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All Journal CAUCHY: Jurnal Matematika Murni dan Aplikasi
Bety Hayat Susanti
Politeknik Siber dan Sandi Negara
Mathematics

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An Extended Cryptanalysis of Peyrin on SIMON-JAMBU64/96: A Study on Reduced-Tuple Attacks Susila Windarta; Wuri Handayani; Bety Hayat Susanti
CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 10, No 2 (2025): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI
Publisher : Mathematics Department, Maulana Malik Ibrahim State Islamic University of Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.18860/cauchy.v10i2.36601

Abstract

This study evaluates and verifies the cryptanalysis of Peyrin \textit{et al.} on the SIMON-JAMBU64/96 Authenticated Encryption (AE) scheme, with the aim of extending the attack to a reduced number of tuples. We adopt both formal analysis and experimental validation, constructing collision-based distinguishers under a chosen-IV model and testing them with a decryption oracle. The main contribution is the demonstration that a distinguishing attack can be performed with just two tuples, showing that JAMBU is more vulnerable than previously assumed. We provide a detailed comparison of data complexity, where the two-tuple attack achieves a lower cost in the second phase ($4 \cdot 2^{48}$ queries) than the three-tuple attack ($6 \cdot 2^{48}$), at the expense of extra verification effort in the third phase. Overall, our results confirm that the SIMON-JAMBU64/96 scheme is susceptible to distinguishing, plaintext forgery, and plaintext-recovery attacks, thereby reaffirming and extending the findings of Peyrin \textit{et al.} to scenarios with more limited adversarial resources.
Security Analysis of Modified ESRKGS-RSA Using Lenstra’s Elliptic Curve Method Bety Hayat Susanti; Aditya Sukhoi Lean Sumule; Mareta Wahyu Ardyani
CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 10, No 2 (2025): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI
Publisher : Mathematics Department, Maulana Malik Ibrahim State Islamic University of Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.18860/cauchy.v10i2.32189

Abstract

The Enhanced and Secure RSA Key Generation Scheme (ESRKGS), introduced in 2014, aimed to improve RSA security by employing a modulus constructed from four prime factors. However, subsequent studies in 2016 revealed that this structure did not provide additional security over standard RSA. In response, a modified version of ESRKGS was proposed in 2021, incorporating dual encoding techniques using a masking parameter γ and double encryption. This study evaluates the security of the modified ESRKGS by simulating an attack scenario in which the adversary is assumed to know of ϕ(N ), enabling recovery of encrypted messages. Additionally, we implement Lenstra’s Elliptic Curve Method (ECM) to assess the factorization resistance of the four-prime modulus when ϕ(N ) is not known. Experimental results indicate that ECM can efficiently factor the modulus into its four constituent primes under practical time constraints. These findings demonstrate that, despite recent modifications, the ESRKGS variant remains vulnerable to factorization based attacks. This highlights the necessity for more rigorous cryptographic design principles in multiprime RSA systems and calls into question the long-term viability of ESRKGS-based schemes in high-security applications.
Co-Authors Aditya Sukhoi Lean Sumule Mareta Wahyu Ardyani Susila Windarta Wuri Handayani