Time-memory trade-off in Toom-Cook multiplication: an application to module-lattice based cryptography
نویسندگان
چکیده
منابع مشابه
Toom-Cook Multiplication: Some Theoretical and Practical Aspects
Toom-Cook multiprecision multiplication is a well-known multiprecision multiplication method, which can make use of multiprocessor systems. In this paper the Toom-Cook complexity is derived, some explicit proofs of the Toom-Cook interpolation method are given, the even-odd method for interpolation is explained, and certain aspects of a 32-bit C++ and assembler implementation, which is in develo...
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The use of Toom-Cook sub-quadratic polynomial multiplication was recently shown to be possible also when the coefficient field does not have elements enough, particularly for F2[x]. This paper focus on how Toom’s strategies can be adapted to polynomials on non-binary small fields. In particular we describe the Toom-3 algorithm for Fp[x] with p ∈ {3, 5, 7}, and some other unbalanced algorithms. ...
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Enumeration algorithms in lattices are a well-known technique for solving the Short Vector Problem (SVP) and improving blockwise lattice reduction algorithms. Here, we propose a new algorithm for enumerating lattice point in a ball of radius 1.156λ1(Λ) in time 3n+o(n), where λ1(Λ) is the length of the shortest vector in the lattice Λ. Then, we show how this method can be used for solving SVP an...
متن کاملTowards Optimal Toom-Cook Multiplication for Univariate and Multivariate Polynomials in Characteristic 2 and 0
Toom-Cook strategy is a well-known method for building algorithms to efficiently multiply dense univariate polynomials. Efficiency of the algorithm depends on the choice of interpolation points and on the exact sequence of operations for evaluation and interpolation. If carefully tuned, it gives the fastest algorithm for a wide range of inputs. This work smoothly extends the Toom strategy to po...
متن کاملTowards Optimal Toom-Cook Multiplication for Univariate and Multivariate Polynomials in Characteristic
Toom-Cook strategy is a well-known method for building algorithms to efficiently multiply dense univariate polynomials. Efficiency of the algorithm depends on the choice of interpolation points and on the exact sequence of operations for evaluation and interpolation. If carefully tuned, it gives the fastest algorithm for a wide range of inputs. This work smoothly extends the Toom strategy to po...
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ژورنال
عنوان ژورنال: IACR Transactions on Cryptographic Hardware and Embedded Systems
سال: 2020
ISSN: 2569-2925
DOI: 10.46586/tches.v2020.i2.222-244