New attacks on RSA with modulus N = p2q using continued fractions by Asbullah, Muhammad Asyraf, Kamel Ariffin, Muhammad Rezal

“…In this paper, we propose two new attacks on RSA with modulus N = p2q using continued fractions. Our first attack is based on the RSA key equation ed - φ(N)k = 1 where φ(N) = p(p - 1)(q - 1). …”
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Algebraic analysis of a rabin-like cryptosystem and its countermeasures by Asbullah, Muhammad Asyraf, Kamel Ariffin, Muhammad Rezal

“…Methods/Analysis: We show that by using the continued fraction’s method and the Coppersmith’s theorems, there exists inappropriate parameter’s size that can affect the security of Rabin-p cryptosystem. …”
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Analysis on the AAβ cryptosystem by Asbullah, Muhammad Asyraf, Kamel Ariffin, Muhammad Rezal

“…For the second and third analysis, we bring in the continued fraction’s method and the Coppersmith’s theorems, which presents several potential ways to retrieve the prime factor of p and q from the AAβ public keys or the plaintext m from the AAβ ciphertext, respectively. …”
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Algebraic cryptanalysis on the AAβ cryptosystem by Asbullah, Muhammad Asyraf, Kamel Ariffin, Muhammad Rezal

“…We begin with the continued fraction’s method, then followed by the Coppersmith’s techniques which present several potential ways to retrieve the prime factor of p and q from the AAβ public keys or the plain text m from the AAβ ciphertext, respectively. …”
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The Blömer-May’s weak key revisited by Mohd Tahir, Rasyid Redha, Asbullah, Muhammad Asyraf, Ariffin, Muhammad Rezal Kamel

“…Note that the said attack can lead a polynomial time factorisation of modulus N via continued fraction method. Later, the attack was reformulated to satisfies xy<N/(4(p+q)). …”
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Determination of a good indicator for estimated prime factor and its modification in Fermat’s Factoring Algorithm by Mohd Tahir, Rasyid Redha, Asbullah, Muhammad Asyraf, Kamel Ariffin, Muhammad Rezal, Mahad, Zahari

“…The main results of mFFA1-EPF focused on three criteria: (i) the approach to select good candidates from a list of convergent continued fraction, (ii) the establishment of new potential initial values based on EPF, and (iii) the application of the above modification upon FFA. …”
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Another proof of wiener's short secret exponent by Asbullah, Muhammad Asyraf, Kamel Ariffin, Muhammad Rezal

“…Wiener’s short secret exponent attack is a well-known crypt-analytical result upon the RSA cryptosystem using a Diophantine’s method called continued fractions. We recall that Wiener’s attack works efficiently on RSA with the condition that the secret exponent d<13N14. …”
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Increment of insecure RSA private exponent bound through perfect square RSA diophantine parameters cryptanalysis by Wan Mohd Ruzai, Wan Nur Aqlili, Nitaj, Abderrahmane, Kamel Ariffin, Muhammad Rezal, Mahad, Zahari, Asbullah, Muhammad Asyraf

“…That is, the unknown [Formula presented] can be found amongst the convergents of [Formula presented] via continued fractions algorithm. Consequently, Coppersmith's theorem is applied to solve for prime factors p and q in polynomial time. …”

On the variants of RSA cryptosystem and its related algebraic cryptanalysis by Ruzai, Wan Nur Aqlili, Kamel Ariffin, Muhammad Rezal, Asbullah, Muhammad Asyraf

“…This review article also emphasizes on the algebraic cryptanaly-sis methods proposed on those variants cryptosystems specifically via the continued fractions method and the lattice reduction method…”
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