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Topic: Polynomial factorization

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	Polynomial Factorization
		A polynomial is of degree k if the largest power of the variable in any term is no greter than k.
		A polynomial with integer coefficients is "prime" if it cannot be expressed as the product of two lower-degree polynomials with integer coefficients.
		The polynomials must be printed in increasing order of degree, and when two or more degrees match they must be sorted by increasing value of coefficients from the greatest to the lowest degree.
	acm.uva.es /p/v4/463.html (244 words)

	Irreducible polynomial -- Facts, Info, and Encyclopedia article (Site not responding. Last check: )
		See also ((mathematics) the resolution of an integer or polynomial into factors such that when multiplied together they give the integer or polynomial) factorization.
		Hence, all irreducible polynomials are of degree 1.
		One can show that every (A number that has no factor but itself and 1) prime element is irreducible; the converse is not true in general but holds in (additional info and facts about unique factorization domain) unique factorization domains.
	www.absoluteastronomy.com /encyclopedia/i/ir/irreducible_polynomial.htm (699 words)

	D. J. Bernstein / Talks
		Estimating factorization time.'' This was a talk on estimating the speed of the quadratic sieve and the number field sieve.
		The number-field sieve tries to factor an integer n by inspecting values of the homogeneous form of a polynomial related to n.
		``Polynomial selection for the number-field sieve, part 2: polynomial merit.'' Abstract written after the talk: ``I discussed the smoothness of the values (a-bm)(a^5+f_4 a^4 b+...+f_0 b^5) that appear in the number-field sieve.
	cr.yp.to /talks.html (5453 words)

	Publications of the SPACES team
		The basic idea underlying this method is the reduction of polynomial factorization over algebraic extension fields to the factorization over the rational number field via linear transformation and the computation of characteristic sets with respect to a proper variable ordering.
		Let f1,andhellip;,fk be k multivariate polynomials which have a finite number of common zeros in the algebraic closure of the ground field, counting the common zeros at infinity.
		When all the polynomials have the same degree, the complexity of this algorithm is polynomial relative to the generic number of solutions.
	www-calfor.lip6.fr /~safey/Spaces/publications.html (13078 words)

	[No title]
		2002.01.28, ``Is a 2048-bit factorization worth $200,000?'' 2004.06.14 (transcript and slides available), ``Factorization myths.'' 2004.07.29 (slides available), ``Factorization myths.'' 2004.11.15 (slides available), ``Three algorithms related to the number-field sieve.'' 2005.02.25 (slides available), ``Building circuits for integer factorization.''
		Relevant talks: 2001.03.23, ``The NSA sieving circuit.'' 2001.05.07 (slides available), ``The NSA sieving circuit.'' 2001.05.14 (slides available), ``An introduction to Schimmler sorting.'' 2002.08.20 (slides available), ``The cost of integer factorization.''
		The distribution of polynomial values; choosing number fields
	cr.yp.to /factorization.html (298 words)

	SINGULAR - History
		Rewritten in C; Singular programming language - Libraries.
		Singular release 1.0 (multivariate polynomial factorization; gcd, syzygies, resolutions, communication links).
		Singular release 3.0 (dynamic modules, name spaces, noncommutative computations, resolution of singularities, absolute factorization, etc.)
	www.singular.uni-kl.de /history.html (175 words)

	Publications by the Algorithms Project
		Abramov (S. A.) and Le (H. On the order of the recurrence produced by the method of creative telescoping.
		- Polynomial ideals for sandpiles and their Gröbner bases.
		- The complete analysis of a polynomial factorization algorithm over finite fields.
	algo.inria.fr /papers/bibgen/algobib.html (2866 words)

	Index of Crypto Papers Available Online
		, Merkle-Hellman Revisited: a Cryptanalysis of the Qu-Vanstone Cryptosystem Based on Group Factorizations, Advances in Cryptology -- Proceedings of CRYPTO '97, vol.
		New Blind Signatures Equivalent to Factorization, Proceedings of the 4th ACM Conference on Computer and Communications Security, pages 92-99, ACM Press, 1997.
		Faster polynomial factorization over high algebraic extensions of finite fields
	www.schneier.com /biblio/year-1997.html (3234 words)

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