Cryptanalysis of RSA Variants with Modified Euler Quotient

Cryptanalysis of RSA Variants with Primes Sharing Most Significant Bits

“…Then by applying Coppersmith's method and lattice reduction techniques, we show that, under the condition δ < 2 − √ 2αβ, one can factor the RSA modulus N . If we apply our attacks to the case where p and q are randomly chosen, that is p − q = O N β with β = 1 2 , then our bounds on δ and d retrieve the existing bounds in the previous attacks in [3,15,18,22].…”

“…We consider the lattice L where the rows of the basis matrix is built by considering the coefficients of the monomials of the polynomials G k,i1,i2,i3 (Xx, Y y, U u) and H k,i1,i2,i3 (Xx, Y y, U u). We note that the lattice L is different from the lattices used in [18,22,15]. Table 1 shows the lattice basis matrix generated by m = 2 and t = 2.…”

“…In [18], Peng et al obtained the better bound δ < 2 − √ α by mixing Coppersmith's method and unravelled linearization techniques. Finally, Zheng et al [22] reconsidered the key equation ed − k p 2 − 1 q 2 − 1 = 1, and obtained a similar bound on d which is applicable for 1 ≤ α < 4.…”

On the Improvement Attack Upon Some Variants of RSA Cryptosystem via the Continued Fractions Method

“…Subsequently, Zheng et al [17] presented a new direction as in [16] for β within [1,4). Following through, Nitaj et al [18] ascertained new weaknesses within the key equation in [12] [18] extended the bound by Bunder et al [12] and enabled one to factor the public modulus N = pq.…”

A Generalized Attack on Some Variants of the RSA Cryptosystem

“…Setting e = N β , they showed that one can solve the equation 1 and find the prime factors p and q if d = N δ and δ < 1 2 (3 − β). This was recently improved to δ < 2 − √ β by Peng et al [17] and by Zheng et al [23] by using lattice reduction techniques and Coppersmith's method.…”