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A Course in Number Theory and Cryptography
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“From r , at least one factor of N is given by the greatest common denominator (gcd) of a r/ 2 ± 1 and N (with probability greater than 1 / 2); the gcd can be computed efficiently using Euclid's algorithm on a classical computer [2] .”
From Experimental realization of Shor's quantum factoring algorithm using nuclear magnetic resonance (2001) · cites this paper as [2]
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Metadata
- Authors
- Koblitz, N.
- Affiliations
- University of Washington (US)
- Corresponding author
- Koblitz, Neal
- ORCID
- Koblitz, Neal
- Venue
- Graduate Texts in Mathematics
- Publisher
- Springer New York
- Published
- 1994
- ISSN
- 0072-5285 (ISSN-L)
- OpenAlex
- W4230398518
- Cited by
- 576
- References
- 0
- Citations by year
- 2026: 9 · 2025: 42 · 2024: 15 · 2023: 26 · 2022: 31 · 2021: 14 · 2020: 35 · 2019: 20 · 2018: 17 · 2017: 10 · 2016: 11 · 2015: 35 · 2014: 24 · 2013: 27 · 2012: 38
- FWCI
- 2.04
- Type
- book
- Language
- en
- Open access
- closed
- Licence
- www.springer.com/tdm (tdm)
- Locations
- Graduate texts in mathematics (publishedVersion)
- CERN Document Server (European Organization for Nuclear Research) (submittedVersion)
- Topics
- Physical Sciences › Computer Science › Computer Networks and Communications › Cryptography and Data Security
- Physical Sciences › Computer Science › Information Systems › Cryptography and Residue Arithmetic
- Physical Sciences › Mathematics › Algebra and Number Theory › Analytic Number Theory Research
- Keywords
- number theory, cryptography, modular arithmetic, public-key cryptography, elliptic curves, primality testing, integer factorization, discrete logarithm problem
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Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
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