## Tables from this paper

## 104 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 \goodbreak generalized Fermat primes

- Computer Science, MathematicsMath. Comput.
- 2019

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.

### 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.

### Faster integer multiplication using short lattice vectors

- Mathematics, Computer ScienceThe Open Book Series
- 2019

It is proved that n-bit integers may be multiplied in O(n \log n \, 4^{\log^* n}) bit operations, and depends in an essential way on Minkowski's theorem concerning lattice vectors in symmetric convex sets.

### 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.

### Polynomial multiplication over finite fields in time O(n log n)

- Mathematics, Computer Science
- 2019

Assuming a widely-believed hypothesis concerning the least prime in an arithmetic progression, we show that two n -bit integers can be multiplied in time O ( n log n ) on a Turing machine with a…

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### Faster Polynomial Multiplication over Finite Fields

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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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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.

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