This paper presents new short decryption exponent attacks on RSA, which successfully leads to the factorization of RSA modulus N = pq in polynomial time. The paper has two parts. In the first part, we report the usage of the small prime difference method of the form |b 2 p − a 2 q| < N γ where the ratio of. The second part of the paper reports four cryptanalytic attacks on t instances of RSA moduli N s = p s q s for s = 1, 2, . . . , t where we use N − a 2 +b 2 ab √ N + 1 as an approximation of φ(N) satisfying generalized key equations of the shape e s d s for unknown positive integers d, k s , d s , k s , and z s , where we establish that t RSA moduli can be simultaneously factored in polynomial time using combinations of simultaneous Diophantine approximations and lattice basis reduction methods. In all the reported attacks, we have found an improved short secret exponent bound, which is considered to be better than some bounds as reported in the literature.
This paper presents the non-associative and non-commutative properties of the 123-avoiding patterns of Aunu permutation patterns. The generating function of the said patterns has been reported earlier by the author [1] [2]. The paper describes how these non-associative and non commutative properties can be established by using the Cayley table on which a binary operation is defined to act on the 123-avoiding and 132-avoiding patterns of Aunu permutations using a pairing scheme. Our results have generated larger matrices from permutations of points of the Aunu patterns of prime cardinality. It follows that the generated symbols can be used in further studies and analysis in cryptography and game theory thereby providing an interdisciplinary approach and applications of these important permutation patterns.
In this study, a mathematical model on the transmission dynamics of tuberculosis was formulated and analyzed. The basic reproduction number ( ) for each model is calculated and determined using the next generation method and condition for elimination (disease free equilibrium) or persistence (endemic equilibrium) in a population. Stability analysis shows that disease free equilibrium is locally asymptotically stable whenever the reproduction is less than unity. Furthermore, tuberculosis case detection continued to persist whenever the reproduction number exceeds unity. However, the models consisting of system of first order nonlinear differential equations.
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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