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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.
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