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The lattice sieve
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What this work says
Outgoing claims: the papers this work cites, builds on, or argues with.
inferredcites →https://doi.org/10.1090/psapm/042openalex-snapshot
Cryptology and Computational Number Theory
inferredcites →https://doi.org/10.1090/s0025-5718-1993-1182953-4openalex-snapshot
The Factorization of the Ninth Fermat Number
What points at this work
Incoming claims: where this work appears in other papers’ reference lists and arguments.
inferred← citeshttps://doi.org/10.1007/10722028_11openalex-snapshot
Strategies in Filtering in the Number Field Sieve
inferred← citeshttps://doi.org/10.1007/3-540-45455-1_34openalex-snapshot
The Function Field Sieve Is Quite Special
inferred← citeshttps://doi.org/10.1007/3-540-45539-6_1openalex-snapshot
Factorization of a 512-Bit RSA Modulus
inferred← citeshttps://doi.org/10.1007/3-540-48329-2_14openalex-snapshot
An implementation of the general number field sieve
inferred← citeshttps://doi.org/10.1007/3-540-58691-1_38openalex-snapshot
Lattice sieving and trial division
inferred← citeshttps://doi.org/10.1007/3-540-61581-4_45openalex-snapshot
A multiple polynomial general number field sieve
inferred← citeshttps://doi.org/10.1007/3-540-61581-4_70openalex-snapshot
Computing discrete logarithms with the general number field sieve
inferred← citeshttps://doi.org/10.1007/978-1-4419-5906-5_465openalex-snapshot
Number Field Sieve for Factoring
inferred← citeshttps://doi.org/10.1007/978-3-030-56880-1_3openalex-snapshot
Comparing the Difficulty of Factorization and Discrete Logarithm: A 240-Digit Experiment
inferred← citeshttps://doi.org/10.1007/978-3-030-71522-9_465openalex-snapshot
Number Field Sieve for Factoring
inferred← citeshttps://doi.org/10.1007/978-3-030-92062-3_3openalex-snapshot
Lattice Enumeration for Tower NFS: A 521-Bit Discrete Logarithm Computation
inferred← citeshttps://doi.org/10.1007/978-3-319-29814-6_16openalex-snapshot
Strategy of Relations Collection in Factoring RSA Modulus
inferred← citeshttps://doi.org/10.1007/978-3-319-72565-9_5openalex-snapshot
Computing Discrete Logarithms in $${\mathbb F}_{{p}^{6}}$$
inferred← citeshttps://doi.org/10.1007/978-3-540-48000-6_16openalex-snapshot
Factorization of RSA-140 Using the Number Field Sieve
inferred← citeshttps://doi.org/10.1007/978-3-540-74735-2_25openalex-snapshot
CAIRN 2: An FPGA Implementation of the Sieving Step in the Number Field Sieve Method
inferred← citeshttps://doi.org/10.1007/978-3-642-13013-7_21openalex-snapshot
Solving a 676-Bit Discrete Logarithm Problem in GF(36n )
inferred← citeshttps://doi.org/10.1007/978-3-642-14623-7_18openalex-snapshot
Factorization of a 768-Bit RSA Modulus
inferred← citeshttps://doi.org/10.1007/978-3-642-29101-2_16openalex-snapshot
Key Length Estimation of Pairing-Based Cryptosystems Using η T Pairing
inferred← citeshttps://doi.org/10.1007/978-3-642-34961-4_5openalex-snapshot
Breaking Pairing-Based Cryptosystems Using η T Pairing over GF(397)
inferred← citeshttps://doi.org/10.1007/978-3-642-41224-0_4openalex-snapshot
SIMD-Based Implementations of Sieving in Integer-Factoring Algorithms
inferred← citeshttps://doi.org/10.1007/978-3-642-42001-6_8openalex-snapshot
An Experiment of Number Field Sieve for Discrete Logarithm Problem over GF(p 12)
inferred← citeshttps://doi.org/10.1007/978-3-662-44709-3_19openalex-snapshot
Cofactorization on Graphics Processing Units
inferred← citeshttps://doi.org/10.1007/978-3-662-45611-8_19openalex-snapshot
Mersenne Factorization Factory
inferred← citeshttps://doi.org/10.1007/978-3-662-48800-3_2openalex-snapshot
The Tower Number Field Sieve
inferred← citeshttps://doi.org/10.1007/978-93-86279-46-0_1openalex-snapshot
Analysis of the Lattice Sieve
inferred← citeshttps://doi.org/10.1007/978-981-10-8968-8_40openalex-snapshot
Special-q Techniques for Number Field Sieve to Solve Integer Factorization
inferred← citeshttps://doi.org/10.1007/978-981-99-8730-6_5openalex-snapshot
We are on the Same Side. Alternative Sieving Strategies for the Number Field Sieve
inferred← citeshttps://doi.org/10.1007/bfb0034863openalex-snapshot
A World Wide Number Field Sieve factoring record: On to 512 bits
inferred← citeshttps://doi.org/10.1007/bfb0055747openalex-snapshot
The solution of McCurley's discrete log challenge
inferred← citeshttps://doi.org/10.1007/bfb0091539openalex-snapshot
Factoring integers with the number field sieve
inferred← citeshttps://doi.org/10.1007/bfb0091541openalex-snapshot
A general number field sieve implementation
inferred← citeshttps://doi.org/10.1007/s00145-023-09487-xopenalex-snapshot
Lattice Enumeration and Automorphisms for Tower NFS: A 521-Bit Discrete Logarithm Computation
inferred← citeshttps://doi.org/10.1007/s11227-020-03351-6openalex-snapshot
Relation collection using Pollard special-q sieving to solve integer factorization and discrete logarithm problem
inferred← citeshttps://doi.org/10.1007/s40993-022-00402-0openalex-snapshot
Fast norm computation in smooth-degree Abelian number fields
inferred← citeshttps://doi.org/10.1016/j.amc.2016.08.019openalex-snapshot
Use of SIMD-based data parallelism to speed up sieving in integer-factoring algorithms
inferred← citeshttps://doi.org/10.1016/j.tcs.2016.03.028openalex-snapshot
The Space Complexity Analysis in the General Number Field Sieve Integer Factorization
inferred← citeshttps://doi.org/10.1017/9781139049801.013openalex-snapshot
The impact of the number field sieve on the discrete logarithm problem in finite fields
inferred← citeshttps://doi.org/10.1080/10586458.1996.10504590openalex-snapshot
An Implementation of the Number Field Sieve
inferred← citeshttps://doi.org/10.1090/mcom/3697openalex-snapshot
A classification of ECM-friendly families using modular curves
inferred← citeshttps://doi.org/10.1090/s0025-5718-02-01482-5openalex-snapshot
Improvements to the general number field sieve for discrete logarithms in prime fields. A comparison with the gaussian integer method
inferred← citeshttps://doi.org/10.1090/s0025-5718-2015-02926-3openalex-snapshot
Root optimization of polynomials in the number field sieve
inferred← citeshttps://doi.org/10.1090/s0025-5718-99-01137-0openalex-snapshot
Using number fields to compute logarithms in finite fields
inferred← citeshttps://doi.org/10.1109/arith.2011.37openalex-snapshot
Efficient SIMD Arithmetic Modulo a Mersenne Number
inferred← citeshttps://doi.org/10.1109/arith.2013.28openalex-snapshot
Relation Collection for the Function Field Sieve
inferred← citeshttps://doi.org/10.1109/nbis.2010.60openalex-snapshot
CAIRN: Dedicated Integer Factoring Devices
inferred← citeshttps://doi.org/10.1109/tit.2016.2528996openalex-snapshot
Fine Tuning the Function Field Sieve Algorithm for the Medium Prime Case
inferred← citeshttps://doi.org/10.1112/s1461157016000164openalex-snapshot
Collecting relations for the number field sieve in
inferred← citeshttps://doi.org/10.13021/mars/4655openalex-snapshot
Number Field Sieve: Pseudocodes and Software Implementation
inferred← citeshttps://doi.org/10.14264/uql.2014.506openalex-snapshot
On the number field sieve: polynomial selection and smooth elements in number fields
inferred← citeshttps://doi.org/10.14495/jsiaml.6.53openalex-snapshot
An experiment of number field sieve for discrete logarithm problem over $\text{GF}(p^n)$
inferred← citeshttps://doi.org/10.1515/jmc-2020-0008openalex-snapshot
Lattice Sieving in Three Dimensions for Discrete Log in Medium Characteristic
inferred← citeshttps://doi.org/10.1515/jmc.2007.007openalex-snapshot
Optimal Parameterization of SNFS
inferred← citeshttps://doi.org/10.1587/transfun.e95.a.204openalex-snapshot
Solving a 676-Bit Discrete Logarithm Problem in GF(36n)
inferred← citeshttps://doi.org/10.1587/transfun.e97.a.236openalex-snapshot
Key Length Estimation of Pairing-Based Cryptosystems Using ηT Pairing over GF(3n)
inferred← citeshttps://doi.org/10.2140/obs.2013.1.113openalex-snapshot
Improved techniques for computing the ideal class group and a system of fundamental units in number fields
inferred← citeshttps://doi.org/10.2140/obs.2013.1.63openalex-snapshot
Finding ECM-friendly curves through a study of Galois properties
inferred← citeshttps://doi.org/10.2140/obs.2019.2.275openalex-snapshot
Higher-dimensional sieving for the number field sieve algorithms
inferred← citeshttps://doi.org/10.22028/d291-25895openalex-snapshot
On the computation of discrete logarithms in finite prime fields
inferred← citeshttps://doi.org/10.22331/q-2021-04-15-433openalex-snapshot
How to factor 2048 bit RSA integers in 8 hours using 20 million noisy qubits
inferred← citeshttps://doi.org/10.2478/v10127-010-0012-yopenalex-snapshot
On the use of the lattice sieve in the 3D NFS
inferred← citeshttps://doi.org/10.25911/5d6272199e44dopenalex-snapshot
Polynomial selection for the number field sieve integer factorisation algorithm
inferred← citeshttps://doi.org/10.2991/icmmcce-15.2015.70openalex-snapshot
Space Complexity Analysis of Sieving in the Number Field Sieve Integer Factorization
inferred← citeshttps://doi.org/10.4028/www.scientific.net/amr.466-467.298openalex-snapshot
Calculation Components Analysis of the Lattice Sieve
inferred← citeshttps://doi.org/10.4213/mvk178openalex-snapshot
Оценки количества чисел со специальным разложением на простые множители
inferred← citeshttps://doi.org/10.4236/apm.2025.159032openalex-snapshot
Kernel Factor Pairs for Semiprime Factorization
inferred← citeshttps://doi.org/10.48550/arxiv.1204.1294openalex-snapshot
New techniques for computing the ideal class group and a system of fundamental units in number fields
inferred← citeshttps://doi.org/10.48550/arxiv.2001.10860openalex-snapshot
A New Angle on Lattice Sieving for the Number Field Sieve
inferred← citeshttps://doi.org/10.70675/03e70022z3b51z4264z86ffz300c571650d3openalex-snapshot
Discrete Logarithm Cryptanalyses : Number Field Sieve and Lattice Tools for Side-Channel Attacks
inferred← citeshttps://doi.org/10.70675/d7889d5ezde87z4d87zbf97z17c5da455b20openalex-snapshot
Cryptographic applications of modular curves
inferred← citeshttps://doi.org/10.70675/dc2bc96dz4f43z463fza85ez090235d220eeopenalex-snapshot
The Discrete Logarithm Problem in Finite Fields with Extensions
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