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» Bit Security of the CDH Problems over Finite Fields
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PKC
2010
Springer
234views Cryptology» more  PKC 2010»
13 years 6 months ago
Solving a 676-Bit Discrete Logarithm Problem in GF(36n)
Abstract. Pairings on elliptic curves over finite fields are crucial for constructing various cryptographic schemes. The T pairing on supersingular curves over GF(3n ) is particula...
Takuya Hayashi, Naoyuki Shinohara, Lihua Wang, Shi...
CORR
2010
Springer
99views Education» more  CORR 2010»
13 years 4 months ago
Security in Distributed Storage Systems by Communicating a Logarithmic Number of Bits
Abstract--We investigate the problem of maintaining an encoded distributed storage system when some nodes contain adversarial errors. Using the error-correction capabilities that a...
Theodoros K. Dikaliotis, Alexandros G. Dimakis, Tr...
FOCM
2008
77views more  FOCM 2008»
13 years 4 months ago
Modular Counting of Rational Points over Finite Fields
Let Fq be the finite field of q elements, where q = ph. Let f(x) be a polynomial over Fq in n variables with m non-zero terms. Let N(f) denote the number of solutions of f(x) = 0 ...
Daqing Wan
ACISP
2010
Springer
13 years 6 months ago
Security Estimates for Quadratic Field Based Cryptosystems
Abstract. We describe implementations for solving the discrete logarithm problem in the class group of an imaginary quadratic field and in the infrastructure of a real quadratic fi...
Jean-François Biasse, Michael J. Jacobson, ...
ICISC
2000
126views Cryptology» more  ICISC 2000»
13 years 6 months ago
Cryptographic Applications of Sparse Polynomials over Finite Rings
Abstract. This paper gives new examples that exploit the idea of using sparse polynomials with restricted coefficients over a finite ring for designing fast, reliable cryptosystems...
William D. Banks, Daniel Lieman, Igor Shparlinski,...