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

1. The owner of the private key does not know the value of m such that C1 = sm(a, b) and C2 = s −m(a, b), and thus he/she can not compute L(C1, C2). 2. If sλ(a, b) = 3 modulo n , then L(a, b) is not invertible modulo n. It follows that the owner of the private key can not decrypt the cipher C = (C1, C2) since he/she can not compute L(C1,C2) L(a,b) . In this short note, in order to decrypt the ciphertext C = (C1, C2), another map L similar to that given in [7] is constructed. More precisely, if L(a, b) is not invertible modulo n, we describe a method how to choose (a, b) such that L(a, b) is invertible modulo n and how to compute L(C1, C2).