Some results on an encryption method using subset-sums of pseudo-recursive sequences

Let A(eta) := {[2(n)eta] : n = 0, 1, 2, ...}, where 1 <= eta < 2. In the recent paper [Discrete Math. Lett. 4 (2020) 31-36], the authors examined the subset-sums of the set A(eta) and then presented an encryption algorithm. The basics of the latter part is that the encoded message is a public natural number N and everyone is allowed to query for the set (A(eta) + A(eta)) boolean AND [1, N] until they find an element of it. Using the results about P (A(eta)), the set of subset-sums of A(eta), it was shown that with the secret key gamma the message can be decoded in logarithmic time, but for an eavesdropper without the key it takes on average more than N/log(2)N time. In this article, we show that the eavesdropper essentially can not figure out the codeword from the found element of S, even if she got that element from the query sequence in a relatively short time.