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Quadratic field
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#	Item
51	Polynomial Selection for Number Field Sieve in Geometric View Min Yang1 , Qingshu Meng2 , zhangyi Wang2 , Lina Wang2 , and Huanguo Zhang2 1 Add to Reading List Source URL: eprint.iacr.org Language: English - Date: 2013-10-06 21:23:52 Abstract algebra General number field sieve Discriminant Quadratic polynomial Mathematics Polynomials Algebra
52	THE FACTORING DEAD: PREPARING FOR THE CRYPTOPOCALYPSE Javed Samuel — javed[at]isecpartners[dot]com iSEC Partners, Inc 123 Mission Street, Suite 1020 San Francisco, CA 94105 Add to Reading List Source URL: www.isecpartners.com Language: English - Date: 2014-04-02 07:42:28 Integer factorization algorithms Finite fields Logarithms Computational hardness assumptions Discrete logarithm Integer factorization Quadratic sieve XTR General number field sieve Abstract algebra Cryptography Mathematics
53	Superfluous Keys in Multivariate Quadratic Asymmetric Systems Christopher Wolf and Bart Preneel K.U.Leuven ESAT-COSIC Kasteelpark Arenberg 10, B-3001 Leuven-Heverlee, Belgium {Christopher.Wolf,Bart.Preneel}@esat.kuleuven Add to Reading List Source URL: eprint.iacr.org Language: English - Date: 2005-01-28 03:37:27 Hidden Field Equations Unbalanced Oil and Vinegar Affine transformation Quadratic polynomial Vector space Polynomial Multivariate cryptography Algebraic geometry Algebra Mathematics Post-quantum cryptography
54	Universally Constructing 12-th Degree Extension Field for Ate Pairing Masaaki Shirase School of Systems Information, Future University Hakodate, 116-2 Kamedanakano, Hakodate, Hokkaido, Japan Add to Reading List Source URL: eprint.iacr.org Language: English - Date: 2010-02-18 23:01:15 Modular arithmetic Quadratic residue Algebraic number theory Group theory Cubic reciprocity Legendre symbol Prime number Elliptic curve Finite field Abstract algebra Number theory Mathematics
55	Equivalent Keys in Multivariate Quadratic Public Key Systems Christopher Wolf1,2 , and Bart Preneel1 1 K.U.Leuven, ESAT-COSIC Kasteelpark Arenberg 10, B-3001 Leuven-Heverlee, Belgium Add to Reading List Source URL: eprint.iacr.org Language: English - Date: 2005-12-22 06:53:55 Finite fields Hidden Field Equations Mathematics Affine geometry Affine transformation Unbalanced Oil and Vinegar Differential geometry Multivariate cryptography Frobenius group Post-quantum cryptography Geometry Abstract algebra
56	MULTIVARIABLE PUBLIC–KEY CRYPTOSYSTEMS JINTAI DING, DIETER SCHMIDT Keywords: public-key, multivariable polynomials 1. Introduction Recently Landau and Diffie gave in a series of articles in the Notices of Add to Reading List Source URL: eprint.iacr.org Language: English - Date: 2004-12-09 16:39:00 Polynomials Quadratic polynomial Quadratic form Homogeneous polynomial Quadratic equation Hidden Field Equations Multivariate cryptography Algebra Mathematics Post-quantum cryptography
57	1 Square root computation over even extension fields Gora Adj 1 Add to Reading List Source URL: eprint.iacr.org Language: English - Date: 2013-07-18 17:22:53 Modular arithmetic Quadratic residue Field theory Exponentials Tonelli–Shanks algorithm Exponentiation by squaring Polynomial basis Quadratic reciprocity Finite field Abstract algebra Mathematics Number theory
58	MQ Challenge: Hardness Evaluation of Solving Multivariate Quadratic Problems ⋆ Takanori Yasuda1 , Xavier Dahan1,6 , Yun-Ju Huang1,2 , Tsuyoshi Takagi1,3,4 , and Kouichi Sakurai1,5 1 Add to Reading List Source URL: eprint.iacr.org Language: English - Date: 2015-03-26 06:14:31 Algebraic geometry QUAD Polynomials Hidden Field Equations XTR System of polynomial equations Quadratic NP XSL attack Mathematics Finite fields Post-quantum cryptography
59	Factorization of a 768-bit RSA modulus version 1.4, February 18, 2010 Thorsten Kleinjung1 , Kazumaro Jens Franke3 , Arjen K. Lenstra1 , Emmanuel Thomé4 , Add to Reading List Source URL: eprint.iacr.org Language: English - Date: 2010-02-18 11:19:25 Number theory Quadratic sieve Special number field sieve General number field sieve Quadratic residue Prime number Factor base Lattice sieving RSA Integer factorization algorithms Cryptography Mathematics
60	Asia Pacific Mathematics Newsletter 1 ClassicalReciprocity Reciprocity Laws Classical Add to Reading List Source URL: www.asiapacific-mathnews.com Language: English - Date: 2014-11-28 01:26:36 Algebraic number theory Modular arithmetic Field theory Number theory Quadratic residue Reciprocity law Algebraic number field Quadratic reciprocity Quartic reciprocity Abstract algebra Mathematics Algebra