On algebraic graph theory and non-bijective multivariate 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 Fn 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 cryptos...
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| Published in: | Algebra and Discrete Mathematics |
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| Date: | 2015 |
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| Format: | Article |
| Language: | English |
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Інститут прикладної математики і механіки НАН України
2015
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/154900 |
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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-bijective multivariate maps in cryptography / V. Ustimenko // Algebra and Discrete Mathematics. — 2015. — Vol. 19, № 2. — С. 152-170. — Бібліогр.: 33 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862637311742705664 |
|---|---|
| author | Ustimenko, V. |
| author_facet | Ustimenko, V. |
| citation_txt | On algebraic graph theory and non-bijective multivariate maps in cryptography / V. Ustimenko // Algebra and Discrete Mathematics. — 2015. — Vol. 19, № 2. — 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 Fn 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 | 2025-11-30T22:45:10Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-154900 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1726-3255 |
| language | English |
| last_indexed | 2025-11-30T22:45:10Z |
| publishDate | 2015 |
| publisher | Інститут прикладної математики і механіки НАН України |
| record_format | dspace |
| spelling | Ustimenko, V. 2019-06-16T06:07:36Z 2019-06-16T06:07:36Z 2015 On algebraic graph theory and non-bijective multivariate maps in cryptography / V. Ustimenko // Algebra and Discrete Mathematics. — 2015. — Vol. 19, № 2. — С. 152-170. — Бібліогр.: 33 назв. — англ. 1726-3255 https://nasplib.isofts.kiev.ua/handle/123456789/154900 Special family of non-bijective multivariate maps Fn of Zmⁿ into itself is constructed for n=2,3,… and composite m. The map Fn 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-bijective multivariate maps in cryptography Article published earlier |
| spellingShingle | On algebraic graph theory and non-bijective multivariate maps in cryptography Ustimenko, V. |
| title | On algebraic graph theory and non-bijective multivariate maps in cryptography |
| title_full | On algebraic graph theory and non-bijective multivariate maps in cryptography |
| title_fullStr | On algebraic graph theory and non-bijective multivariate maps in cryptography |
| title_full_unstemmed | On algebraic graph theory and non-bijective multivariate maps in cryptography |
| title_short | On algebraic graph theory and non-bijective multivariate maps in cryptography |
| title_sort | on algebraic graph theory and non-bijective multivariate maps in cryptography |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/154900 |
| work_keys_str_mv | AT ustimenkov onalgebraicgraphtheoryandnonbijectivemultivariatemapsincryptography |