Geodesic
Application of the lattice theory to the analysis of digital signature schemes
Matematičeskie voprosy kriptografii, Tome 9 (2018), pp. 73-84

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With the use of lattice theory four attacks on digital signature schemes described in the national standard GOST R 34.10-2012 are analysed. These attacks are based on the lattice theory. Upper asymptotic bounds for the probability of successful implementation are obtained. A conclusion is made that the considered attacks are unable to lower the security estimate of the Russian standardized signature scheme. 
@article{MVK_2018_9_a3,
     author = {A. M. Guselev},
     title = {Application of the lattice theory to the analysis of digital signature schemes},
     journal = {Matemati\v{c}eskie voprosy kriptografii},
     pages = {73--84},
     publisher = {mathdoc},
     volume = {9},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MVK_2018_9_a3/}
}
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A. M. Guselev. Application of the lattice theory to the analysis of digital signature schemes. Matematičeskie voprosy kriptografii, Tome 9 (2018), pp. 73-84. http://geodesic.mathdoc.fr/item/MVK_2018_9_a3/