Geodesic
Constructing of one-way functions based on undecidability of the endomorphism problem in groups
Prikladnaâ diskretnaâ matematika, no. 13 (2011), pp. 32-33 
S. Y. Erofeev; V. A. Romankov. Constructing of one-way functions based on undecidability of the endomorphism problem in groups. Prikladnaâ diskretnaâ matematika, no. 13 (2011), pp. 32-33. http://geodesic.mathdoc.fr/item/PDM_2011_13_a16/
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     author = {S. Y. Erofeev and V. A. Romankov},
     title = {Constructing of one-way functions based on undecidability of the endomorphism problem in groups},
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     pages = {32--33},
     year = {2011},
     number = {13},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/PDM_2011_13_a16/}
}
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Voir la notice de l'article provenant de la source Math-Net.Ru

The paper proposes a scheme for constructing one-way function in a group with decidable word problem and undecidable endomorphism problem, and a corresponding authentication protocol. Possible prerequisites for reliability of the proposed scheme are analysed.

[1] Levin L. A., “One-way Functions and Pseudorandom Generators”, Combinatorica, 7:4 (1987), 357–363 | DOI | MR | Zbl

[2] Levin L. A., “Odnostoronnie funktsii”, Problemy peredachi informatsii, 39:1 (2003), 103–117 | MR | Zbl

[3] Romankov V. A., “Ob uravneniyakh v svobodnykh metabelevykh gruppakh”, Sibirskii matematicheskii zhurnal, 20:3 (1979), 671–673 | MR

[4] Romankov V. A., “O nerazreshimosti problemy endomorfnoi svodimosti v svobodnykh nilpotentnykh gruppakh i v svobodnykh koltsakh”, Algebra i logika, 16:4 (1977), 457–471 | MR

[5] Grigoriev D., Shpilrain V., “Zero-knowledge authentication schemes from actions on graphs, groups, or rings”, Ann. Pure Appl. Logic, 162 (2010), 194–200 | DOI | MR