Summary: This paper discusses an asymmetric cryptosystem \(C^*\) which consists of public transformations of complexity \(O(m^2n^3)\) and secret transformations of complexity \(O((mn)^2(m+\log n))\), where each complexity is measured in the total number of bit-operations for processing an \(mn\)-bit message block. Each public key of \(C^*\) is an \(n\)-tuple of quadratic \(n\)-variate polynomials over \(\mathrm{GF}(2^m)\) and can be used for both verifying signatures and encrypting plaintexts. This paper also shows that for \(C^*\) it is practically infeasible to extract the \(n\)-tuple of \(n\)-variate polynomials representing the inverse of the corresponding public key.
[For the entire collection see Zbl 0651.00027.]