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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.
Randomness Test of LightMAC-Based Pseudorandom Number Generator (PRNG) with NIST SP 800-22 Revision 1A Test Bety Hayat Susanti; Wahyu Achmad Fadiel; Yeni Farida; Obrina Briliyant
CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 11, No 2 (2026): 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.v11i2.43424

Abstract

Random numbers are essential for ensuring the security and unpredictability of cryptographic systems; however, resource-constrained devices still lack effective lightweight random number generators. This gap leaves encryption, authentication, and key generation vulnerable, exposing critical infrastructure to adversarial exploitation. This study presents the development and statistical evaluation of a Pseudo-Random Number Generator (PRNG) based on the LightMAC construction instantiated with the PRESENT lightweight block cipher. The proposed PRNG operates by iteratively processing a fixed seed message through LightMAC-PRESENT with a varying counter. The randomness of the generated bit sequences was rigorously analyzed using the NIST SP 800-22 Revision 1A test suite. The evaluation encompassed multiple implementation configurations, including two seed message lengths ($|x|$) of 64 bits and 128 bits, two key lengths for the underlying PRESENT cipher of 80 bits and 128 bits, and three counter lengths of 8 bits, 16 bits, and 32 bits. The results demonstrate that the LightMAC-PRESENT-based PRNG satisfies the NIST statistical requirements under specific parameter configurations. For a 64-bit seed message, a 128-bit PRESENT key combined with an 8-bit or 16-bit counter successfully passes all tests. For a 128-bit seed message, the generator achieves compliance with an 80-bit key and a 128-bit key. The optimal configuration identified is a 128-bit seed message, an 80-bit key, and a 16-bit counter, which passes all tests across all key-pattern variations. These findings provide critical insights into the optimal parameters for secure, efficient, lightweight deterministic random bit generation in resource-constrained environments.
Co-Authors Aditya Sukhoi Lean Sumule Mareta Wahyu Ardyani Obrina Briliyant Susila Windarta Wahyu Achmad Fadiel Wuri Handayani Yeni Farida