Improved Low-depth SHA3 Quantum Circuit for Fault-tolerant Quantum Computers

To build an efficient security system in the post-quantum era, it is possible to find the minimum security parameters for defending a fault-tolerant quantum computer by estimating the quantum resources required for an quantum attack. In a fault-tolerant quantum computer, errors must reach an acceptable level through error detection and error correction, which additionally uses quantum resources. As the depth of the quantum circuit increases, the computation time per qubit increases, and errors in quantum computers increases. Therefore, in terms of errors in quantum circuits, it is appropriate to reduce the depth by increasing the number of qubits. This paper proposes an low-depth quantum circuit implementations of SHA3 for fault-tolerant quantum computers to reduce errors. The proposed SHA3 quantum circuit is implemented in the direction of reducing the quantum circuit depth through a trade-off between the number of qubits, quantum gate, and quantum depth in each function. Compared to the-state-of-art works, proposed method decreased T-depth and Full-depth by 30.3\% and 80.05\%, respectively. We expect that this work will contribute to the establishment of minimum security parameters for SHA3 in the quantum era

Optimized Quantum Implementation of SEED

With the advancement of quantum computers, it has been demonstrated that Shor\u27s algorithm enables public key cryptographic attacks to be performed in polynomial time. In response, NIST conducted a Post-Quantum Cryptography Standardization competition. Additionally, due to the potential reduction in the complexity of symmetric key cryptographic attacks to square root with Grover\u27s algorithm, it is increasingly challenging to consider symmetric key cryptography as secure. In order to establish secure post-quantum cryptographic systems, there is a need for quantum post-quantum security evaluations of cryptographic algorithms. Consequently, NIST is estimating the strength of post-quantum security, driving active research in quantum cryptographic analysis for the establishment of secure post-quantum cryptographic systems. In this regard, this paper presents a depth-optimized quantum circuit implementation for SEED, a symmetric key encryption algorithm included in the Korean Cryptographic Module Validation Program (KCMVP). Building upon our implementation, we conduct a thorough assessment of the post-quantum security for SEED. Our implementation for SEED represents the first quantum circuit implementation for this cipher

Depth-Optimized Implementation of ASCON Quantum Circuit

The development of quantum computers, which employ a different paradigm of computation, is posing a threat to the security of cryptography. Narrowing down the scope to symmetric-key cryptography, the Grover search algorithm is probably the most influential in terms of its impact on security. Recently, there have been efforts to estimate the complexity of the Grover’s key search for symmetric key ciphers and evaluate their post-quantum security. In this paper, we present a depth-optimized implementation of a quantum circuit for ASCON, which is a symmetric key cipher that has recently been standardized in the NIST (National Institute of Standards and Technology) Lightweight Cryptography standardization. As far as we know, this is the first implementation of a quantum circuit for the ASCON AEAD (Authenticated Encryption with Associated Data) scheme. To our understanding, reducing the depth of the quantum circuit for the target cipher is the most effective approach for Grover’s key search. We demonstrate the optimal Grover’s key search cost for ASCON, along with a proposed depth-optimized quantum circuit. Further, based on the estimated cost, we evaluate the post-quantum security strength of ASCON according to relevant evaluation criteria and state-of-the-art research

Depth-Optimized Quantum Implementation of ARIA

The advancement of large-scale quantum computers poses a threat to the security of current encryption systems. In particular, symmetric-key cryptography significantly is impacted by general attacks using the Grover\u27s search algorithm. In recent years, studies have been presented to estimate the complexity of Grover\u27s key search for symmetric-key ciphers and assess post-quantum security. In this paper, we propose a depth-optimized quantum circuit implementation for ARIA, which is a symmetric key cipher included as a validation target the Korean Cryptographic Module Validation Program (KCMVP). Our quantum circuit implementation for ARIA improves the depth by more than 88.2% and Toffoli depth by more than 98.7% compared to the implementation presented in Chauhan et al.\u27s SPACE\u2720 paper. Finally, we present the cost of Grover\u27s key search for our circuit and evaluate the post-quantum security strength of ARIA according to relevant evaluation criteria provided NIST

Grover on SPECK: Quantum Resource Estimates

Grover search algorithm reduces the security level of symmetric key cryptography with $n$-bit secret key to $O(2^{n/2})$. In order to evaluate the Grover search algorithm, the target block cipher should be implemented in quantum circuits. Recently, many research works evaluated required quantum resources of AES block ciphers by optimizing the expensive substitute layer. However, only few works devoted to ARX-based lightweight block ciphers, which are active research area. In this paper, we present optimized implementations of SPECK 32/64 and SPECK 64/128 block ciphers for quantum computers. To the best of our knowledge, this is the first implementation of SPECK in quantum circuits. Primitive operations, including addition, rotation, and exclusive-or, for SPECK block cipher are finely optimized to achieve the optimal quantum circuit, in terms of qubits, Toffoli gate, CNOT gate, and X gate. The proposed method can be applied to other ARX-based lightweight block ciphers, such as LEA, HIGHT and CHAM block ciphers

Improved Quantum Analysis of SPECK and LowMC (Full Version)

As the prevalence of quantum computing is growing in leaps and bounds over the past few years, there is an ever-growing need to analyze the symmetric-key ciphers against the upcoming threat. Indeed, we have seen a number of research works dedicated to this. Our work delves into this aspect of block ciphers, with respect to the SPECK family and LowMC family. The SPECK family received two quantum analysis till date (Jang et al., Applied Sciences, 2020; Anand et al., Indocrypt, 2020). We revisit these two works, and present improved benchmarks SPECK (all 10 variants). Our implementations incur lower full depth compared to the previous works. On the other hand, the quantum circuit of LowMC was explored earlier in Jaques et al.\u27s Eurocrypt 2020 paper. However, there is an already known bug in their paper, which we patch. On top of that, we present two versions of LowMC (on L1, L3 and L5 variants) in quantum, both of which incur significantly less full depth than the bug-fixed implementation

Quantum Implementation and Resource Estimates for RECTANGLE and KNOT

With the advancement of the quantum computing technologies, a large body of research work is dedicated to revisit the security claims for ciphers being used. An adversary with access to a quantum computer can employ certain new attacks which would not be possible in the current pre-quantum era. In particular, the Grover\u27s search algorithm is a generic attack against symmetric key cryptographic primitives, that can reduce the search complexity to square root. To apply the Grover\u27s search algorithm, one needs to implement the target cipher as a quantum circuit. Although relatively recent, this field of research has attracted serious attention from the research community, as several ciphers (like AES, GIFT, SPECK, SIMON etc.) are being implemented as quantum circuits. In this work, we target the lightweight block cipher RECTANGLE and the Authenticated Encryption with Associated Data (AEAD) KNOT which is based on RECTANGLE; and implement those in the ProjectQ library (an open-source quantum compatible library designed by researchers from ETH Zurich). AEADs are considerably more complex to implement than a typical block/stream cipher, and ours is among the first works to do this

Quantum Implementation and Analysis of DEFAULT

In this paper, we present the quantum implementation and analysis of the recently proposed block cipher, DEFAULT. DEFAULT is consisted of two components, namely DEFAULT-LAYER and DEFAULT-CORE. Two instances of DEFAULT-LAYER is used before and after DEFAULT-CORE (the so-called `sandwich construction\u27). We discuss about the the various choices made to keep the cost for the basic quantum circuit and that of the Grover\u27s oracle search, and compare it with the levels of quantum security specified by the United States\u27 National Institute of Standards and Technology (NIST). All in all, our work nicely fits in the research trend of finding the possible quantum vulnerability of symmetric key ciphers

Quantum Neural Network based Distinguisher for Differential Cryptanalysis on Simplified Block Ciphers

Differential cryptanalysis is a block cipher analysis technology that infers a key by using the difference characteristics. Input differences can be distinguished using a good difference characteristic, and this distinguishing task can lead to key recovery. Artificial neural networks are a good solution for distinguishing tasks. For this reason, recently, neural distinguishers have been actively studied. We propose a distinguisher based on a quantum-classical hybrid neural network by utilizing the recently developed quantum neural network. To our knowledge, we are the first attempt to apply quantum neural networks for neural distinguisher. The target ciphers are simplified ciphers (S-DES, S-AES, S-PRESENT-[4]), and a quantum neural distinguisher that classifies the input difference from random data was constructed using the Pennylane library. Finally, we obtained quantum advantages in this work: improved accuracy and reduced number of parameters. Therefore, our work can be used as a quantum neural distinguisher with high reliability for simplified ciphers

Quantum Analysis of AES

Quantum computing is considered among the next big leaps in computer science. While a fully functional quantum computer is still in the future, there is an ever-growing need to evaluate the security of the symmetric key ciphers against a potent quantum adversary. Keeping this in mind, our work explores the key recovery attack using the Grover\u27s search on the three variants of AES (-128, -192, -256). In total, we develop a pool of 20 implementations per AES variant (thus totaling in 60), by taking the state-of-the-art advancements in the relevant fields into account. In a nutshell, we present the least Toffoli depth and full depth implementations of AES, thereby improving from Zou et al.\u27s Asiacrypt\u2720 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 86 percent. Furthermore, we analyze the Jaques et al.\u27s Eurocrypt\u2720 implementations in details, fix the bugs (arising from some problem of the quantum computing tool used and not related to their coding) and report corrected benchmarks. To the best of our finding, our work improves from all the previous works (including the Asiacrypt\u2722 paper by Huang and Sun and the Asiacrypt\u2723 paper by Liu et al.) in terms of various quantum circuit complexity metrics (Toffoli depth, full depth, Toffoli/full depth - qubit count product, full depth - gate count product, etc.). Also, our bug-fixing of Jaques et al.\u27s Eurocrypt\u2720 implementations seem to improve from the authors\u27 own bug-fixing, thanks to our architecture consideration. Equipped with the basic AES implementations, we further investigate the prospect of the Grover\u27s search. We also propose three 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 for circuit complexity (like, depth-squared - qubit count product, depth - gate count product)