dual lattice of ℤ-latticedual basis of ℤ-lattice15A0315A0903B35In this article, we formalize in Mizar [5] the definition of dual lattice and their properties. We formally prove that a set of all dual vectors in a rational lattice has the construction of a lattice. We show that a ...
lattice struc ture of its submodule lattice. Citing Louis H. Rowen "this important example (the lattice of all the submodules of a module) is the raison d'etre for the study of lattice theory by ring theorists". Indeed, many module-theoretic results can be proved by using lattice ...
Module-Lattice -based Key Encapsulation Mechanism Standard by NIST i.e. FIPS 203. Motivation ML-KEM has been standardized by NIST as post-quantum secure key encapsulation mechanism (KEM), which can be used for key establishment, between two parties, communicating over insecure channel. ...
Module-Lattice-Based Digital Signature Standard by NIST i.e. FIPS 204. Motivation ML-DSA has been standardized by NIST as post-quantum secure digital signature algorithm (DSA), which can be used for verifying the authenticity of digital messages, giving recipient party confidence that the message...
certain parametrisations of Hawk this applies to secret key recovery and we reduce signature forgery in the random oracle model to a new problem called the one more short vector problem. Keywords: Post-Quantum Cryptography, Signatures, Module Lattice ...
In particular, the key and ciphertext sizes of our new construction are about half the size, the KEM offers CCA instead of only passive security, the security is based on a more general (and flexible) lattice problem, and our optimized implementation results in essentially the same running ...
Ring-SIS,andLWEwithRing-LWE,respectively.Weprovethat these average-case problems are at least as hard as standard lattice problems restricted tomodulelattices(whichthemselvesbridgearbitraryandideallattices).Asthesenewproblemsenlarge the toolbox of the lattice-based cryptographer, they could prove useful ...
certain parametrisations of Hawk this applies to secret key recovery and we reduce signature forgery in the random oracle model to a new problem called the one more short vector problem. Keywords: Post-Quantum Cryptography, Signatures, Module Lattice ...
Most lattice-based cryptographic schemes are built upon the assumed hardness of the Short Integer Solution (SIS) and Learning With Errors (LWE) problems. T... A Langlois,D Stehlé - 《Designs Codes & Cryptography》 被引量: 51发表: 2015年 Electrical Networks, Symplectic Reductions, and Applicat...