## Tables from this paper

## 101 Citations

Fast arithmetic for faster integer multiplication

- Computer Science, MathematicsArXiv
- 2015

This work obtains the same result K = 4 using simple modular arithmetic as a building block, and a careful complexity analysis, based on a conjecture about the existence of sufficiently many primes of a certain form.

Fast integer multiplication using generalized Fermat primes

- Computer Science, Mathematics
- 2015

An alternative algorithm, which relies on arithmetic modulo generalized Fermat primes, is used to obtain conjecturally the same result K = 4 via a careful complexity analysis in the deterministic multitape Turing model.

Faster Polynomial Multiplication over Finite Fields

- Computer Science, MathematicsJ. ACM
- 2017

This work establishes the bound Mp(n) = O(n log n 8log* n log p), where log* n = min{k ϵ N: log …k×… log n ≤ 1} stands for the iterated logarithm.

Faster polynomial multiplication over nite elds

- Computer Science, Mathematics

The case that R is the nite eld Fp=Z/pZ for some prime p, the standard bit complexity model based on deterministic multitape Turing machines is more realistic in this setting, as it takes into account the dependence on p.

A babystep-giantstep method for faster deterministic integer factorization

- Computer ScienceMath. Comput.
- 2018

This paper combines Strassen's approach with a babystep-giantstep method to improve the currently best known bound by a superpolynomial factor.

Dirichlet's proof of the three-square theorem: An algorithmic perspective

- MathematicsMath. Comput.
- 2019

It is explained how to turn Dirichlet’s proof of the Gauss–Legendre three-square theorem into an algorithm; if one assumes the Extended Riemann Hypothesis (ERH), there is a random algorithm for expressing n = x + y + z where the expected number of bit operations is O((lgn)(lg lgn)−1 ·M(lgn).

Efficient Big Integer Multiplication in Cryptography

- Computer Science, Mathematics
- 2017

This paper determines the complexities by taking into account the cost of single word multiplication, single word addition and double word addition on different platforms, and presents the best multiplication algorithm complexities for NIST primes on different implementation platforms.

Faster polynomial multiplication over finite fields using cyclotomic coefficient rings

- Computer Science, MathematicsJ. Complex.
- 2019

Implementation of the DKSS Algorithm for Multiplication of Large Numbers

- Computer ScienceISSAC
- 2015

The Schönhage-Strassen algorithm (SSA) is the de-facto standard for multiplication of large integers. For N-bit numbers it has a time bound of O(N log N log log N). De, Kurur, Saha and Saptharishi…

Faster truncated integer multiplication

- Computer Science, MathematicsArXiv
- 2017

These problems may be solved in asymptotically 75% of the time required to compute the full 2n-bit product, assuming that the underlying integer multiplication algorithm relies on computing cyclic convolutions of real sequences.

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This work establishes the bound Mp(n) = O(n log n 8log* n log p), where log* n = min{k ϵ N: log …k×… log n ≤ 1} stands for the iterated logarithm.

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