Geodesic
Compactly supported functions in cryptography algorithms
Prikladnaâ diskretnaâ matematika, no. 2 (2017), pp. 73-83

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In the paper, we propose a new symmetric block cipher based on the orthogonal finite functions (OFF) in the Sobolev's space. To encrypt a plaintext $a=a_1a_2\dots a_n$, we first convert $a$ to a polynomial $a(x)=a_1+a_2x+\dots+a_nx^{n-1}$, then approximate $a(x)$ by a linear combination $F(x)=\sum_{i=1}^nr_if_i(x)$, where $f=(f_1,f_2,\dots,f_n)$ is an OFF-basis not having the orthogonality property, and finally compute the ciphertext $b=b_1b_2\dots b_n$, where $b_i=F(k_i)$ for some values $k_i$ of $x$, $i=1,2,\dots,n$. The numbers $k_1,\dots,k_n$ and some parameters of functions in $f$ form the key of the cipher. To decrypt the ciphertext $b$, we first, given $b_1,\dots,b_n$ and key parameters in $f$, compute the approximation coefficients $r_1,\dots,r_n$, next, given $k_1,\dots,k_n$, compute $x'_1,\dots,x'_n$ such that $a(x'_i)=r_i$ for $i=1,2,\dots,n$, then construct $a(x)$ by the Lagrange method, and finally convert $a(x)$ to $a$.
Keywords: OFF, finite functions, cryptography, encryption. 
A. V. Shchurenko; V. L. Leontiev. Compactly supported functions in cryptography algorithms. Prikladnaâ diskretnaâ matematika, no. 2 (2017), pp. 73-83. http://geodesic.mathdoc.fr/item/PDM_2017_2_a5/
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     author = {A. V. Shchurenko and V. L. Leontiev},
     title = {Compactly supported functions in cryptography algorithms},
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     pages = {73--83},
     year = {2017},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/PDM_2017_2_a5/}
}
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