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Scientific Reports

Implementing Grover’s on AES-based AEAD schemes

Surajit Mandal, Ravi Anand, Mostafizar Rahman, Santanu Sarkar, Takanori Isobe

Published Sep 10, 2024• 9 citations
Publisher

Abstract

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 $$\textsf{MAXDEPTH} = 2^{40}$$ , 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.

DOI
10.1038/s41598-024-69188-8

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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 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.
Quantum computing advancements pose security challenges for cryptography. Specifically, Grover’s search algorithm affects the reduction in the search complexity of symmetric-key encryption and hash functions. Recent efforts have been made to estimate the complexity of Grover’s search and evaluate post-quantum security. In this paper, we propose a depth-optimized quantum circuit implementation for ASCON, including both symmetric-key encryption and hashing algorithms, as a part of the lightweight cryptography standardization by NIST (National Institute of Standards and Technology). As far as we know, this is the first implementation of a quantum circuit for the ASCON AEAD (Authenticated Encryption with Associated Data) scheme, which is a symmetric-key algorithm. Also, our quantum circuit implementation of the ASCON-HASH achieves a reduction of more than 88.9% in the Toffoli depth and more than 80.5% in the full depth compared to the previous work. As per our understanding, the most effective strategy against Grover’s search involves minimizing the depth of the quantum circuit for the target cipher. We showcase the optimal Grover’s search cost for ASCON and introduce a proposed quantum circuit optimized for depth. Furthermore, we utilize the estimated cost to evaluate post-quantum security strength of ASCON, employing the relevant evaluation criteria and the latest advancements in research.
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.
Our work explores the key recovery attack using the Grover's search on the three variants of AES (-128, -192, -256). In total, we develop a pool of 26 implementations per AES variant (totaling 78), by taking the state-of-the-art advancements in the relevant fields into account. We present the least Toffoli depth and full depth implementations of AES, thereby improving from Zou et al.'s Asiacrypt'20 paper by more than 97 percent for each variant of AES. We show that the qubit count - Toffoli depth product is reduced from theirs by more than 87 percent. Furthermore, we analyze the Jaques et al.'s Eurocrypt'20 implementations in detail, fix the bugs (arising from some problem of the quantum computing tool used), and report corrected benchmarks (which seem to improve from the authors' own bug-fixing, thanks to our architecture consideration). To the best of our finding, our work improves from all the previous works (including the Asiacrypt'22 paper by Huang and Sun, the Asiacrypt'23 paper by Liu et al. and the Asiacrypt'24 paper by Shi and Feng) in terms of various quantum circuit complexity metrics. To be more precise, we estimate the currently best-known quantum attack complexities for AES-128 ( 2 156.2630 ), AES-192 ( 2 221.5801 ) and AES-256 ( 2 286.0731 ). Additionally, we achieve the least Toffoli depth - qubit count product for AES-128 ( 121920 , improving from 130720 by Shi and Feng in Asiacrypt'24), AES-192 ( 161664 , improving from 188880 by Liu et al. in Asiacrypt'23) and AES-256 ( 206528 , improving from 248024 by Liu et al. in Asiacrypt'23) so far. We further investigate the prospect of the Grover's search. We propose four new implementations of the S-box, one new implementation of the MixColumn; as well as five new architecture (one is motivated by the architecture by Jaques et al. in Eurocrypt'20, and the rest four are entirely our innovation). Under the MAXDEPTH constraint (specified by NIST), the circuit depth metrics (Toffoli depth, T -depth and full depth) become crucial factors and parallelization for often becomes necessary. We provide the least depth implementation in this respect that offers the best performance in terms of metrics like depth-squared - qubit count product, depth - gate count product.
In this paper, we propose a quantum circuit for the SPEEDY block cipher for the first time and estimate its security strength based on the post-quantum security strength presented by NIST. The strength of post-quantum security for symmetric key cryptography is estimated at the cost of the Grover key retrieval algorithm. Grover’s algorithm in quantum computers reduces the n-bit security of block ciphers to n2 bits. The implementation of a quantum circuit is required to estimate the Grover’s algorithm cost for the target cipher. We estimate the quantum resource required for Grover’s algorithm by implementing a quantum circuit for SPEEDY in an optimized way and show that SPEEDY provides either 128-bit security (i.e., NIST security level 1) or 192-bit security (i.e., NIST security level 3) depending on the number of rounds. Based on our estimated cost, increasing the number of rounds is insufficient to satisfy the security against quantum attacks on quantum computers.
Key recovery attack on SPN ciphers such as AES is NP hard in complexity. Previous studies have estimated the quantum resources required for implementing Grover’s key search for AES, but these are largely theoretical in nature. The key challenges to implement Grover’s algorithm on current quantum hardware include the number of available qubits, noise, and decoherence. However, the rapid advancement of hardware has brought us closer to practical realization for the cryptanalysis of light-weight SPN ciphers. This study presents an efficient quantum circuit implementation of Mini-AES, a 16-bit variant of AES, employing standard CNOT and Toffoli gates. To the best of our knowledge, our work provides the first complete quantum implementations of all core Mini-AES components for the quantum oracle. The effects of noise are emulated for each module of the quantum oracle and quantified. Furthermore, Grover’s algorithm is applied to Mini-AES to perform successful key recovery through a known-plaintext attack, demonstrating significant amplitude amplification while using near-optimal Grover’s iterations, thereby reducing the total quantum volume. The optimal Grover’s iterations have been obtained empirically as well as validated with finite-shot analysis. Notably, the application of Grover’s algorithm reveals key clustering behavior in Mini-AES, which has been corroborated through classical simulation.