Notes on two methods for direct construction of probabilistic LFSR sequences of third order

TL;DR

This paper discusses two methods for directly constructing third-order probabilistic LFSR sequences and highlights issues in an existing RSA-based encryption scheme that uses such sequences.

Contribution

It introduces two methods for constructing probabilistic LFSR sequences of third order and analyzes errors in a related RSA encryption scheme.

Findings

Identified mistakes in the decryption procedure of the existing scheme

Proposed methods for constructing third-order probabilistic LFSR sequences

Clarified the structure of sequences used in cryptographic applications

Abstract

In \cite{Tm}, the authors give two public key encryptions based on third order linear sequences modulo $n^2$, where $n=pq$ is an RSA integer. In their scheme (3), there are two mistakes in the decryption procedure