Algebraic techniques for number field computations (extended abstract) Jean-Fran¸cois Biasse1 , Michael J. Jacobson, Jr.2? , and Alan K. Silvester3 ´ Ecole Polytechnique, 91128 Palaiseau, France

Source URL: www.lix.polytechnique.fr

• Algebra
• Abstract algebra
• Mathematics
• Finite fields
• Group theory
• Logarithms
• Algebraic number theory
• Numerical linear algebra
• XTR
• Discrete logarithm
• Gaussian elimination
• Quadratic field

DR. KRISTA E. WIEGAND Director, Global Security Program Howard H. Baker Jr. Center for Public Policy University of Tennessee, Knoxville 1640 Cumberland Ave. Knoxville, TN

Source URL: www.kristawiegand.com

• Political science
• International relations
• Global politics
• Conflict
• Conflict resolution
• Dispute resolution
• Family therapy
• Reconciliation
• Wiegand
• Peace and conflict studies
• American University School of International Service
• Territorial dispute

Smoothness Testing of Polynomials over Finite Fields Jean-Franc ¸ ois Biasse and Michael J. Jacobson Jr. Department of Computer Science, University of Calgary 2500 University Drive NW

Source URL: www.lix.polytechnique.fr

• Mathematics
• Multiplication
• Polynomials
• Algebra
• Multiplication algorithm
• Computer algebra
• ToomCook multiplication
• Karatsuba algorithm
• Degree of a polynomial
• Finite field
• Remainder
• Computational complexity of mathematical operations

Se urity Estimates for Quadrati Field Based Cryptosystems Jean-Fran ois Biasse1 , Mi hael J. Ja obson, Jr.2 ? , and Alan K. Silvester3 1 

Source URL: www.lix.polytechnique.fr

• Mathematics
• Logarithms
• Mathematical analysis
• Discrete mathematics
• Binary logarithm
• 108
• Factorial
• Prime number
• Common logarithm
• P

PUMP: A Programmable Unit for Metadata Processing Udit Dhawan1 Nikos Vasilakis1 Jonathan M. Smith1 Thomas F. Knight, Jr.3 1

Source URL: nikos.vasilak.is

Practical improvements to class group and regulator computation of real quadratic fields Jean-Fran¸cois Biasse1 and Michael J. Jacobson, Jr.2? ´ Ecole Polytechnique, 91128 Palaiseau, France

Source URL: www.lix.polytechnique.fr

• Algebra
• Mathematics
• Abstract algebra
• Algebraic number theory
• Integer factorization algorithms
• Quadratic forms
• Field theory
• Numerical linear algebra
• Quadratic sieve
• Factorization
• Factor base
• Ideal class group

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