A Montgomery-like square root for the Number Field Sieve

Lecture Notes in Computer Science - Algorithmic Number Theory ◽

10.1007/bfb0054859 ◽

1998 ◽

pp. 151-168 ◽

Cited By ~ 11

Author(s):

Phong Nguyen

Keyword(s):

Number Field ◽

Square Root ◽

Number Field Sieve

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Computing a square root for the number field sieve

Lecture Notes in Mathematics - The development of the number field sieve ◽

10.1007/bfb0091540 ◽

1993 ◽

pp. 95-102 ◽

Cited By ~ 10

Author(s):

Jean-Marc Couveignes

Keyword(s):

Number Field ◽

Square Root ◽

Number Field Sieve

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Square Root Algorithms for the Number Field Sieve

Arithmetic of Finite Fields - Lecture Notes in Computer Science ◽

10.1007/978-3-642-31662-3_15 ◽

2012 ◽

pp. 208-224 ◽

Cited By ~ 1

Author(s):

Emmanuel Thomé

Keyword(s):

Number Field ◽

Square Root ◽

Number Field Sieve

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Cryptology Beyond Shannon's Information Theory: Preparing for When the Enemy Knows the Systemm with Technical Focus on Number Field Sieve Cryptanalysis Algorithms for Most Efficient Prime Factorization on Composites

SSRN Electronic Journal ◽

10.2139/ssrn.2553544 ◽

2013 ◽

Cited By ~ 1

Author(s):

Yogesh Malhotra

Keyword(s):

Information Theory ◽

Number Field ◽

Prime Factorization ◽

Number Field Sieve

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Analysis and Improvements to the Special Number Field Sieve for Discrete Logarithm Problems

2021 IEEE 5th International Conference on Cryptography, Security and Privacy (CSP) ◽

10.1109/csp51677.2021.9357589 ◽

2021 ◽

Author(s):

Liwei Liu ◽

Maozhi Xu ◽

Guoqing Zhou

Keyword(s):

Number Field ◽

Discrete Logarithm ◽

Number Field Sieve ◽

Special Number

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A Kilobit Special Number Field Sieve Factorization

Advances in Cryptology – ASIACRYPT 2007 - Lecture Notes in Computer Science ◽

10.1007/978-3-540-76900-2_1 ◽

2007 ◽

pp. 1-12 ◽

Cited By ~ 24

Author(s):

Kazumaro Aoki ◽

Jens Franke ◽

Thorsten Kleinjung ◽

Arjen K. Lenstra ◽

Dag Arne Osvik

Keyword(s):

Number Field ◽

Number Field Sieve ◽

Special Number

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AVX-512-based Parallelization of Block Sieving and Bucket Sieving for the General Number Field Sieve Method

10.5220/0010515200002998 ◽

2021 ◽

Author(s):

Pritam Pallab ◽

Abhijit Das

Keyword(s):

Number Field ◽

Sieve Method ◽

Number Field Sieve ◽

General Number

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Extended Tower Number Field Sieve: A New Complexity for the Medium Prime Case

Advances in Cryptology – CRYPTO 2016 - Lecture Notes in Computer Science ◽

10.1007/978-3-662-53018-4_20 ◽

2016 ◽

pp. 543-571 ◽

Cited By ~ 64

Author(s):

Taechan Kim ◽

Razvan Barbulescu

Keyword(s):

Number Field ◽

Number Field Sieve ◽

Prime Case

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The Tower Number Field Sieve

Advances in Cryptology – ASIACRYPT 2015 - Lecture Notes in Computer Science ◽

10.1007/978-3-662-48800-3_2 ◽

2015 ◽

pp. 31-55 ◽

Cited By ~ 25

Author(s):

Razvan Barbulescu ◽

Pierrick Gaudry ◽

Thorsten Kleinjung

Keyword(s):

Number Field ◽

Number Field Sieve

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Strategies in Filtering in the Number Field Sieve

Lecture Notes in Computer Science - Algorithmic Number Theory ◽

10.1007/10722028_11 ◽

2000 ◽

pp. 209-231 ◽

Cited By ~ 16

Author(s):

Stefania Cavallar

Keyword(s):

Number Field ◽

Number Field Sieve

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Improvements to the general number field sieve for discrete logarithms in prime fields. A comparison with the gaussian integer method

Mathematics of Computation ◽

10.1090/s0025-5718-02-01482-5 ◽

2002 ◽

Vol 72 (242) ◽

pp. 953-968 ◽

Cited By ~ 42

Author(s):

Antoine Joux ◽

Reynald Lercier

Keyword(s):

Number Field ◽

Gaussian Integer ◽

Discrete Logarithms ◽

Number Field Sieve ◽

General Number ◽

Prime Fields

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