Studying the performance of artificial neural networks on problems related to cryptography

Cryptosystems rely on the assumption that a number of mathematical problems are computationally intractable, in the sense that they cannot be solved in polynomial time. Numerous approaches have been applied to address these problems. In this paper, we consider artificial neural networks and study their performance on approximation problems related to cryptography. 2005 Elsevier Ltd. All rights reserved.

[1]  Arne Winterhof,et al.  A note on the interpolation of the Diffie-Hellman mapping , 2001 .

[2]  George D. Magoulas,et al.  Effective Backpropagation Training with Variable Stepsize , 1997, Neural Networks.

[3]  Geoffrey E. Hinton,et al.  Learning internal representations by error propagation , 1986 .

[4]  Adi Shamir,et al.  A method for obtaining digital signatures and public-key cryptosystems , 1978, CACM.

[5]  Gerasimos C. Meletiou,et al.  Explicit form for the discrete logarithm over the field ${\rm GF}(p,k)$ , 1993 .

[6]  M. N. Vrahatis,et al.  Adaptive stepsize algorithms for on-line training of neural networks , 2001 .

[7]  Michael N. Vrahatis,et al.  Artificial nonmonotonic neural networks , 2001, Artif. Intell..

[8]  Igor E. Shparlinski,et al.  Polynomial representations of the Diffie-Hellman mapping , 2001, Bulletin of the Australian Mathematical Society.

[9]  Martin E. Hellman,et al.  Hiding information and signatures in trapdoor knapsacks , 1978, IEEE Trans. Inf. Theory.

[10]  Taher El Gamal A public key cryptosystem and a signature scheme based on discrete logarithms , 1984, IEEE Trans. Inf. Theory.

[11]  Halbert White,et al.  Connectionist nonparametric regression: Multilayer feedforward networks can learn arbitrary mappings , 1990, Neural Networks.

[12]  Andrew M. Odlyzko,et al.  Discrete Logarithms in Finite Fields and Their Cryptographic Significance , 1985, EUROCRYPT.

[13]  Arne Winterhof,et al.  Polynomial Interpolation of the Discrete Logarithm , 2002, Des. Codes Cryptogr..

[14]  Gary L. Mullen,et al.  A polynomial representation for logarithms in GF(q) , 1986 .

[15]  Alfred Menezes,et al.  Handbook of Applied Cryptography , 2018 .

[16]  Allan Pinkus,et al.  Approximation theory of the MLP model in neural networks , 1999, Acta Numerica.

[17]  Andrew M. Odlyzko,et al.  Discrete Logarithms: The Past and the Future , 2000, Des. Codes Cryptogr..

[18]  Martin A. Riedmiller,et al.  A direct adaptive method for faster backpropagation learning: the RPROP algorithm , 1993, IEEE International Conference on Neural Networks.

[19]  Martin Fodslette Møller,et al.  A scaled conjugate gradient algorithm for fast supervised learning , 1993, Neural Networks.

[20]  Harald Niederreiter,et al.  A short proof for explicit formulas for discrete logarithms in finite fields , 1990, Applicable Algebra in Engineering, Communication and Computing.

[21]  Dimitris K. Tasoulis,et al.  Cryptography through Interpolation, Approximation and Computational Intelligence Methods , 2003 .

[22]  Donald F. Specht,et al.  Probabilistic neural networks , 1990, Neural Networks.

[23]  D. Signorini,et al.  Neural networks , 1995, The Lancet.

[24]  Stephen C. Pohlig,et al.  An Improved Algorithm for Computing Logarithms over GF(p) and Its Cryptographic Significance , 2022, IEEE Trans. Inf. Theory.

[25]  Gary L. Mullen,et al.  A note on discrete logarithms in finite fields , 1992, Applicable Algebra in Engineering, Communication and Computing.

[26]  Ueli Maurer,et al.  The Relationship Between Breaking the Diffie-Hellman Protocol and Computing Discrete Logarithms , 1999, SIAM J. Comput..

[27]  Leonard M. Adleman,et al.  A subexponential algorithm for the discrete logarithm problem with applications to cryptography , 1979, 20th Annual Symposium on Foundations of Computer Science (sfcs 1979).

[28]  Igor E. Shparlinski,et al.  On Certain Exponential Sums and the Distribution of Diffie–Hellman Triples , 1999 .

[29]  Kurt Hornik,et al.  Multilayer feedforward networks are universal approximators , 1989, Neural Networks.

[30]  Michael N. Vrahatis,et al.  A FIRST STUDY OF THE NEURAL NETWORK APPROACH IN THE RSA CRYPTOSYSTEM , 2002 .

[31]  M. N. Vrahatisa,et al.  A class of gradient unconstrained minimization algorithms with adaptive stepsize , 1999 .

[32]  Whitfield Diffie,et al.  New Directions in Cryptography , 1976, IEEE Trans. Inf. Theory.