On algebraic graph theory and non-bijectivemultivariate maps in cryptography
Special family of non-bijective multivariate maps Fn of Zmⁿ into itself is constructed for n = 2,3, ... and composite m.The map F is injective on Ωn = {x|x1+x2+: : : xn ∈ Zm*} and solution of the equation Fn(x) = b, x ∈ Ωn can be reduced to the solution of equation zr = α, z ∈ Zm*, (r, φ(m)) = 1. Th...
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| Published in: | Algebra and Discrete Mathematics |
|---|---|
| Date: | 2015 |
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| Format: | Article |
| Language: | English |
| Published: |
Інститут прикладної математики і механіки НАН України
2015
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/158006 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | On algebraic graph theory and non-bijectivemultivariate maps in cryptography / V. Ustimenko // Algebra and Discrete Mathematics. — 2015. — Vol. 20, № 1. — С. 152–170. — Бібліогр.: 33 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862565367905255424 |
|---|---|
| author | Ustimenko, V. |
| author_facet | Ustimenko, V. |
| citation_txt | On algebraic graph theory and non-bijectivemultivariate maps in cryptography / V. Ustimenko // Algebra and Discrete Mathematics. — 2015. — Vol. 20, № 1. — С. 152–170. — Бібліогр.: 33 назв. — англ. |
| collection | DSpace DC |
| container_title | Algebra and Discrete Mathematics |
| description | Special family of non-bijective multivariate maps Fn of Zmⁿ into itself is constructed for n = 2,3, ... and composite m.The map F is injective on Ωn = {x|x1+x2+: : : xn ∈ Zm*} and solution of the equation Fn(x) = b, x ∈ Ωn can be reduced to the solution of equation zr = α, z ∈ Zm*, (r, φ(m)) = 1. The “hidden RSA cryptosystem” is proposed. Similar construction is suggested for the case Ωn = Zm*ⁿ.
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| first_indexed | 2025-11-26T00:08:40Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-158006 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1726-3255 |
| language | English |
| last_indexed | 2025-11-26T00:08:40Z |
| publishDate | 2015 |
| publisher | Інститут прикладної математики і механіки НАН України |
| record_format | dspace |
| spelling | Ustimenko, V. 2019-06-22T12:34:11Z 2019-06-22T12:34:11Z 2015 On algebraic graph theory and non-bijectivemultivariate maps in cryptography / V. Ustimenko // Algebra and Discrete Mathematics. — 2015. — Vol. 20, № 1. — С. 152–170. — Бібліогр.: 33 назв. — англ. 1726-3255 https://nasplib.isofts.kiev.ua/handle/123456789/158006 Special family of non-bijective multivariate maps Fn of Zmⁿ into itself is constructed for n = 2,3, ... and composite m.The map F is injective on Ωn = {x|x1+x2+: : : xn ∈ Zm*} and solution of the equation Fn(x) = b, x ∈ Ωn can be reduced to the solution of equation zr = α, z ∈ Zm*, (r, φ(m)) = 1. The “hidden RSA cryptosystem” is proposed. Similar construction is suggested for the case Ωn = Zm*ⁿ. en Інститут прикладної математики і механіки НАН України Algebra and Discrete Mathematics On algebraic graph theory and non-bijectivemultivariate maps in cryptography Article published earlier |
| spellingShingle | On algebraic graph theory and non-bijectivemultivariate maps in cryptography Ustimenko, V. |
| title | On algebraic graph theory and non-bijectivemultivariate maps in cryptography |
| title_full | On algebraic graph theory and non-bijectivemultivariate maps in cryptography |
| title_fullStr | On algebraic graph theory and non-bijectivemultivariate maps in cryptography |
| title_full_unstemmed | On algebraic graph theory and non-bijectivemultivariate maps in cryptography |
| title_short | On algebraic graph theory and non-bijectivemultivariate maps in cryptography |
| title_sort | on algebraic graph theory and non-bijectivemultivariate maps in cryptography |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/158006 |
| work_keys_str_mv | AT ustimenkov onalgebraicgraphtheoryandnonbijectivemultivariatemapsincryptography |