Results 21 to 30 of about 169,709 (230)
Logarithm of the Discrete Fourier Transform
International Journal of Mathematics and Mathematical Sciences, 2007 The discrete Fourier transform defines a unitary matrix operator. The logarithm of this operator is computed, along with the projection maps onto its eigenspaces. A geometric interpretation of the discrete Fourier transform is also given.
Michael Aristidou, Jason Hanson
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Quantum computation of discrete logarithms in semigroups
Journal of Mathematical Cryptology, 2014 We describe an efficient quantum algorithm for computing discrete logarithms in semigroups using Shor's algorithms for period finding and the discrete logarithm problem as subroutines.
Childs Andrew M., Ivanyos Gábor
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Logarithm of multivector in real 3D Clifford algebras
Nonlinear Analysis, 2023 Closed form expressions for a logarithm of general multivector (MV) in basis-free form in real geometric algebras (GAs) Clp,q are presented for all n = p + q = 3.
Artūras Acus, Adolfas Dargys
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A kilobit hidden SNFS discrete logarithm computation [PDF]
, 2016 We perform a special number field sieve discrete logarithm computation in a 1024-bit prime field. To our knowledge, this is the first kilobit-sized discrete logarithm computation ever reported for prime fields.
A Commeine +22 more
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The discrete logarithm problem in Bergman's non-representable ring
Journal of Mathematical Cryptology, 2012 Bergman's ring , parameterized by a prime number p, is a ring with p5 elements that cannot be embedded in a ring of matrices over any commutative ring. This ring was discovered in 1974.
Banin Matan, Tsaban Boaz
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Cryptanalysis of the cryptosystems based on the generalized hidden discrete logarithm problem [PDF]
Computer Science Journal of MoldovaIn this paper, we will solve an important form of hidden discrete logarithm problem (HDLP) and a generalized form of HDLP (GHDLP) over non-commutative associative algebras (FNAAs). We will reduce them to discrete logarithm problem (DLP) in a finite field
Yanlong Ma
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Quasi-subfield Polynomials and the Elliptic Curve Discrete Logarithm Problem
Journal of Mathematical Cryptology, 2020 We initiate the study of a new class of polynomials which we call quasi-subfield polynomials. First, we show that this class of polynomials could lead to more efficient attacks for the elliptic curve discrete logarithm problem via the index calculus ...
Huang Ming-Deh +4 more
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Pairing-Free for Public Key Encryption With Equality Test Scheme
IEEE Access, 2021 The modular exponentiation has been proved better in terms of computational efficiency as compared to bilinear pairing. Therefore, discrete logarithm, a concept of modular exponentiation may be incorporated to present improved security schemes. With this
Huijun Zhu +3 more
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Computing Small Discrete Logarithms Faster [PDF]
, 2012 Computations of small discrete logarithms are feasible even in "secure" groups, and are used as subroutines in several cryptographic protocols in the literature. For example, the Boneh–Goh–Nissim degree-2-homomorphic public-key encryption system uses generic square-root discrete-logarithm methods for decryption.
Bernstein, D.J., Lange, T.
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A Tight Upper Bound for the Third-Order Asymptotics for Most Discrete Memoryless Channels [PDF]
, 2013 This paper shows that the logarithm of the epsilon-error capacity (average error probability) for n uses of a discrete memoryless channel is upper bounded by the normal approximation plus a third-order term that does not exceed 1/2 log n + O(1) if the ...
Tan, Vincent Y. F., Tomamichel, Marco
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