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Factoring polynomials with rational coefficients
 MATH. ANN
, 1982
"... In this paper we present a polynomialtime algorithm to solve the following problem: given a nonzero polynomial fe Q[X] in one variable with rational coefficients, find the decomposition of f into irreducible factors in Q[X]. It is well known that this is equivalent to factoring primitive polynomia ..."
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Cited by 958 (11 self)
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for factoring polynomials over small finite fields, combined with Hensel's lemma. Next we look for the irreducible factor h o of f in
Vector bundles over an elliptic curve
 Proc. London Math. Soc
, 1957
"... THE primary purpose of this paper is the study of algebraic vector bundles over an elliptic curve (defined over an algebraically closed field k). The interest of the elliptic curve lies in the fact that it provides the first nontrivial case, Grothendieck (6) having shown that for a rational curve e ..."
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Cited by 293 (0 self)
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THE primary purpose of this paper is the study of algebraic vector bundles over an elliptic curve (defined over an algebraically closed field k). The interest of the elliptic curve lies in the fact that it provides the first nontrivial case, Grothendieck (6) having shown that for a rational curve
Selecting Cryptographic Key Sizes
 TO APPEAR IN THE JOURNAL OF CRYPTOLOGY, SPRINGERVERLAG
, 2001
"... In this article we offer guidelines for the determination of key sizes for symmetric cryptosystems, RSA, and discrete logarithm based cryptosystems both over finite fields and over groups of elliptic curves over prime fields. Our recommendations are based on a set of explicitly formulated parameter ..."
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Cited by 319 (8 self)
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In this article we offer guidelines for the determination of key sizes for symmetric cryptosystems, RSA, and discrete logarithm based cryptosystems both over finite fields and over groups of elliptic curves over prime fields. Our recommendations are based on a set of explicitly formulated
Rational Points on Elliptic Curves
, 1992
"... Abstract. We give a quantitative bound for the number of Sintegral points on an elliptic curve over a number field K in terms of the number of primes dividing the denominator of the jinvariant, the degree [K: Q], and the number of primes in S. Let K be a number field of degree d and MK the set of ..."
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Cited by 121 (1 self)
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Abstract. We give a quantitative bound for the number of Sintegral points on an elliptic curve over a number field K in terms of the number of primes dividing the denominator of the jinvariant, the degree [K: Q], and the number of primes in S. Let K be a number field of degree d and MK the set
DOUBLING RATIONAL NORMAL CURVES
, 2008
"... In this paper, we study double structures supported on rational normal curves. After recalling the general construction of double structures supported on a smooth curve described in [11], we specialize it to double structures on rational normal curves. To every double structure we associate a tripl ..."
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In this paper, we study double structures supported on rational normal curves. After recalling the general construction of double structures supported on a smooth curve described in [11], we specialize it to double structures on rational normal curves. To every double structure we associate a
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
Rational Maps and Images of Rational Points of Curves over Finite Fields
"... Abstract. We give a survey and some new results about covers of curves related to images of rational points. In particular, we discuss exceptional covers and exceptional polynomials and pairs of covers which have the same image on rational points. Our approach uses group theoretic translations of ..."
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Abstract. We give a survey and some new results about covers of curves related to images of rational points. In particular, we discuss exceptional covers and exceptional polynomials and pairs of covers which have the same image on rational points. Our approach uses group theoretic transla
Results 1  10
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1,015,333