Ajtai lattice
WebJan 1, 2006 · Recently, Ajtai discovered a fascinating connection between the worst-case complexity and the average-case complexity of some wellknown lattice problems. Later, Ajtai and Dwork proposed a cryptosystem inspired by Ajtai's work, provably secure if a particular lattice problem is difficult in the worst-case. WebAbstract. Lattices have received considerable attention as a potential source of computational hardness to be used in cryptography, after a breakthrough result of Ajtai …
Ajtai lattice
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WebMay 24, 2024 · The research of lattice-based cryptography dates back to the seminal work of Ajtai [ 2 ], which first based the security of cryptographic primitives on the difficulty of solving some lattice problems such as the approximate shortest vector problem and the closest vector problem. WebA sieve algorithm for the shortest lattice vector problem (Ajtai, Kumar & Sivakumar - STOC 2001) which provably solves SVP in the Euclidean norm. It holds a special place in the historical development of lattice algorithms as the first method to solve a hard lattice problem in single exponential time 2 O (n) 2^{O(n)}.
WebLattices have also played an important role in cryptography where they are more often used for showing weaknesses of cryptographic algorithms. However, new public key systems … WebWe study a relaxed notion of lattice trapdoor called approximate trapdoor, which is defined to be able to invert Ajtai’s one-way function approximately instead of exactly. The primary moti-vation of our study is to improve the efficiency of the cryptosystems built from lattice trapdoors, including the hash-and-sign signatures.
Web4 Ajtai M. Generating hard instances of lattice problems[C] //Proc of the 28th Annual ACM Symposium on Theory of Computing . New York:ACM Press, 1996:99-108. New York:ACM Press, 1996:99-108. 5 Nguyen P Q. WebLattice-based cryptography is the generic term for constructions of cryptographic primitives that involve lattices, either in the construction itself or in the security proof. Lattice-based …
WebMay 22, 2005 · Previous lattice-based public-key cryptosystems such as the one by Ajtai and Dwork were only based on unique-SVP, a special case of SVP. The new cryptosystem is much more efficient than previous cryptosystems: the public key is of size Õ ( n 2 ) and encrypting a message increases its size by Õ ( n )(in previous cryptosystems these …
Ajtai received his Candidate of Sciences degree in 1976 from the Hungarian Academy of Sciences. Since 1995 he has been an external member of the Hungarian Academy of Sciences. In 1998 he was an Invited Speaker of the International Congress of Mathematicians in Berlin. In 2012 he was elected as … See more Miklós Ajtai (born 2 July 1946) is a computer scientist at the IBM Almaden Research Center, United States. In 2003, he received the Knuth Prize for his numerous contributions to the field, including a classic See more 1. Ajtai, M. (September 1979). "Isomorphism and higher order equivalence". Annals of Mathematical Logic. 16 (3): 181–203. See more • Miklós Ajtai home page • Miklós Ajtai publications indexed by Microsoft Academic • Miklós Ajtai at the Mathematics Genealogy Project See more One of Ajtai's results states that the length of proofs in propositional logic of the pigeonhole principle for n items grows faster than any polynomial in n. He also proved that the … See more • Ajtai, Miklós (10 May 2008). "Optimal lower bounds for the Korkine-Zolotareff parameters of a lattice and for Schnorr's algorithm for the shortest vector problem". Theory of Computing. 4: 21–51. doi:10.4086/toc.2008.v004a002. • Ajtai, Miklós (5 October 2005). … See more shapes with 4 lettersWebGenerating Hard Instances of Lattice Problems. M. Ajtai. Published 1996. Mathematics, Computer Science. Electron. Colloquium Comput. Complex. We give a random class of … shapes with 2 pairs of parallel linesWebLattice-based cryptography offers a great deal of promise for the most realistic, stable post-quantum cryptosystem, with the worst-case/average-case minimization as seen by Ajtai and Dwork , along with certain lattice concerns that are shown to be NP-Hard . While several lattice-based cryptosystems improve simplicity, scalability, and ... shapes with 4 straight sidesWebApr 11, 2024 · I know that when the domain is { 0, 1 } m in function h ( x) = A x for A ← $ Z q n × m, this function is called Ajtai hash function. So when the domain is extended to Z q m, is it also called Ajtai hash function? When the domain is extended to Z q m it is no longer collision resistant, so one should be careful in what one means by "hash ... shapes with 3 horizontal sidesWeblattice: [noun] a framework or structure of crossed wood or metal strips. a window, door, or gate having a lattice. a network or design resembling a lattice. poocher swampWebMay 4, 1997 · Ajtai, Generating Hard Instances of Lattice Problems, Proceedings 28th Annual ACM Symposium on Theory of Computing, 1996 2. M. Ajtai, C. Dwork, A Public-Key Cryptosystem with Average-Case/Worst-Case Equivalence, Electronic Colloquium on Computational Complexity TR96-065, http:// www.eccc.uni-trier.de/ eccc-local/Lists/TR- … shapes with 4 square unitsWeb(Lattice) Cryptography The Short Integer Solution (SIS) Problem Ajtai’s one-way function (SIS) Parameters: m;n;q 2Z Key: A 2Zn m q Input: x 2f0;1gm Output: f A(x) = Ax mod q m … pooches in the ballpark