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pro vyhledávání: '"Holden, Joshua"'
Autor:
Holden, Joshua
Public-key cryptography has become a popular way to motivate the teaching of concepts in elementary number theory, abstract algebra, and introduction to proof courses, as well as in cryptography courses. Unfortunately, many experts expect quantum com
Externí odkaz:
http://arxiv.org/abs/2207.00558
Publikováno v:
p-Adic Numbers, Ultrametric Analysis and Applications, 2020, Vol. 12, No. 1, pp. 12-28
The "self-power" map $x \mapsto x^x$ modulo $m$ and its generalized form $x \mapsto x^{x^n}$ modulo $m$ are of considerable interest for both theoretical reasons and for potential applications to cryptography. In this paper, we use $p$-adic methods,
Externí odkaz:
http://arxiv.org/abs/1609.06696
Akademický článek
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Autor:
Holden, Joshua
Cette thèse constitue une étude systématique du lexique du déné sųłiné, une langue athabaskane du nord-ouest canadien. Elle présente les définitions et les patrons de combinatoire syntaxique et lexicale de plus de 200 unités lexicales,
Externí odkaz:
http://hdl.handle.net/1866/4616
Autor:
Friedrichsen, Matthew, Holden, Joshua
Publikováno v:
Involve 12 (2019) 63-78
The map x -> x^x modulo p is related to a variation of the digital signature scheme in a similar way to the discrete exponentiation map, but it has received much less study. We explore the number of fixed points of this map by a statistical analysis
Externí odkaz:
http://arxiv.org/abs/1403.5548
Autor:
Holden, Joshua, Robinson, Margaret M.
Publikováno v:
Journal of the Australian Mathematical Society, 92: 163-178, 2012
Brizolis asked for which primes p greater than 3 does there exist a pair (g, h) such that h is a fixed point of the discrete exponential map with base g, or equivalently h is a fixed point of the discrete logarithm with base g. Zhang (1995) and Cobel
Externí odkaz:
http://arxiv.org/abs/1105.5346
Autor:
Cloutier, Daniel R., Holden, Joshua
Publikováno v:
Involve, 3:197--213, 2010. Substantially revised
The discrete logarithm is a problem that surfaces frequently in the field of cryptography as a result of using the transformation g^a mod n. This paper focuses on a prime modulus, p, for which it is shown that the basic structure of the functional gr
Externí odkaz:
http://arxiv.org/abs/math/0605024
Publikováno v:
Cryptologia, 30:69--77, 2006
For a recent student conference, the authors developed a day-long design problem and competition suitable for engineering, mathematics and science undergraduates. The competition included a cryptography problem, for which a workshop was run during th
Externí odkaz:
http://arxiv.org/abs/cs/0509053