The DOI matches its Crossref record; 5 of the 5 references it cites were found in a registry or an index.
Modular multiplication without trial division
Open accessAbstract
Let N > 1 . We present a method for multiplying two integers (called N-residues) modulo N while avoiding division by N. N-residues are represented in a nonstandard way, so this method is useful only if several computations are done modulo one N. The addition and subtraction algorithms are unchanged.
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Citations
Cites
A method for obtaining digital signatures and public-key cryptosystems
Rivest, R. L., Shamir, A., & Adleman, L. (1978) · Communications of the ACM · doi:10.1145/359340.359342 · Cited by 13,462
A method for obtaining digital signatures and public-key cryptosystems
Rivest, R. L., Shamir, A., & Adleman, L. (1983) · Communications of the ACM · doi:10.1145/357980.358017 · Cited by 13,012
Fast Probabilistic Algorithms for Verification of Polynomial Identities
Schwartz, J. T. (1980) · Journal of the ACM · doi:10.1145/322217.322225 · Cited by 1,701
A monte carlo method for factorization
Pollard, J. M. (1975) · BIT · doi:10.1007/bf01933667 · Cited by 402
Theorems on factorization and primality testing
Pollard, J. M. (1974) · Mathematical Proceedings of the Cambridge Philosophical Society · doi:10.1017/s0305004100049252 · Cited by 402
Cited by
Handbook of applied cryptography
(1997) · Choice Reviews Online · doi:10.5860/choice.34-4512 · Cited by 10,357
Remote timing attacks are practical
Brumley, D., & Boneh, D. (2005) · Computer Networks · doi:10.1016/j.comnet.2005.01.010 · Cited by 871
Practical Covertly Secure MPC for Dishonest Majority – Or: Breaking the SPDZ Limits
Damgård, I., Keller, M., Larraia, E., Pastro, V., Scholl, P., & Smart, N. P. (2013) · Lecture Notes in Computer Science · doi:10.1007/978-3-642-40203-6_1 · Cited by 458
Fast Algorithms for Signal Processing
Blahut, R. E. (2010) · doi:10.1017/cbo9780511760921 · Cited by 274
Speeding up the computations on an elliptic curve using addition-subtraction chains
Morain, F., & Olivos, J. (1990) · RAIRO - Theoretical Informatics and Applications · doi:10.1051/ita/1990240605311 · Cited by 258
Metadata
- Authors
- Montgomery, P. L.
- Venue
- Mathematics of Computation
- Publisher
- American Mathematical Society (AMS)
- Published
- 1985
- Volume
- 44
- Issue
- 170
- Pages
- 519-521
- ISSN
- 0025-5718 (ISSN-L)
- 1088-6842
- OpenAlex
- W2004814164
- Cited by
- 2,669
- References
- 5
- FWCI
- 12.67
- Type
- journal article
- Language
- en
- Open access
- bronze
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- Montgomery, P. L. (1985). Modular multiplication without trial division. Mathematics of Computation. https://doi.org/10.1090/s0025-5718-1985-0777282-x
Data sources
Bibliographic data: Semantic Scholar, OpenAlex, Crossref.
Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
