Matrix M: Reducing Ciphertext Repetition and Structural Leakage in Block Ciphers

Kerim Yıldırım

doi:10.35377/saucis...1926017

Matrix M: Reducing Ciphertext Repetition and Structural Leakage in Block Ciphers

Abstract

This study aims to reduce repetitions and structural traces on the ciphertext side of existing block ciphers. Within this scope, the message-transformation layer called Matrix M was designed not as a new block cipher or a new mode of operation, but as a deterministic and reversible transformation layer added before existing ciphers such as AES, PRESENT, CLEFIA, MISTY1, and KASUMI. The evaluation was conducted as an ECB stress test, where block equality is intentionally visible, and repetition leakage can be measured directly. To analyze whether Matrix M produces the intended effect, a benchmark was designed and conducted over 24 full-profile datasets. In the analysis, performance, output expansion, distribution, diffusion, and structural leakage indicators were measured together on the same datasets. The results show that Matrix M reduces the ratio of repeating ciphertext blocks and the dominant block density in all examined ciphers, while increasing the ratio of unique blocks. The findings also reveal that it weakens the direct reflection of repetition patterns in the plaintext onto the ciphertext. These effects are interpreted as changes in the block-equality classes presented to the ECB mode rather than as cipher-internal diffusion improvements. The evaluation also shows the expected cost of this transformation layer, including about 25% wire expansion and, in the AES-ECB case, an approximately 12x increase in total processing time. The main contribution of Matrix M can be summarized as a blurring of structural traces on the ciphertext side and reducing repetition-based leakage under the stated empirical observer model.

Keywords

Ethical Statement

It is declared that during the preparation process of this study, scientific and ethical principles were followed, and all the studies benefited from are stated in the bibliography.

References

M. Dworkin, “Recommendation for block cipher modes of operation: Methods and techniques,” NIST Special Publication 800-38A, National Institute of Standards and Technology, 2001, doi: 10.6028/NIST.SP.800-38A.
N. Mouha and M. Dworkin, “Report on the block cipher modes of operation in the NIST SP 800-38 series,” NIST Interagency/Internal Report 8459, National Institute of Standards and Technology, 2024, doi: 10.6028/NIST.IR.8459.
M. Dworkin and N. Mouha, “Recommendation for block cipher modes of operation: Methods for format-preserving encryption,” NIST Special Publication 800-38G Revision 1 (2nd Public Draft), National Institute of Standards and Technology, 2025, doi: 10.6028/NIST.SP.800-38Gr1.2pd.
M. Sönmez Turan, K. A. McKay, J. Kang, J. Kelsey, and D. Chang, “Ascon-based lightweight cryptography standards for constrained devices: Authenticated encryption, hash, and extendable output functions,” NIST Special Publication 800-232, National Institute of Standards and Technology, Gaithersburg, MD, 2025, doi: 10.6028/NIST.SP.800-232.
National Institute of Standards and Technology, “Advanced Encryption Standard (AES),” FIPS PUB 197, NIST, 2001, doi: 10.6028/NIST.FIPS.197.
A. Bogdanov et al., “PRESENT: An ultra-lightweight block cipher,” in Cryptographic Hardware and Embedded Systems – CHES 2007, vol. 4727, Lecture Notes in Computer Science, Springer, 2007, pp. 450–466, doi: 10.1007/978-3-540-74735-2 31.
Sony Corporation, “The 128-bit blockcipher CLEFIA algorithm specification,” rev. 1.0, Jun. 1, 2007. Accessed: Oct. 15, 2026. [Online]. Available: https://www.sony.co.jp/en/Products/cryptography/clefia/download/.
K. Ohta and M. Matsui, “A description of the MISTY1 encryption algorithm,” RFC 2994, IETF, Nov. 2000, doi: 10.17487/RFC2994.

ETSI/3GPP, “Specification of the 3GPP confidentiality and integrity algorithms; Document 2: KASUMI specification,” TS 135 202 / 3GPP TS 35.202, ETSI, 2021.
ETSI/3GPP, “Specification of the 3GPP confidentiality and integrity algorithms; Document 3: Implementors test data,” TS 135 203 / 3GPP TS 35.203, ETSI, 2021.
C. E. Shannon, “A mathematical theory of communication,” Bell Syst. Tech. J., vol. 27, no. 3, pp. 379–423, 1948, doi: 10.1002/j.1538-7305.1948.tb01338.x.
A. Rukhin et al., “A statistical test suite for random and pseudorandom number generators for cryptographic applications,” NIST Special Publication 800-22 Revision 1a, National Institute of Standards and Technology, 2010, doi: 10.6028/NIST.SP.800-22r1a.
K. Yıldırım, G. Dalkılıç, and N. Duru, “Formally analyzed M-coupon protocol with confirmation code (MCWCC),” Turkish J. Electr. Eng. Comput. Sci., vol. 27, no. 1, pp. 484–498, 2019, doi: 10.3906/elk-1712-288.
K. Yıldırım, G. Dalkılıç, and N. Duru, “Security analysis of Hsiang M-coupon protocol,” J. Fac. Eng. Archit. Gazi Univ., vol. 34, no. 4, pp. 1705–1724, 2019, doi: 10.17341/gazimmfd.571490.
P. Rogaway, “Evaluation of some blockcipher modes of operation,” Cryptography Research and Evaluation Committees, Japan, CRYPTREC EX-2012- 2010R1 (No. 2012), pp. 1–159, 2011. Accessed: Oct. 15, 2026. [Online]. Available: https://www.cryptrec.go.jp/exreport/cryptrec-ex-2012-2010r1.pdf.
M. Liskov, R. L. Rivest, and D. Wagner, “Tweakable block ciphers,” in Advances in Cryptology – CRYPTO 2002, vol. 2442, Lecture Notes in Computer Science, Springer, 2002, pp. 31–46, doi: 10.1007/3-540-45708-9 3.
P. Rogaway, “Efficient instantiations of tweakable blockciphers and refinements to modes OCB and PMAC,” in Advances in Cryptology – ASIACRYPT 2004, vol. 3329, Lecture Notes in Computer Science, Springer, 2004, pp. 16–31, doi: 10.1007/978-3-540-30539-2 2.
M. Dworkin, “Recommendation for block cipher modes of operation: The XTS-AES mode for confidentiality on storage devices,” NIST Special Publication 800-38E, National Institute of Standards and Technology, 2010, doi: 10.6028/NIST.SP.800-38E.
S. Halevi and P. Rogaway, “A parallelizable enciphering mode,” in Topics in Cryptology – CT-RSA 2004, vol. 2964, Lecture Notes in Computer Science, Springer, 2004, pp. 292–304, doi: 10.1007/978-3-540-24660-2 23.
M. Dworkin, “Recommendation for block cipher modes of operation: Methods for format-preserving encryption,” NIST Special Publication 800-38G, National Institute of Standards and Technology, 2016, doi: 10.6028/NIST.SP.800-38G.
M. Bellare and P. Rogaway, “Encode-then-encipher encryption: How to exploit nonces or redundancy in plaintexts for efficient cryptography,” in Advances in Cryptology – ASIACRYPT 2000, vol. 1976, Lecture Notes in Computer Science, Springer, 2000, pp. 317–330, doi: 10.1007/3-540-44448-3 24.
P. Rogaway and T. Shrimpton, “A provable-security treatment of the key-wrap problem,” in Advances in Cryptology – EUROCRYPT 2006, vol. 4004, Lecture Notes in Computer Science, Springer, 2006, pp. 373–390, doi: 10.1007/11761679 23.
D. Harkins, “Synthetic initialization vector (SIV) authenticated encryption using the Advanced Encryption Standard (AES),” RFC 5297, IETF, Oct. 2008, doi: 10.17487/RFC5297.
K. Yıldırım and H. E. Demiray, “Methods for integrating symmetric and asymmetric encryption schemes: Scrambled and combined KEM-DEM,” J. Fac. Eng. Archit. Gazi Univ., vol. 23, no. 3, pp. 539–548, 2008.
J. Kaur, A. Cintas Canto, M. Mozaffari Kermani, and R. Azarderakhsh, “A survey on the implementations, attacks, and countermeasures of the current NIST lightweight cryptography standard: ASCON,” ACM Comput. Surv., vol. 58, no. 1, Art. no. 6, pp. 6:1–6:16, 2026, doi: 10.1145/3744640.
S. Khan, P. A. F. L. Martins, B. Sousa, and V. Pereira, “A comprehensive review on lightweight cryptographic mechanisms for industrial Internet of Things systems,” ACM Comput. Surv., vol. 58, no. 1, Art. no. 23, pp. 23:1–23:37, 2026, doi: 10.1145/3757734.
P. S. Suryateja and K. V. Rao, “A survey on lightweight cryptographic algorithms in IoT,” Cybern. Inf. Technol., vol. 24, no. 1, pp. 21–34, 2024, doi: 10.2478/cait-2024-0002.
J. Soto-Cruz, E. Ruiz-Ibarra, J. Vázquez-Castillo, A. Espinoza-Ruiz, A. Castillo-Atoche, and J. Mass-Sanchez, “A survey of efficient lightweight cryptography for power-constrained microcontrollers,” Technologies, vol. 13, no. 1, Art. no. 3, 2025, doi: 10.3390/technologies13010003. K. Yıldırım Sakarya University Journal of Computer and Information Sciences 9 (5) 2026, 1400–1416
K. U. Sarker, “A systematic review on lightweight security algorithms for a sustainable IoT infrastructure,” Discover Internet of Things, vol. 5, Art. no. 47, 2025, doi: 10.1007/s43926-025-00150-4.
B. Gușița, A. A. Anton, C. S. Stângaciu, D. Stanescu, L. I. Gaina, and M. V. Micea, “Securing IoT edge: A survey on lightweight cryptography, anonymous routing and communication protocol enhancements,” Int. J. Inf. Secur., vol. 24, no. 3, Art. no. 149, 2025, doi: 10.1007/s10207-025-01071-7.
S. Kumar, D. Kumar, R. Dangi, G. Choudhary, N. Dragoni, and I. You, “A review of lightweight security and privacy for resource-constrained IoT devices,” Comput. Mater. Continua, vol. 78, no. 1, pp. 31–63, 2024, doi: 10.32604/cmc.2023.047084.
H. Madushan, I. Salam, and J. Alawatugoda, “A review of the NIST lightweight cryptography finalists and their fault analyses,” Electronics, vol. 11, no. 24, Art. no. 4199, 2022, doi: 10.3390/electronics11244199.
M. Naseer, S. Tariq, N. Riaz, N. Ahmed, and M. Hussain, “S-box security analysis of NIST lightweight cryptography candidates: A critical empirical study,” arXiv preprint, 2024, doi: 10.48550/arXiv.2404.06094.
R. Ganesh, B. U. I. Khan, A. R. Khan, and A. B. Kamsin, “A panoramic survey of the Advanced Encryption Standard: From architecture to security analysis, key management, real-world applications, and post-quantum challenges,” Int. J. Inf. Secur., vol. 24, no. 5, Art. no. 216, 2025, doi: 10.1007/s10207-025- 01116-x.
K. D. Tsaregorodtsev, “Format-preserving encryption: A survey,” Matematicheskie Voprosy Kriptografii (Mathematical Questions of Cryptography), vol. 13, no. 2, pp. 133–153, 2022, doi: 10.4213/mvk412.
R. Avanzi, O. Dunkelman, and K. Minematsu, “MATTER: A wide-block tweakable block cipher,” Cryptology ePrint Archive, Paper 2024/1186, 2024. Accessed: Oct. 15, 2026. [Online]. Available: https://eprint.iacr.org/2024/1186.
C. Dobraunig, K. Matusiewicz, B. Mennink, and A. Tereschenko, “Efficient instances of Docked Double Decker with AES, and application to authenticated encryption,” Cryptology ePrint Archive, Report 2024/084, 2024. Accessed: Oct. 15, 2026. [Online]. Available: https://eprint.iacr.org/2024/084.
A. Tanaka, R. Shiba, K. Sakamoto, M. Rahman, T. Shiraya, and T. Isobe, “ASURA: An efficient large-state tweakable block cipher for ARM environment,” in Progress in Cryptology – INDOCRYPT 2024, vol. 15495, Lecture Notes in Computer Science, Springer, pp. 143–164, 2024, doi: 10.1007/978-3-031- 80308-6 7.
A. Jha, M. Khairallah, M. Nandi, and A. Saha, “Tight security of TNT and beyond: Attacks, proofs and possibilities for the cascaded LRW paradigm,” in Advances in Cryptology – EUROCRYPT 2024, vol. 14651, Lecture Notes in Computer Science, Springer, pp. 249–279, 2024, doi: 10.1007/978-3-031-58716- 0 9.
J. Wang, T. Huang, G. Zeng, T. Ding, S. Wu, and S. Sun, “THF: Designing low-latency tweakable block ciphers,” IACR Trans. Symmetric Cryptol., vol. 2025, no. 4, pp. 125–166, 2025, doi: 10.46586/tosc.v2025.i4.125-166.
J. Dani, K. Nakka, and N. Saxena, “A machine learning-based framework for assessing cryptographic indistinguishability of lightweight block ciphers,” in Proc. 22nd Annu. Int. Conf. Privacy, Security, and Trust (PST), 2025, doi: 10.1109/PST65910.2025.11268861.
W. Wu and M. Guo, “Improved integral neural distinguisher model for lightweight cipher PRESENT,” Cybersecurity, vol. 7, Art. no. 65, 2024, doi: 10.1186/s42400-024-00258-0.
M. Katagi and S. Moriai, “The 128-bit blockcipher CLEFIA,” RFC 6114, IETF, Mar. 2011, doi: 10.17487/RFC6114.
The pyca/cryptography developers, “Symmetric encryption,” Cryptography Documentation. Accessed: May 24, 2026. [Online]. Available: https:// cryptography.io/en/latest/hazmat/primitives/symmetric-encryption/.
H. Feistel, “Cryptography and computer privacy,” Sci. Amer., vol. 228, no. 5, pp. 15–23, May 1973, doi: 10.1038/scientificamerican0573-15.
A. F. Webster and S. E. Tavares, “On the design of S-boxes,” in Advances in Cryptology – CRYPTO ’85 Proceedings, vol. 218, Lecture Notes in Computer Science, Springer, 1986, pp. 523–534, doi: 10.1007/3-540-39799-X 41.

Details

Primary Language

English

Subjects

Information Security and Cryptology, Cryptography, Data Security and Protection

Journal Section

Research Article

Authors

Kerim Yıldırım ^*
0000-0002-6648-4971
Türkiye

Early Pub Date

October 27, 2026

Publication Date

October 30, 2026

Submission Date

April 9, 2026

Acceptance Date

July 4, 2026

Published in Issue

Year 2026 Volume: 9 Number: 5

DOI

https://doi.org/10.35377/saucis...1926017

IZ

https://izlik.org/JA42FL53EP

Cite

RIS / Bibtex

APA

Yıldırım, K. (2026). Matrix M: Reducing Ciphertext Repetition and Structural Leakage in Block Ciphers. Sakarya University Journal of Computer and Information Sciences, 9(5), 1400-1416. https://doi.org/10.35377/saucis...1926017

AMA

1.Yıldırım K. Matrix M: Reducing Ciphertext Repetition and Structural Leakage in Block Ciphers. SAUCIS. 2026;9(5):1400-1416. doi:10.35377/saucis.1926017

Chicago

Yıldırım, Kerim. 2026. “Matrix M: Reducing Ciphertext Repetition and Structural Leakage in Block Ciphers”. Sakarya University Journal of Computer and Information Sciences 9 (5): 1400-1416. https://doi.org/10.35377/saucis. 1926017.

EndNote

Yıldırım K (October 1, 2026) Matrix M: Reducing Ciphertext Repetition and Structural Leakage in Block Ciphers. Sakarya University Journal of Computer and Information Sciences 9 5 1400–1416.

IEEE

[1]K. Yıldırım, “Matrix M: Reducing Ciphertext Repetition and Structural Leakage in Block Ciphers”, SAUCIS, vol. 9, no. 5, pp. 1400–1416, Oct. 2026, doi: 10.35377/saucis...1926017.

ISNAD

Yıldırım, Kerim. “Matrix M: Reducing Ciphertext Repetition and Structural Leakage in Block Ciphers”. Sakarya University Journal of Computer and Information Sciences 9/5 (October 1, 2026): 1400-1416. https://doi.org/10.35377/saucis. 1926017.

JAMA

1.Yıldırım K. Matrix M: Reducing Ciphertext Repetition and Structural Leakage in Block Ciphers. SAUCIS. 2026;9:1400–1416.

MLA

Yıldırım, Kerim. “Matrix M: Reducing Ciphertext Repetition and Structural Leakage in Block Ciphers”. Sakarya University Journal of Computer and Information Sciences, vol. 9, no. 5, Oct. 2026, pp. 1400-16, doi:10.35377/saucis. 1926017.

Vancouver

1.Kerim Yıldırım. Matrix M: Reducing Ciphertext Repetition and Structural Leakage in Block Ciphers. SAUCIS. 2026 Oct. 1;9(5):1400-16. doi:10.35377/saucis. 1926017