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Artin's Primitive Root Conjecture – A Survey

Pieter Moree
2012 Integers  
The first part of the survey is intended for a rather general audience and rather colloquial, whereas the second part is intended for number theorists and ends with several open problems.  ...  Wojciec Gajda wrote a section on 'Artin for K-theory of number fields,' and Hester Graves (together with me) on 'Artin's conjecture and Euclidean domains.'  ...  For small k, k-cycles of the discrete logarithm problem are studied in Holden and Moree [235] (for more experimental work in this direction see [232, 233] ), see also Glebsky and Shparlinski [178]  ... 
doi:10.1515/integers-2012-0043 fatcat:3fobrigit5etbbwug7jidmscwa

Some Fundamental Theorems in Mathematics [article]

Oliver Knill
2022 arXiv   pre-print
This fundamental theorem of Lucas of 1878 [451] tells that the sequence F (n) is a strong divisibility sequence.  ...  Open problems fuel new research and new concepts.  ...  This was the first of the 23 problems posed by Hilbert in 1900. The answer is surprising: one has a choice. One can accept either the "yes" or the "no" as a new axiom.  ... 
arXiv:1807.08416v4 fatcat:lw7lbsxyznfrnaozilxapihmdy

Design of large polyphase filters in the Quadratic Residue Number System

Gian Carlo Cardarilli, Alberto Nannarelli, Yann Oster, Massimo Petricca, Marco Re
2010 2010 Conference Record of the Forty Fourth Asilomar Conference on Signals, Systems and Computers  
The algorithm consists of a sequence of overlapped operations: 1) digit recurrence logarithm, 2) sequential multiplication, and 3) on-line antilogarithm.  ...  analyze a spectrum allocation problem between two classes of users.  ... 
doi:10.1109/acssc.2010.5757589 fatcat:ccxnu5owr5fyrcjcqukumerueq

Theoretical and experimental investigation of the insertion loss of a dissipative muffler

Christian Pommer, Viggo Tarnow
1986 Journal of the Acoustical Society of America  
This paper shows the design sequence, the results for a uniform elliptic ring used as a baseline, and application to designing various flextensionals for several new major Navy sonar transmit array programs  ...  A new VQ codebook for thc new speaker is therefore generated, and it is a one-to-one projected image of the VQ codebook of the standard speaker onto the feature space of the new speaker.  ...  This allowed building of a sequence of steps which are based on equal frequency intervals in hertz, rather than on a logarithmic series.  ... 
doi:10.1121/1.2024087 fatcat:tcee6inawvhubc6ftuk2ffhyce

On the Analysis of Public-Key Cryptologic Algorithms

Andrea Miele
2015
For the security of ECC, the discrete logarithm problem in the group of points of the elliptic curve must be hard.  ...  If h is an element of 〈g 〉 the discrete logarithm problem is the problem of finding an integer k ∈ Z ≥0 such that h = kg .  ...  Each row contains a value d , the class number h −d of the imaginary quadratic field Q( −d ) with discriminant −d , the root used (commonly referred to as the j -invariant), the elliptic curve E = E a,  ... 
doi:10.5075/epfl-thesis-6603 fatcat:kijyxks7kvagtc7rj4lr6qreiu

Subgroup Cryptosystems [chapter]

Arjen K. Lenstra
Encyclopedia of Cryptography and Security  
Hence, for proper divisors s of d the resulting discrete logarithm problem reduces to the discrete logarithm in a proper subfield of F p d which is widely believed to be considerably easier than the problem  ...  The value n is called the discrete logarithm of h with respect to g, or n = log g h. Computing n is aptly known as the discrete logarithm problem (DLP).  ...  Het is bijvoorbeeld eenvoudig twee priemgetallen met elkaar te vermenigvuldigen, maar het is onbekend of het omgekeerde, factoriseren, ook snel kan.  ... 
doi:10.1007/0-387-23483-7_418 fatcat:gg3uycmc65a6thhy4gtslscxae

Speaker comfort and increase of voice level in lecture rooms

Jonas Brunskog, Anders C. Gade, Gaspar Payà Bellester, Lilian Reig Calbo
2008 Journal of the Acoustical Society of America  
indicate that all three of these characteristics do affect listeners' percept of a consonant, but not sufficiently to completely account for the percept.  ...  The current work identifies acoustic characteristics of reduced 'flaps' and presents phonetic identification data for continua that manipulate these characteristics.  ...  We then propose a new method for blindly estimating the reverberation time to resolve the problem.  ... 
doi:10.1121/1.2934367 fatcat:xr6gp4ldo5bylnxytx2iumrdmi

Fine‐structure processing, frequency selectivity and speech perception in hearing‐impaired listeners

Olaf Strelcyk, Torsten Dau
2008 Journal of the Acoustical Society of America  
indicate that all three of these characteristics do affect listeners' percept of a consonant, but not sufficiently to completely account for the percept.  ...  The current work identifies acoustic characteristics of reduced 'flaps' and presents phonetic identification data for continua that manipulate these characteristics.  ...  We then propose a new method for blindly estimating the reverberation time to resolve the problem.  ... 
doi:10.1121/1.2935148 fatcat:nqyyia5pubamnhqgonegghrudm

A design methodology for 2D sparse NDE arrays using an efficient implementation of refracted-ray TFM

Jerzy Dziewierz, Timothy Lardner, Anthony Gachagan
2013 2013 IEEE International Ultrasonics Symposium (IUS)  
Background, Motivation and Objective Developing new technologies that enable the repair or replacement of diseased or injured tissues and organs is a major focus of tissue engineering.  ...  Recent advances in the field of tissue engineering include the engineering of skin, cartilage, and bladder, all of which are relatively thin tissues that can rely on diffusion for the delivery of oxygen  ...  The authors acknowledge the ANR and DGA for their support under the project Metactif, grant ANR-11-ASTR-015.  ... 
doi:10.1109/ultsym.2013.0035 fatcat:th5znfh7y5bklfdbmhb4u6iq2i

On the average-case hardness of total search problems

Chethan Kamath, Krzysztof Pietrzak
2020
A search problem lies in the complexity class FNP if a solution to the given instance of the problem can be verified efficiently.  ...  The complexity class TFNP consists of all search problems in FNP that are total in the sense that a solution is guaranteed to exist.  ...  Another example is the widely-deployed DSA (Digital Signature Algorithm) and EC-DSA (Elliptic-Curve DSA) signature schemes which have discrete-logarithm problem (DLP), the problem of computing the discrete  ... 
doi:10.15479/at:ista:7896 fatcat:y4qocnt2a5he5exw2wl322oxmq

ANALYSIS OF CRYPTOGRAPHIC ALGORITHMS AGAINST THEORETICAL AND IMPLEMENTATION ATTACKS [article]

SILVIA MELLA
2018
In order to soften the a-priori knowledge on the injection technique needed by the attacker, we present a new approach for DFA based on clustering, called J-DFA.  ...  A peculiar result of this method is that, besides the preferred candidate for the key, it also provides the preferred models for the fault.  ...  For instance, integer factorization for RSA, the discrete logarithm problem for the Diffie-Hellman protocol or the shortest vector problem for lattice based cryptosystems.  ... 
doi:10.13130/mella-silvia_phd2018-02-27 fatcat:phzf464ql5gvrdmhmbjzglsk4e

Automatic generation of high speed elliptic curve cryptography code

Daniele Canavese, A. Lioy
2016
Antonio Lioy for giving me the opportunity to work in the Computer and Network Security Group and working with such great people in all these years.  ...  Acknowledgments First of all, I would like to thank prof.  ...  In 2010, Dahshan and Irvine [81] proposed a fast key distribution method based on the elliptic curve discrete logarithm problem for low power and processing constrained devices such as the MANET nodes  ... 
doi:10.6092/polito/porto/2652694 fatcat:winvbqkgvzb2xgqjxyycupgvne