CRYPTANALYSIS OF RSA KEY EQUATION OF N=p^2q FOR SMALL |2q – p| USING CONTINUED FRACTION - Asbullah, Muhammad Asyraf; Abd Rahman, Normahirah Nek; Kamel Ariffin, Muhammad Rezal; Sapar, Siti Hasana; Yunos, Faridah (Malaysian Journal of Science, 2020)
This paper presents a new factoring technique on the modulus , where and are large prime numbers. Suppose there exists an integer satisfies the equation , for some unknown integer and is the Euler’s totient function. Our method exploits the term to be the closest integer to the unknown parameter . Hence we show that the unknown parameters and can be recovered from the list of the continued fractions expansion of Furthermore, we present an algorithm to compute the prime factors of in polynomial time after obtaining the correct tuple and.