On algebraic graph theory and non-bijective multivariate maps in cryptography

• Published in: Algebra and Discrete Mathematics
• Date: 2015
• Main Author: Ustimenko, V.
• Format: Article
• Language: English
• Published: Інститут прикладної математики і механіки НАН України 2015
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/154900
• 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.

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...