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» Is There a Shortage of Primes for Cryptography
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CORR
2008
Springer
98views Education» more  CORR 2008»
13 years 7 months ago
Divisibility, Smoothness and Cryptographic Applications
This paper deals with products of moderate-size primes, familiarly known as smooth numbers. Smooth numbers play an crucial role in information theory, signal processing and crypto...
David Naccache, Igor Shparlinski
PAIRING
2007
Springer
14 years 1 months ago
Remarks on Cheon's Algorithms for Pairing-Related Problems
— In EUROCRYPT 2006, Cheon proposed breakthrough algorithms for pairing-related problems such as the q-weak/strong Diffie-Hellman problem. Using that the exponents of an element ...
Shunji Kozaki, Taketeru Kutsuma, Kazuto Matsuo
ANTS
2010
Springer
250views Algorithms» more  ANTS 2010»
13 years 11 months ago
A Subexponential Algorithm for Evaluating Large Degree Isogenies
An isogeny between elliptic curves is an algebraic morphism which is a group homomorphism. Many applications in cryptography require evaluating large degree isogenies between ellip...
David Jao, Vladimir Soukharev
ANTS
2006
Springer
94views Algorithms» more  ANTS 2006»
13 years 11 months ago
Fast Bounds on the Distribution of Smooth Numbers
Let P(n) denote the largest prime divisor of n, and let (x, y) be the number of integers n x with P(n) y. In this paper we present improvements to Bernstein's algorithm, whi...
Scott T. Parsell, Jonathan Sorenson
ASAP
2004
IEEE
160views Hardware» more  ASAP 2004»
13 years 11 months ago
Architectural Support for Arithmetic in Optimal Extension Fields
Public-key cryptosystems generally involve computation-intensive arithmetic operations, making them impractical for software implementation on constrained devices such as smart ca...
Johann Großschädl, Sandeep S. Kumar, Ch...