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International Conference on VLSI Design

Quantum Analysis of LESCA

Sumanta Chakraborty, Debajyoti Mandal, SK Hafizul Islam

Published Jan 4, 2025• 0 citations
Publisher

Abstract

This paper explores the complexity measurements of applying Grover's search algorithm on a dynamic, key-dependent, lightweight stream cipher, LESCA (LightwEight Stream Cipher Algorithm). For this purpose, we present our algorithms to implement LESCA in quantum paradigm, probably the first, to the best of our knowledge. After that, we provide the cost measurements of the quantum implementation of LESCA and the quantum cost for applying Grover's search on LESCA. We show that LESCA meets the quantum security levels 1, 3, and 5 defined by National Institute of Standards and Technology (NIST).

DOI
10.1109/vlsid64188.2025.00084

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This paper explores the complexity measurements of applying Grover's search algorithm on a dynamic, key-dependent, lightweight stream cipher, LESCA (LightwEight Stream Cipher Algorithm). For this purpose, we present our algorithms to implement LESCA in quantum paradigm, probably the first, to the best of our knowledge. After that, we provide the cost measurements of the quantum implementation of LESCA and the quantum cost for applying Grover's search on LESCA. We show that LESCA meets the quantum security levels 1, 3, and 5 defined by National Institute of Standards and Technology (NIST).
The rapid advancements in quantum technologies have introduced significant threats to the security of conventional cryptographic systems. In particular, the evaluation of quantum resource requirements—measured in terms of circuit depth and qubit count—has become essential for analyzing the resilience of widely used schemes such as AES and RSA, as well as cryptographic hash functions like SHA-2. At the same time, the widespread adoption of Internet of Things (IoT) applications has increased the exposure to cybersecurity risks, which are further exacerbated by the emerging capabilities of quantum adversaries. To address these challenges, the U.S. National Institute of Standards and Technology (NIST) launched a competition to standardize lightweight hash functions and defined five quantum security levels to assess their robustness. In this work, we conduct a resource analysis of the NIST Lightweight Hash Function finalists against the Grover search algorithm, providing detailed insights into their quantum resistance. The findings contribute to a more comprehensive understanding of the security strength of lightweight hash functions in the post-quantum era.
Abstract A significant amount of study is being done to review the security promises made for the various ciphers now in use as a result of the development of quantum computing technology. A general attack against symmetric key cryptography primitives that can reduce search costs to the square root is Grover's search algorithm. To implement Grover's algorithm, it is necessary that the target cipher be implemented as a quantum circuit. Despite being relatively new, this area of study has received significant attention from the research community. The authors have estimated the cost of Grover's key search attack against the stream cipher Atom, for the first time, under circuit depth restrictions defined in National Institute of Standards and Technology (NIST) PQC standardisation process. The authors implement the quantum circuit of Atom in QISKIT, (open‐source software development kit for working with quantum computers running on IBM Quantum Experience). The results are also compared with other existing literature on LFSR‐based stream ciphers, such as Grain‐v1, Grain‐128‐AEAD, and Lizard. The authors also find that, to the best of their knowledge, in the existing literature on estimating the cost of Grover's attack on symmetric ciphers, Atom is the only 128‐bit key cipher that meets the threshold of ≈2 170 set by NIST for quantum security of 128‐bit key ciphers. The authors also analyse the security of Atom against quantum TMDTO attacks.
NIST(National Institute of Standards and Technology) estimates the Grover key search cost required for symmetric key cryptography as the postquantum security strength. The Grover search algorithm is applicable to key recovery in symmetric key cryptography, and for this, the target encryption process must be implemented as a quantum circuit. In this paper, we present an optimized implementation of Simplified AES as a quantum circuit. Substitution, Mix Columns, and Key Expansion are implemented efficiently, and as a result of resource analysis, qubits, quantum gates, and circuit depth are significantly reduced compared to the previous result.
Extensive research is currently underway to determine the security of existing ciphers in light of the advancements in quantum computing. Against symmetric key cryptography, Grover’s search algorithm is a prominent attack, capable of reducing search costs to the square root. For using Grover’s algorithm, it is imperative to embed the target cipher into a quantum circuit. Even so, this area of research is relatively new; it has garnered significant attention from the research community. In this study, we provide the first estimation of the cost of Grover’s key search attack against the AES-based AEAD schemes Rocca-S, AEGIS-128, and Tiaoxin-346. Our analysis considers circuit depth restrictions specified in NIST’s PQC standardization process. Considering NIST’s maximum depth constraints, We present the overall cost of these attacks using gate count and depth-times-width metrics. We observed that for MAXDEPTH=240\textsf{MAXDEPTH} = 2^{40}MAXDEPTH=240 , Rocca-S, AEGIS-128, and Tiaoxin-346 can be retrieved using Grover’s search algorithm with gate count of 1.09 × 2253, 1.14 × 2124, and 1.22 × 2124 respectively. Concerning the current updated values by NIST, these ciphers are secure in terms of the cost of implementing Grover’s attack for key recovery. The quantum circuits of these ciphers are implemented using QISKIT, an open-source software development kit (SDK) designed for working with quantum computers running on the IBM Quantum Experience platform.
Abstract Grover’s algorithm reduces the security level of the target cipher from n-bit to n/2-bit. To implement Grover’s algorithm, a quantum circuit capable of performing the target cipher operations must be constructed. In this paper, we propose a quantum circuit implementation scheme for the involutive lightweight block cipher (IVLBC) block cipher. We utilized the DORCIS tool to implement the quantum circuit for the S-box and applied Gaussian elimination to construct the quantum circuit for matrix multiplication. Subsequently, we evaluated the overall quantum resource consumption required for the implementation. Based on this, we performed a quantum attack on IVLBC using Grover’s algorithm, calculating the attack cost using the NCT gate library, and further analyzed its security. Finally, we conducted a comparative analysis of the classical attack complexity and quantum attack complexity of IVLBC, highlighting the potential of using quantum complexity as a standard for future security assessments.
Abstract The advent of quantum computing necessitates a rigorous reassessment of classical cryptographic primitives, particularly lightweight block ciphers (LBCs) deployed in resource-constrained environments. This work presents a comprehensive quantum implementation and security analysis of the Feistel-based LBC MIBS against quantum cryptanalysis. Using the inherent reversibility of its structure, we develop a novel ancilla-free quantum circuit that optimizes qubit count and depth. For MIBS-64 and MIBS-80, our implementation achieves quantum costs of 23,371 and 24,363, requiring 128 and 144 qubits, respectively, with a depth of 4,768. We subsequently quantify the cipher’s vulnerability to Grover’s key-search algorithm under the NIST PQC security constraint M A X D E P T H MAXDEPTH\mathtt{M}\mathtt{A}\mathtt{X}\mathtt{D}\mathtt{E}\mathtt{P}\mathtt{T}\mathtt{H}MAXDEPTH . By constructing Grover oracles using inner parallelization with multiple plaintext-ciphertext pairs to suppress false positives, we demonstrate total quantum attack costs of approximately 2 94 for MIBS-64 and 2 111 for MIBS-80. These values fall below NIST’s Level-1 security threshold (2 170 ), confirming the susceptibility of both MIBS variants to quantum key-recovery attacks despite their classical lightweight efficiency.