19,058 research outputs found
Efficient Big Integer Multiplication and Squaring Algorithms for Cryptographic Applications
Public-key cryptosystems are broadly employed to provide security for digital information. Improving the efficiency of public-key
cryptosystem through speeding up calculation and using fewer resources are among themain goals of cryptography research. In this
paper, we introduce new symbols extracted from binary representation of integers called Big-ones.We present a modified version
of the classicalmultiplication and squaring algorithms based on the Big-ones to improve the efficiency of big integermultiplication
and squaring in number theory based cryptosystems. Compared to the adopted classical and Karatsuba multiplication algorithms
for squaring, the proposed squaring algorithm is 2 to 3.7 and 7.9 to 2.5 times faster for squaring 32-bit and 8-Kbit numbers,
respectively. The proposed multiplication algorithm is also 2.3 to 3.9 and 7 to 2.4 times faster for multiplying 32-bit and 8-Kbit
numbers, respectively.The number theory based cryptosystems, which are operating in the range of 1-Kbit to 4-Kbit integers, are
directly benefited from the proposed method since multiplication and squaring are the main operations in most of these systems
A Structure result for bricks in Heisenberg groups
We show that for a sufficiently big \textit{brick} of the
-dimensional Heisenberg group over the finite field
, the product set contains at least many
cosets of some non trivial subgroup of
Asymmetric Leakage from Multiplier and Collision-Based Single-Shot Side-Channel Attack
The single-shot collision attack on RSA proposed by Hanley et al. is studied focusing on the difference between two operands of multiplier. It is shown that how leakage from integer multiplier and long-integer multiplication algorithm can be asymmetric between two operands. The asymmetric leakage is verified with experiments on FPGA and micro-controller platforms. Moreover, we show an experimental result in which success and failure of the attack is determined by the order of operands. Therefore, designing operand order can be a cost-effective countermeasure. Meanwhile we also show a case in which a particular countermeasure becomes ineffective when the asymmetric leakage is considered. In addition to the above main contribution, an extension of the attack by Hanley et al. using the signal-processing technique of Big Mac Attack is presented
ALHEP symbolic algebra program for high-energy physics
ALHEP is the symbolic algebra program for high-energy physics. It deals with
amplitudes calculation, matrix element squaring, Wick theorem, dimensional
regularization, tensor reduction of loop integrals and simplification of final
expressions. The program output includes: Fortran code for differential cross
section, Mathematica files to view results and intermediate steps and TeX
source for Feynman diagrams. The PYTHIA interface is available. The project
website http://www.hep.by/alhep contains up-to-date executables, manual and
script examples.Comment: 33 pages, 4 figure
A note on Freiman models in Heisenberg groups
Green and Ruzsa recently proved that for any , any small squaring set
in a (multiplicative) abelian group, i.e. , has a Freiman
-model: it means that there exists a group and a Freiman -isomorphism
from into such that .
In an unpublished note, Green proved that such a result does not necessarily
hold in non abelian groups if . The aim of this paper is improve
Green's result by showing that it remains true under the weaker assumption
Spartan Daily, January 27, 1938
Volume 26, Issue 72https://scholarworks.sjsu.edu/spartandaily/2709/thumbnail.jp
Spartan Daily, January 27, 1938
Volume 26, Issue 72https://scholarworks.sjsu.edu/spartandaily/2709/thumbnail.jp
Seven Staggering Sequences
When my "Handbook of Integer Sequences" came out in 1973, Philip Morrison
gave it an enthusiastic review in the Scientific American and Martin Gardner
was kind enough to say in his Mathematical Games column that "every
recreational mathematician should buy a copy forthwith." That book contained
2372 sequences. Today the "On-Line Encyclopedia of Integer Sequences" contains
117000 sequences. This paper will describe seven that I find especially
interesting. These are the EKG sequence, Gijswijt's sequence, a numerical
analog of Aronson's sequence, approximate squaring, the integrality of n-th
roots of generating functions, dissections, and the kissing number problem.
(Paper for conference in honor of Martin Gardner's 91st birthday.)Comment: 12 pages. A somewhat different version appeared in "Homage to a Pied
Puzzler", E. Pegg Jr., A. H. Schoen and T. Rodgers (editors), A. K. Peters,
Wellesley, MA, 2009, pp. 93-11
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