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Electronic Colloquium on Computational Complexity

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Reports tagged with Factoring:
TR97-061 | 12th November 1997
Eli Biham, Dan Boneh, Omer Reingold

Generalized Diffie-Hellman Modulo a Composite is not Weaker than Factoring

The Diffie-Hellman key-exchange protocol may naturally be
extended to k>2 parties. This gives rise to the generalized
Diffie-Hellman assumption (GDH-Assumption).
Naor and Reingold have recently shown an efficient construction
of pseudo-random functions and reduced the security of their
construction to the GDH-Assumption.
In this note, we ... more >>>

TR00-078 | 18th July 2000
Jean-Pierre Seifert

Using fewer Qubits in Shor's Factorization Algorithm via Simultaneous Diophantine Approximation}

While quantum computers might speed up in principle
certain computations dramatically, in pratice, though
quantum computing technology is still in its infancy.
Even we cannot clearly envison at present what the
hardware of that machine will be like.
Nevertheless, we can be quite confident that it will be
more >>>

TR05-047 | 10th April 2005
Kooshiar Azimian, Mahmoud Salmasizadeh, Javad Mohajeri

Weak Composite Diffie-Hellman is not Weaker than Factoring

In1985, Shmuley proposed a theorem about intractability of Composite Diffie-Hellman [Sh85]. The Theorem of Shmuley may be paraphrased as saying that if there exist a probabilistic poly-time oracle machine which solves the Diffie-Hellman modulo an
RSA-number with odd-order base then there exist a probabilistic algorithm which factors the modulo. ... more >>>

TR08-043 | 12th April 2008
Gábor Ivanyos, Marek Karpinski, Nitin Saxena

Schemes for Deterministic Polynomial Factoring

In this work we relate the deterministic
complexity of factoring polynomials (over
fields) to certain combinatorial objects we
m-schemes. We extend the known conditional
deterministic subexponential time polynomial
factoring algorithm for finite fields to get an
underlying m-scheme. We demonstrate ... more >>>

TR08-074 | 19th July 2008
Neeraj Kayal, Timur Nezhmetdinov

Factoring groups efficiently

We give a polynomial time algorithm that computes a
decomposition of a finite group G given in the form of its
multiplication table. That is, given G, the algorithm outputs two
subgroups A and B of G such that G is the direct product
of A ... more >>>

TR08-099 | 19th November 2008
Gábor Ivanyos, Marek Karpinski, Lajos Rónyai, Nitin Saxena

Trading GRH for algebra: algorithms for factoring polynomials and related structures

In this paper we develop techniques that eliminate the need of the Generalized
Riemann Hypothesis (GRH) from various (almost all) known results about deterministic
polynomial factoring over finite fields. Our main result shows that given a
polynomial f(x) of degree n over a finite field k, we ... more >>>

TR14-056 | 18th April 2014
Zeev Dvir, Rafael Mendes de Oliveira

Factors of Sparse Polynomials are Sparse

Revisions: 1 , Comments: 1

We show that if $f(x_1,\ldots,x_n)$ is a polynomial with $s$ monomials and $g(x_1,\ldots,x_n)$ divides $f$ then $g$
has at most $\max(s^{O(\log s \log\log s)},d^{O(\log d)})$ monomials, where $d$ is a bound on the individual degrees
of $f$. This answers a question of von zur Gathen and Kaltofen (JCSS ... more >>>

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