the most efficient known classical factoring algorithm, the ge ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Public-key Cryptosystem
Public-key cryptography, or asymmetric cryptography, is the field of cryptographic systems that use pairs of related keys. Each key pair consists of a public key and a corresponding private key. Key pairs are generated with cryptographic algorithms based on mathematical problems termed one-way functions. Security of public-key cryptography depends on keeping the private key secret; the public key can be openly distributed without compromising security. In a public-key encryption system, anyone with a public key can encrypt a message, yielding a ciphertext, but only those who know the corresponding private key can decrypt the ciphertext to obtain the original message. For example, a journalist can publish the public key of an encryption key pair on a web site so that sources can send secret messages to the news organization in ciphertext. Only the journalist who knows the corresponding private key can decrypt the ciphertexts to obtain the sources' messages—an eavesdropp ... [...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 Th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Johannes Buchmann
Johannes Alfred Buchmann (born November 20, 1953, in Cologne) is a German computer scientist, mathematician and professor emeritus at the department of computer science of the Technische Universität Darmstadt. He is known for his research in algorithmic number theory, algebra, post-quantum cryptography and IT security. In 1993, he received the Gottfried Wilhelm Leibniz Prize together with Claus-Peter Schnorr for his work in algorithmic number theory and cryptography. Buchmann also developed the stateful hash-based signature scheme XMSS, the first future-proof secure and practical signature scheme with minimal security requirements, which was declared the first international standard for post-quantum signature schemes in 2018. In addition, he further developed IT security research in Germany. His efforts led to the creation of ATHENE, the largest research center for IT security in Europe. For this he received the Konrad Zuse Medal for Services to Computer Science of the Gese ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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