Compactly supported functions in cryptography algorithms | Prikladnaya Diskretnaya Matematika - Applied Discrete Mathematics. 2017. № 36. DOI: 10.17223/20710410/36/6

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 = a₁a₂ ...a_n, we first convert a to a polynomial a(x) = a₁ + a₂x +.....+ a_nxⁿ-1, then approximate n a(x) by a linear combination F(x) = E r_j/_j(x), where / = (f₁,f₂,..., f_n) is an j=1 OFF-basis not having the orthogonality property, and finally compute the ciphertext b = b₁b₂ ... b_n, where b_j = F(k_j) for some values k_j of x, i = 1,2,..., n. The numbers k₁,..., k_n and some parameters of functions in / form the key of the cipher. To decrypt the ciphertext b, we first, given b₁,...,b_n and key parameters in /, compute the approximation coefficients r₁,..., r_n, next, given k₁,..., k_n, compute x'_x, ...,x'_n such that a(xj) = r_j for i = 1,2,..., n, then construct a(x) by the Lagrange method, and finally convert a(x) to a.