Geodesic
Global optimization problems associated with cryptographic analysis of asymmetric ciphers
Prikladnaâ diskretnaâ matematika, no. 2 (2008), pp. 113-119

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The aim of this article is to establish relation between well-known problems of cryptographic analysis and global optimization problems which can be associated with SAT representation of cryptographic algorithms where bits of key are part of SAT solution string. The SAT forms for factorization problem, for logarithmic problem and for logarithmic problem on elliptic curves are constructed. For numerical solution, some low relaxation algorithms are adapted. The results of numerical experiments give us more then 50% bits for unknowns in SAT factorization form. 
@article{PDM_2008_2_a23,
     author = {V. I. Dulkeyt and R. T. Faizullin and I. G. Khnikin},
     title = {Global optimization problems associated with cryptographic analysis of asymmetric ciphers},
     journal = {Prikladna\^a diskretna\^a matematika},
     pages = {113--119},
     publisher = {mathdoc},
     number = {2},
     year = {2008},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/PDM_2008_2_a23/}
}
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V. I. Dulkeyt; R. T. Faizullin; I. G. Khnikin. Global optimization problems associated with cryptographic analysis of asymmetric ciphers. Prikladnaâ diskretnaâ matematika, no. 2 (2008), pp. 113-119. http://geodesic.mathdoc.fr/item/PDM_2008_2_a23/