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. WebIn this article, we give a digital signature by using Lindner–Peikert cryptosystem. The security of this digital signature is based on the assumptions about hardness of Ring-LWE and Ring-SIS problems, along with providing public key and signature of
Ajtai lattice
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WebJun 4, 2012 · More precisely, secretkey decryptionsucceeds Anotherfeature lattice-basedconstruction [KSW08,LOS 10]constructions based bilinearmaps) nativelysupport inner product predicates over widerange (polynomial-size)fields, exponentiallylarge lattice-basedsystems has been noted elsewhere well,e.g., [BF11]. 1.1 Overview ourConstruction …
WebMay 25, 1999 · Ajtai recently found a random class of lattices of integer points for which he could prove the following worst-case/average-case equivalence result: If there is a probabilistic polynomial time algorithm which finds a short vector in a random lattice from the class, then there is also a probabilistic polynomial time algorithm which solves … WebA euclidean lattice is the set of all integer linear combinations of some n linearly independent vectors belonging to a euclidean space. There are many algorithmic problems related to lattices. ... Ajtai [1] proposed the first worst-case to average-case reduction for a lattice problem, by providing a reductionfromSIVP
WebJan 2, 2024 · Lattice CryptographyHard on average problems (Ajtai and LWE)Public Key Cryptosystems (Regev and GPV) ... x ∈ {0, 1}mOutput: fA(x) = Ax mod qmxT×nAfAxTheorem (Ajtai 96)For m > n lg q, if lattice problems (SIVP) are hard to approximatein the worst-case, then fA(x) = Ax mod q is a one-way function.Daniele … WebAjtai’s function and lattice problems Cryptanalysis (Inversion) Given A and y, nd small solution x 2f0;1gm to inhomogeneous linear system Ax = y (mod q) Inverting Ajtai’s …
WebApr 10, 2016 · For standard parameters, the shortest (in Euclidean norm) nonzero vectors in Ajtai's lattice have norm about $\sqrt{n \log q} \gg d = 1$. Thus, short vectors in Euclidean norm (which is what typical lattice-basis reduction algorithms deliver) may not be sufficient to yield a collision. Instead, finding a collision requires finding a shortest ...
Web15, 20]), none of them is based on the worst-case hardness of a lattice problem. Our main result is a new public key cryptosystem whose security is based on O(n1.5)-uSVP. In [1], Ajtai presented a family of one-way hash functions based on the worst-case hardness of several lattice problems. book cover boosterWeb(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 … book cover backgroundsWeblattice can be generated in polynomial time together with a short vector in it, and (b) assuming that certain worst-case lattice problems have no polynomial time solutions, … book cover buntingWebLattices 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 … book cover backsideAjtai 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 god of the empty graveWebSep 17, 1999 · The Ajtai random class of lattices. Ajtai has recently given a reduction from the problem of approximating a short basis for a lattice in the worst case, to the problem … book cover bookhttp://qikan.cqvip.com/Qikan/Article/Detail?id=7105041068 book cover clip art black and white