Results 1  10
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354,753
New Algorithms for Finding Irreducible Polynomials over Finite Fields
 Mathematics of Computation
, 1990
"... . We present a new algorithm for finding an irreducible polynomial of specified degree over a finite field. Our algorithm is deterministic, and it runs in polynomial time for fields of small characteristic. We in fact prove the stronger result that the problem of finding irreducible polynomials of s ..."
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Cited by 83 (5 self)
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. We present a new algorithm for finding an irreducible polynomial of specified degree over a finite field. Our algorithm is deterministic, and it runs in polynomial time for fields of small characteristic. We in fact prove the stronger result that the problem of finding irreducible polynomials
Requirements for Internet Hosts  Application and Support
 STD 3, RFC 1123, IETF
, 1989
"... This RFC is an official specification for the Internet community. It incorporates by reference, amends, corrects, and supplements the primary protocol standards documents relating to hosts. Distribution of this document is unlimited. Summary This RFC is one of a pair that defines and discusses the r ..."
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Cited by 319 (1 self)
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This RFC is an official specification for the Internet community. It incorporates by reference, amends, corrects, and supplements the primary protocol standards documents relating to hosts. Distribution of this document is unlimited. Summary This RFC is one of a pair that defines and discusses the requirements for Internet host software. This RFC covers the application and support protocols; its companion RFC1122 covers the communication protocol layers: link layer, IP layer, and transport layer.
Subquadratictime factoring of polynomials over finite fields
 Math. Comp
, 1998
"... Abstract. New probabilistic algorithms are presented for factoring univariate polynomials over finite fields. The algorithms factor a polynomial of degree n over a finite field of constant cardinality in time O(n 1.815). Previous algorithms required time Θ(n 2+o(1)). The new algorithms rely on fast ..."
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Cited by 76 (10 self)
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Abstract. New probabilistic algorithms are presented for factoring univariate polynomials over finite fields. The algorithms factor a polynomial of degree n over a finite field of constant cardinality in time O(n 1.815). Previous algorithms required time Θ(n 2+o(1)). The new algorithms rely on fast
A factorization of the Conway polynomial
 Comment. Math. Helvetici
, 1999
"... It is tempting to conjecture that there is some interesting relationship between the Conway polynomial ∇L(z) of a link L and ∇K(z), where K is a knot obtained by banding together the components of L. Obviously they cannot be equal since only terms of even or odd degree appear in ∇L(z), according to ..."
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Cited by 10 (0 self)
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It is tempting to conjecture that there is some interesting relationship between the Conway polynomial ∇L(z) of a link L and ∇K(z), where K is a knot obtained by banding together the components of L. Obviously they cannot be equal since only terms of even or odd degree appear in ∇L(z), according
Network Centric Warfare: Developing and Leveraging Information Superiority
 Command and Control Research Program (CCRP), US DoD
, 2000
"... the mission of improving DoD’s understanding of the national security implications of the Information Age. Focusing upon improving both the state of the art and the state of the practice of command and control, the CCRP helps DoD take full advantage of the opportunities afforded by emerging technolo ..."
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Cited by 308 (5 self)
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the mission of improving DoD’s understanding of the national security implications of the Information Age. Focusing upon improving both the state of the art and the state of the practice of command and control, the CCRP helps DoD take full advantage of the opportunities afforded by emerging technologies. The CCRP pursues a broad program of research and analysis in information superiority, information operations, command and control theory, and associated operational concepts that enable us to leverage shared awareness to improve the effectiveness and efficiency of assigned missions. An important aspect of the CCRP program is its ability to serve as a bridge between the operational, technical, analytical, and educational communities. The CCRP provides leadership for the command and control research community by: n n
CONSTRUCTING IRREDUCIBLE POLYNOMIALS OVER FINITE FIELDS
"... Abstract. We describe a new method for constructing irreducible polynomials modulo a prime number p. The method mainly relies on Chebotarev’s density theorem. ..."
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Abstract. We describe a new method for constructing irreducible polynomials modulo a prime number p. The method mainly relies on Chebotarev’s density theorem.
Polynomial Factorization Algorithms over Number Fields
 JOURNAL OF SYMBOLIC COMPUTATION 38 (2004) 14291443
, 2004
"... The aim of this paper is to describe two new factorization algorithms for polynomials. The first factorizes polynomials modulo the prime ideal of a number field. The second factorizes polynomials over a number field. ..."
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Cited by 4 (0 self)
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The aim of this paper is to describe two new factorization algorithms for polynomials. The first factorizes polynomials modulo the prime ideal of a number field. The second factorizes polynomials over a number field.
Efficient Algorithms for Solving Overdefined Systems of Multivariate Polynomial Equations
 IN ADVANCES IN CRYPTOLOGY, EUROCRYPT’2000, LNCS 1807
, 2000
"... The security of many recently proposed cryptosystems is based on the difficulty of solving large systems of quadratic multivariate polynomial equations. This problem is NPhard over any field. When the number of equations m is the same as the number of unknowns n the best known algorithms are exhaus ..."
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Cited by 182 (20 self)
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The security of many recently proposed cryptosystems is based on the difficulty of solving large systems of quadratic multivariate polynomial equations. This problem is NPhard over any field. When the number of equations m is the same as the number of unknowns n the best known algorithms
Fast Construction of Irreducible Polynomials over Finite Fields
 J. Symbolic Comput
, 1993
"... The main result of this paper is a new algorithm for constructing an irreducible polynomial of specified degree n over a finite field F q . The algorithm is probabilistic, and is asymptotically faster than previously known algorithms for this problem. It uses an expected number of O~(n 2 + n log q) ..."
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Cited by 60 (6 self)
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The main result of this paper is a new algorithm for constructing an irreducible polynomial of specified degree n over a finite field F q . The algorithm is probabilistic, and is asymptotically faster than previously known algorithms for this problem. It uses an expected number of O~(n 2 + n log q
Results 1  10
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354,753