| Summary: | The aim of the research was to conduct a cryptographic
analysis of an encryption scheme developed
on the basis of nonpositional polynomial notations to
estimate the algorithm strength. Nonpositional polynomial
notations (NPNs) are residue number systems (RNSs)
based on irreducible polynomials over GF(2). To evaluate
if the algorithms developed on the basis of NPNs are
secure, mathematical models of cryptanalysis involving
algebraic, linear and differential methods have been designed.
The cryptanalysis is as follows. A system of nonlinear
equations is obtained from a function transforming
plaintext into ciphertext with a key. Next, a possibility of
transition of the nonlinear system to a linear one is considered.
The cryptanalysis was conducted for the cases with
known: 1) ciphertext; 2) plaintext and the related ciphertext;
3) plaintext file format; and 4) ASCII-encoded plaintext.
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