Details

Autor(en) / Beteiligte

• Nitaj, Abderrahmane
• Kamel Ariffin, Muhammad Rezal Bin
• Adenan, Nurul Nur Hanisah
• Lau, Terry Shue Chien
• Chen, Jiahui

Titel

Security Issues of Novel RSA Variant

Ist Teil von

• IEEE access, 2022, Vol.10, p.53788-53796

Ort / Verlag

Piscataway: IEEE

Erscheinungsjahr

2022

Link zum Volltext

Quelle

Elektronische Zeitschriftenbibliothek

Beschreibungen/Notizen

• The RSA is one of the current default cryptosystems that provides security with applications such as encryptions and digital signatures. It is important to further study the weak characteristics of the RSA to ensure correct utilisation in order not to be susceptible to adversaries. In this paper, we give detailed analysis on security of the Murru-Saettone variant of the RSA cryptosystem that utilised a cubic Pell <inline-formula> <tex-math notation="LaTeX">ed-k\left ({p^{2}+p+1}\right )\left ({q^{2}+q+1}\right )=1 </tex-math></inline-formula> as key equation and <inline-formula> <tex-math notation="LaTeX">N=pq </tex-math></inline-formula> as RSA modulus. We propose some attacks on this variant when the prime difference <inline-formula> <tex-math notation="LaTeX">|p-q| </tex-math></inline-formula> is small. Our first approach is to utilise the continued fractions algorithm to determine the parameter <inline-formula> <tex-math notation="LaTeX">d </tex-math></inline-formula> which enables us to determine the secret <inline-formula> <tex-math notation="LaTeX">p </tex-math></inline-formula> and <inline-formula> <tex-math notation="LaTeX">q </tex-math></inline-formula>. Our second approach considers the Coppersmith's method and lattice basis reduction to factor the modulus <inline-formula> <tex-math notation="LaTeX">N </tex-math></inline-formula>. Our attacks improve recent cryptanalyses on the cubic Pell equation variant of RSA. Furthermore, our attacks prove that under small prime difference scenario, the number of susceptible private exponents for the cubic Pell equation variant of RSA is much larger than the standard RSA.