This paper presents cryptanalysis attack on RSA variant with modulus $N=p^rq$ for $r\geq 2$ with three public and private exponents $(e_1,d_1),$ $(e_2,d_2),$ $(e_3,d_3)$ sharing the same modulus $N$ where $p$ and $q$ are consider to be primes having the same bit size. Our attack shows that we get the private exponent $\sigma

It was shown in Sadiq (2013) that succession parameters under the Aunu permutation patterns can be used as vertices of the graph model resulting from different transition of the automata scheme employed. This paper generates a graph model using the Aunu permutation patterns governed by some properties as embedded in method of construction of a typical game of chance scheme. A finite automata model was constructed from the game of chance using the (123) avoiding class of the Aunu permutation patterns.Furthermore, the paper illustrated some useful relationship between the field of automata theory and Combinatorics; it also highlights some important applications of the Aunu Permutation Patterns in graph theory.

The importance of keeping information secret cannot be overemphasized especially in today,s digital world where eavesdroppers are rampant in our chanels of communication. This made the use of strong encryption schemes inevitable in order to safeguard the security of our system. RSA cryptosystem and its variants have been designed to provide confidentiality and integrity of data in our medium of communication. This paper reports new short decryption exponent attack on prime power with modulus $N=p^rq$ for $r\geq 2$ using continued fraction method which makes it vulnerable to Diophantine attack and breaks the security of the cryptosystem by factoring the modulus into its prime factors since the hardness relies on the integer factorization problem. The paper also shows that if the short decryption exponent $d

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