Peter L. Montgomery

6.8k total citations · 3 hit papers
32 papers, 3.2k citations indexed

About

Peter L. Montgomery is a scholar working on Artificial Intelligence, Information Systems and Computational Theory and Mathematics. According to data from OpenAlex, Peter L. Montgomery has authored 32 papers receiving a total of 3.2k indexed citations (citations by other indexed papers that have themselves been cited), including 18 papers in Artificial Intelligence, 14 papers in Information Systems and 12 papers in Computational Theory and Mathematics. Recurrent topics in Peter L. Montgomery's work include Coding theory and cryptography (14 papers), Cryptography and Residue Arithmetic (14 papers) and Polynomial and algebraic computation (7 papers). Peter L. Montgomery is often cited by papers focused on Coding theory and cryptography (14 papers), Cryptography and Residue Arithmetic (14 papers) and Polynomial and algebraic computation (7 papers). Peter L. Montgomery collaborates with scholars based in United States, Switzerland and France. Peter L. Montgomery's co-authors include Robert Silverman, Kristin Lauter, Mathieu Ciet, Marc Jóye, Arjen K. Lenstra, Joppe W. Bos, Thorsten Kleinjung, John Brillhart, Brian Murphy and Bruce Dodson and has published in prestigious journals such as Mathematics of Computation, IEEE Transactions on Computers and American Mathematical Monthly.

In The Last Decade

Peter L. Montgomery

28 papers receiving 2.9k citations

Hit Papers

Modular multiplication without trial division 1985 2026 1998 2012 1985 1985 1987 400 800 1.2k
What are hit papers?

Hit papers significantly outperform the citation benchmark for their cohort. A paper qualifies if it has ≥500 total citations, achieves ≥1.5× the top-1% citation threshold for papers in the same subfield and year (this is the minimum needed to enter the top 1%, not the average within it), or reaches the top citation threshold in at least one of its specific research topics.

  1. Modular multiplication without trial division
    1985 1.4k citations Peter L. Montgomery Mathematics of Computation profile →
  2. Modular Multiplication Without Trial Division
    1985 800 citations Peter L. Montgomery Mathematics of Computation profile →
  3. Speeding the Pollard and elliptic curve methods of factorization
    1987 501 citations Peter L. Montgomery Mathematics of Computation profile →

Peers — A (Enhanced Table)

Peers by citation overlap · career bar shows stage (early→late) cites · hero ref

Name h Career Trend Papers Cites
Peter L. Montgomery United States 12 2.8k 2.6k 413 360 190 32 3.2k
Fréderik Vercauteren Belgium 21 2.0k 0.7× 1.3k 0.5× 362 0.9× 341 0.9× 251 1.3× 58 2.3k
Arjen K. Lenstra United States 21 1.0k 0.4× 560 0.2× 329 0.8× 283 0.8× 293 1.5× 55 1.4k
J. M. Pollard United Kingdom 13 1.2k 0.4× 810 0.3× 441 1.1× 299 0.8× 158 0.8× 23 1.6k
Darrel Hankerson United States 12 1.6k 0.6× 1.5k 0.6× 179 0.4× 355 1.0× 611 3.2× 25 2.2k
Steven D. Galbraith⋆ United Kingdom 18 1.3k 0.5× 875 0.3× 215 0.5× 235 0.7× 270 1.4× 57 1.6k
Jacques Stern France 20 2.0k 0.7× 719 0.3× 712 1.7× 275 0.8× 675 3.6× 49 2.5k
Marc Jóye France 19 1.6k 0.6× 866 0.3× 123 0.3× 375 1.0× 261 1.4× 73 1.9k
M.A. Hasan Canada 27 1.9k 0.7× 1.7k 0.6× 279 0.7× 162 0.5× 252 1.3× 156 2.3k
Kenneth G. Paterson United Kingdom 25 2.1k 0.7× 836 0.3× 424 1.0× 347 1.0× 1.2k 6.1× 111 3.0k
Michael J. Wiener Canada 7 1.2k 0.4× 676 0.3× 112 0.3× 387 1.1× 570 3.0× 15 1.5k

Countries citing papers authored by Peter L. Montgomery

Since Specialization
Citations

This map shows the geographic impact of Peter L. Montgomery's research. It shows the number of citations coming from papers published by authors working in each country. You can also color the map by specialization and compare the number of citations received by Peter L. Montgomery with the expected number of citations based on a country's size and research output (numbers larger than one mean the country cites Peter L. Montgomery more than expected).

Fields of papers citing papers by Peter L. Montgomery

Since Specialization
Physical SciencesHealth SciencesLife SciencesSocial Sciences

This network shows the impact of papers produced by Peter L. Montgomery. Nodes represent research fields, and links connect fields that are likely to share authors. Colored nodes show fields that tend to cite the papers produced by Peter L. Montgomery. The network helps show where Peter L. Montgomery may publish in the future.

Co-authorship network of co-authors of Peter L. Montgomery

This figure shows the co-authorship network connecting the top 25 collaborators of Peter L. Montgomery. A scholar is included among the top collaborators of Peter L. Montgomery based on the total number of citations received by their joint publications. Widths of edges represent the number of papers authors have co-authored together. Node borders signify the number of papers an author published with Peter L. Montgomery. Peter L. Montgomery is excluded from the visualization to improve readability, since they are connected to all nodes in the network.

All Works

20 of 20 papers shown
1.
Bos, Joppe W., Thorsten Kleinjung, Arjen K. Lenstra, & Peter L. Montgomery. (2011). Efficient SIMD Arithmetic Modulo a Mersenne Number. Infoscience (Ecole Polytechnique Fédérale de Lausanne). 5677. 213–221. 8 indexed citations
2.
Montgomery, Peter L., et al.. (2010). Side Channel Leakage Profiling in Software. 3 indexed citations
3.
Montgomery, Peter L., et al.. (2010). The period of the Bell numbers modulo a prime. Mathematics of Computation. 79(271). 1793–1800. 8 indexed citations
4.
Bhaskar, Raghav, et al.. (2009). An Observation about Variations of the Diffie-Hellman Assumption. 3(3). 309–318. 1 indexed citations
5.
Bhaskar, Raghav, et al.. (2008). Vulnerabilities in Anonymous Credential Systems. Electronic Notes in Theoretical Computer Science. 197(2). 141–148.
6.
Ciet, Mathieu, Marc Jóye, Kristin Lauter, & Peter L. Montgomery. (2006). Trading Inversions for Multiplications in Elliptic Curve Cryptography. Designs Codes and Cryptography. 39(2). 189–206. 51 indexed citations
7.
Dodson, Bruce, et al.. (2000). Factorization of a 512-bit RSA modulus. Centrum Wiskunde & Informatica (CWI), the national research institute for mathematics and computer science in the Netherlands. 7. 1–21. 24 indexed citations
8.
Dodson, Bruce, Arjen K. Lenstra, Paul Leyland, et al.. (1999). Factorization of RSA-140 Using the Number Field Sieve. Queueing Systems. 195–207. 1 indexed citations
9.
Montgomery, Peter L., et al.. (1994). Division by invariant integers using multiplication. ACM SIGPLAN Notices. 29(6). 61–72. 11 indexed citations
10.
Montgomery, Peter L.. (1994). A survey of modern integer factorization algorithms. Centrum Wiskunde & Informatica (CWI), the national research institute for mathematics and computer science in the Netherlands. 7(4). 337–366. 21 indexed citations
11.
Montgomery, Peter L.. (1993). New solutions of 𝑎^{𝑝-1}≡1 (mod 𝑝²). Mathematics of Computation. 61(203). 361–363. 17 indexed citations
12.
Montgomery, Peter L.. (1993). New Solutions of a p - 1 ≡1 (mod p 2 ). Mathematics of Computation. 61(203). 361–361. 5 indexed citations
13.
Montgomery, Peter L.. (1992). An FFT extension of the elliptic curve method of factorization. 29 indexed citations
14.
Montgomery, Peter L., et al.. (1991). 6631. American Mathematical Monthly. 98(9). 870–870. 1 indexed citations
15.
Montgomery, Peter L. & Robert Silverman. (1990). An FFT extension to the 𝑃-1 factoring algorithm. Mathematics of Computation. 54(190). 839–854. 9 indexed citations
16.
Brillhart, John, Peter L. Montgomery, & Robert Silverman. (1988). Tables of Fibonacci and Lucas factorizations. Mathematics of Computation. 50(181). 251–260. 11 indexed citations
17.
Montgomery, Peter L.. (1987). Speeding the Pollard and elliptic curve methods of factorization. Mathematics of Computation. 48(177). 243–264. 501 indexed citations breakdown →
18.
Montgomery, Peter L.. (1987). Speeding the Pollard and Elliptic Curve Methods of Factorization. Mathematics of Computation. 48(177). 243–243. 63 indexed citations
19.
Montgomery, Peter L.. (1985). Modular Multiplication Without Trial Division. Mathematics of Computation. 44(170). 519–519. 800 indexed citations breakdown →
20.
Montgomery, Peter L., et al.. (1979). E2686. American Mathematical Monthly. 86(2). 131–131.

Rankless uses publication and citation data sourced from OpenAlex, an open and comprehensive bibliographic database. While OpenAlex provides broad and valuable coverage of the global research landscape, it—like all bibliographic datasets—has inherent limitations. These include incomplete records, variations in author disambiguation, differences in journal indexing, and delays in data updates. As a result, some metrics and network relationships displayed in Rankless may not fully capture the entirety of a scholar's output or impact.

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