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Page 101 of Mathematical Reviews Vol. , Issue 98A [page]

1998 Mathematical Reviews  
The running times are given in arithmetical operations on integers that are at most n, that is, of size logn at worst.  ...  In this paper the authors describe unconditional, deterministic, polynomial-time algorithms that prove primality for certain classes of primes.  ... 

Research on Quantum Annealing Integer Factorization Based on Different Columns

Baonan Wang, Xiaoting Yang, Dan Zhang
2022 Frontiers in Physics  
This paper proposes the influence of different column methods on the final integer factorization, puts forward a new dimension reduction formula, simplifies the integer factorization model based on quantum  ...  of the quantum annealing algorithm.  ...  FUNDING This work was supported by the grant of Shanghai Sailing Plan of "Science and Technology Innovation Action Plan" of China (No. 21YF1415100).  ... 
doi:10.3389/fphy.2022.914578 fatcat:6cx2gbcefrallmlmhgy4feoaci

Performance Analysis of Fermat Factorization Algorithms

Hazem M. Bahig, Mohammed A., Khaled A., Amer AlGhadhban, Hatem M.
2020 International Journal of Advanced Computer Science and Applications  
Second, we conduct extensive experimental studies on nine different integer factorization algorithms and measure the performance of each algorithm based on two parameters: the number of bits for the odd  ...  The difficulty encountered in breaking RSA derives from the difficulty in finding a polynomial time for integer factorization.  ...  Q3) Many integer factorization algorithms have the same number of iterations, theoretically, but which one is the fastest over different data distributions?  ... 
doi:10.14569/ijacsa.2020.0111242 fatcat:z6tpb5hudrfolforprbhx4ou44

Page 4781 of Mathematical Reviews Vol. , Issue 911 [page]

1991 Mathematical Reviews  
This paper addresses the computational complexity of the integer factorization problem; its goal is to present algorithms whose run- ning time can be rigorously proved.  ...  The main result can be stated in terms of the function L(n) = exp(,/logn loglogn). The author proves that there is a randomized algorithm that will factor n in expected time L(n)V4/3+()), H. W.  ... 

Page 195 of Behavior Research Methods Vol. 44, Issue 1 [page]

2012 Behavior Research Methods  
A lower number of runs decreases computation time but increases the risk that the algorithm may not converge to the global maximum of the likelihood function.  ...  The argument runs allows changing the number of runs of the LM algorithm from different random start values.  ... 

A Rigorous Time Bound for Factoring Integers

H. W. Lenstra, Carl Pomerance
1992 Journal of The American Mathematical Society  
They are obliged to B. de Smit for pointing out an error in an earlier version of § 12. They also gratefully acknowledge help with several of the references from P. van Emde Boas, A.  ...  ACKNOWLEDGMENTS The authors are grateful to the Institute for Advanced Study (Princeton) for hospitality and support while this paper was being written.  ...  This means that, for a given value of the input, the running time of the algorithm may not be constant; instead, it has a distribution.  ... 
doi:10.2307/2152702 fatcat:2dr3kozxcnbq5bt3w6vy5torsa

A rigorous time bound for factoring integers

H. W. Lenstra, Carl Pomerance
1992 Journal of The American Mathematical Society  
They are obliged to B. de Smit for pointing out an error in an earlier version of § 12. They also gratefully acknowledge help with several of the references from P. van Emde Boas, A.  ...  ACKNOWLEDGMENTS The authors are grateful to the Institute for Advanced Study (Princeton) for hospitality and support while this paper was being written.  ...  This means that, for a given value of the input, the running time of the algorithm may not be constant; instead, it has a distribution.  ... 
doi:10.1090/s0894-0347-1992-1137100-0 fatcat:xwymcy6yrzbbvlzq5otuxywpp4

Untitled Item

Oluyemi Amujo, M.B Hammawa, A.Y. Atumoshi, A. Abdulrahman
2021 figshare.com  
The strength of modern cryptography algorithms are based on the factors such as keys-space, transmission techniques and fundamental process of executing one-way/trapdoor functions which are said to be  ...  This paper focuses on quantum cryptography and how it contributes value to a long-time strategy pertaining to completely secure key distribution.  ...  The number field sieve by Lenstra, Lenstra, Manasee, and Pollard with modifications by Adlemann and Pomerance is a factoring algorithm proved under a certain set of assumptions to factor integers in  ... 
doi:10.6084/m9.figshare.17134601.v1 fatcat:ihx6rf65izdnzmcqsqmx7v65i4

An algorithm for detecting contention-based covert timing channels on shared hardware

Jie Chen, Guru Venkataramani
2014 Proceedings of the Third Workshop on Hardware and Architectural Support for Security and Privacy - HASP '14  
In this work, we propose an algorithm to detect the possible presence of covert timing channels on shared hardware that use contention-based patterns for communication.  ...  Recent studies have shown the vulnerability of popular computing environments, such as cloud, to these covert timing channels.  ...  The value of t can be picked from a wide range, and is tempered by ↵ factor which ensures that t is neither too low (when the probability of a certain number of events within t follows Poisson distribution  ... 
doi:10.1145/2611765.2611766 dblp:conf/isca/0020V14 fatcat:lzhjsfx75rc35oaqjj4yecxdlu

On the Difficulty of Computing Logarithms Over GF (q^m)

Martin E. Hellman
1980 1980 IEEE Symposium on Security and Privacy  
He also noted that the running time for the modified algorithm should be of the same form as for factoring, namely exp {sqrt [k in(q) ln(ln(q))]}. (1) This function grows faster than any polynomial in  ...  However, Adleman has recently observed that certain fast algorithms for factoring integers are also applicable to computing discrete logs over GF(q), the Galois field with q elements (q denotes a prime  ... 
doi:10.1109/sp.1980.10015 dblp:conf/sp/Hellman80 fatcat:ihftf72hljenhmaeqrej323hnm

Efficient calculation of exact probability distributions of integer features on RNA secondary structures

Ryota Mori, Michiaki Hamada, Kiyoshi Asai
2014 BMC Genomics  
Results: A general method to efficiently compute the distribution of any integer scalar/vector function on the secondary structure is proposed.  ...  Conclusions: The proposed method provides a clear and comprehensive procedure to construct algorithms for distributions of various integer features.  ...  Acknowledgements The authors thank to Toutai Mituyama and Yukiteru Ono for their help in integration of the software to the web page.  ... 
doi:10.1186/1471-2164-15-s10-s6 pmid:25560710 pmcid:PMC4304215 fatcat:yqayfs54qfgjjij55igjhkn5wa

Discrete Logarithms: The Past and the Future [chapter]

Andrew Odlyzko
2000 Towards a Quarter-Century of Public Key Cryptography  
This factor has stimulated an outpouring of research on the complexity of discrete logs. This paper is a brief survey of the current state of the art in algorithms for discrete logs.  ...  However, they were rather obscure, just like integer factorization. Unlike the latter, they could not even invoke any famous quotes of Gauss (cf.  ...  The very first analyses of the asymptotic running time of index calculus algorithms appeared in the 1970s, and were of the form (4.4). (Most of these analyses were for integer factorization methods.)  ... 
doi:10.1007/978-1-4757-6856-5_3 fatcat:75jkuihodratlmbf74eyasedyy

Process Scheduling in DSC and the Large Sparse Linear Systems Challenge

A. Dı́az, M. Hitz, E. Kaltofen, A. Lobo, T. Valente
1995 Journal of symbolic computation  
In the first we have implemented an algorithm that can prove a number of more than 1,000 decimal digits prime in about 2 months elapsed time on some 20 computers.  ...  New features of our DSC system for distributing a symbolic computation task over a network of processors are described.  ...  (vi) We document experiments with DSC on a parallel version of the Cantor/Zassenhaus polynomial factorization algorithm and the Goldwasser-Kilian/Atkin (GKA) integer primality test.  ... 
doi:10.1006/jsco.1995.1015 fatcat:ozsef3adbfeh3pfyrmbmt4cw5e

Page 6096 of Mathematical Reviews Vol. , Issue 2000i [page]

2000 Mathematical Reviews  
One of the important factors in the running time of the number field sieve is the choice of a polynomial defining an appropriate number field.  ...  Such integers were previously proposed for various cryptographic applications. When r ~ log p our algorithm runs in polynomial time (in logN).  ... 

Note on Integer Factoring Algorithms II [article]

N. A. Carella
2007 arXiv   pre-print
These algorithms are practical, and can factor large classes of balanced integers N = pq, p < q < 2p in superpolynomial time. Further, an extension of the Fermat factoring method is proposed.  ...  This note introduces a new class of integer factoring algorithms. Two versions of this method will be described, deterministic and probabilistic.  ...  A multiplicative algorithm produces the factors of on integer by a process of multiplications, and an additive algorithm produces the factors of on integer by a process of additions.  ... 
arXiv:math/0702227v1 fatcat:udrkv6znorcolj3vgwmp77xhpi
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