Geodesic
Mapping enlargements preserving identification property
Prikladnaâ diskretnaâ matematika, no. 13 (2011), pp. 26-27
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Mappings defined on a Cartesian power of a finite set with the property to be identified on a subset of co-domain coordinates are considered. A mapping enlargement preserving the identification property is suggested. In the secret sharing schemes based on involutions, the result can be applied to specify authorized subsets when a new patticipant is added. 
@article{PDM_2011_13_a12,
     author = {L. N. Andreeva},
     title = {Mapping enlargements preserving identification property},
     journal = {Prikladna\^a diskretna\^a matematika},
     pages = {26--27},
     year = {2011},
     number = {13},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/PDM_2011_13_a12/}
}
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L. N. Andreeva. Mapping enlargements preserving identification property. Prikladnaâ diskretnaâ matematika, no. 13 (2011), pp. 26-27. http://geodesic.mathdoc.fr/item/PDM_2011_13_a12/

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[3] Andreeva L. N., “K kriptoanalizu involyutivnykh shifrov s chastichno izvestnymi involyutsiyami”, Vestnik Tomskogo gosuniversiteta, 2006, Prilozhenie No 17, 109–112