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.

Using different chaotic systems in secure communication, nonlinear control, and many other applications has revealed that these systems have several drawbacks in different aspects. This can cause unfavorable effects to chaos-based applications. Therefore, presenting a chaotic map with complex behaviors is considered important. In this paper, we introduce a new 2D chaotic map, namely, the 2D infinite-collapse-Sine model (2D-ICSM). Various metrics including Lyapunov exponents and bifurcation diagrams are used to demonstrate the complex dynamics and robust hyperchaotic behavior of the 2D-ICSM. Furthermore, the cross-correlation coefficient, phase space diagram, and Sample Entropy algorithm prove that the 2D-ICSM has a high sensitivity to initial values and parameters, extreme complexity performance, and a much larger hyperchaotic range than existing maps. To empirically verify the efficiency and simplicity of the 2D-ICSM in practical applications, we propose a symmetric secure communication system using the 2D-ICSM. Experimental results are presented to demonstrate the validity of the proposed system.

Asymmetric key cryptosystem is a vital element in securing our communication in cyberspace. It encrypts our transmitting data and authenticates the originality and integrity of the data. The Rivest–Shamir–Adleman (RSA) cryptosystem is highly regarded as one of the most deployed public-key cryptosystem today. Previous attacks on the cryptosystem focus on the effort to weaken the hardness of integer factorization problem, embedded in the RSA modulus, N = p q . The adversary used several assumptions to enable the attacks. For examples, p and q which satisfy Pollard’s weak primes structures and partial knowledge of least significant bits (LSBs) of p and q can cause N to be factored in polynomial time, thus breaking the security of RSA. In this paper, we heavily utilized both assumptions. First, we assume that p and q satisfy specific structures where p = a m + r p and q = b m + r q for a , b are positive integers and m is a positive even number. Second, we assume that the bits of r p and r q are the known LSBs of p and q respectively. In our analysis, we have successfully factored N in polynomial time using both assumptions. We also counted the number of primes that are affected by our attack. Based on the result, it may poses a great danger to the users of RSA if no countermeasure being developed to resist our attack.

This paper presents an analysis toward estimating the algorithm running time on the Rabin-p cryptosystem. Next, we evaluate the memory cost for system parameters and accumulators for the Rabin-p encryption and decryption procedure, respectively. We then conduct a comparative analysis between three Rabin-like cryptosystems, namely the Rabin-p, the Rabin-Takagi and the HIME(R) cryptosystem. In summation, we conclude that Rabin-p cryptosystem performs faster and used less storage in comparison to the other two Rabin-like cryptosystems in consideration.

The present work introduces an analysis framework to comprehend the dynamics of a 3D plasma model, which has been proposed to describe the pellet injection in tokamaks. The analysis of the system reveals the existence of a complex transition from transient chaos to steady periodic behavior. Additionally, without adding any kind of forcing term or controllers, we demonstrate that the system can be changed to become a multi-stable model by injecting more power input. In this regard, we observe that increasing the power input can fluctuate the numerical solution of the system from coexisting symmetric chaotic attractors to the coexistence of infinitely many quasi-periodic attractors. Besides that, complexity analyses based on Sample entropy are conducted, and they show that boosting power input spreads the trajectory to occupy a larger range in the phase space, thus enhancing the time series to be more complex and random. Therefore, our analysis could be important to further understand the dynamics of such models, and it can demonstrate the possibility of applying this system for generating pseudorandom sequences.