Grover search algorithm is the most representative quantum attack method that threatens the security of symmetric key cryptography. If the Grover search algorithm is applied to symmetric key cryptography, the security level of target symmetric key cryptography can be lowered from n-bit to n2-bit. When applying Grover’s search algorithm to the block cipher that is the target of potential quantum attacks, the target block cipher must be implemented as quantum circuits. Starting with the AES block cipher, a number of works have been conducted to optimize and implement target block ciphers into quantum circuits. Recently, many studies have been published to implement lightweight block ciphers as quantum circuits. In this paper, we present optimal quantum circuit designs of symmetric key cryptography, including PRESENT and GIFT block ciphers. The proposed method optimized PRESENT and GIFT block ciphers by minimizing qubits, quantum gates, and circuit depth. We compare proposed PRESENT and GIFT quantum circuits with other results of lightweight block cipher implementations in quantum circuits. Finally, quantum resources of PRESENT and GIFT block ciphers required for the oracle of the Grover search algorithm were estimated.
Grover search algorithm is the most representative quantum attack method that threatens the security of symmetric key cryptography. If the Grover search algorithm is applied to symmetric key cryptography, the security level of target symmetric key cryptography can be lowered from n-bit to n2-bit. When applying Grover’s search algorithm to the block cipher that is the target of potential quantum attacks, the target block cipher must be implemented as quantum circuits. Starting with the AES block cipher, a number of works have been conducted to optimize and implement target block ciphers into quantum circuits. Recently, many studies have been published to implement lightweight block ciphers as quantum circuits. In this paper, we present optimal quantum circuit designs of symmetric key cryptography, including PRESENT and GIFT block ciphers. The proposed method optimized PRESENT and GIFT block ciphers by minimizing qubits, quantum gates, and circuit depth. We compare proposed PRESENT and GIFT quantum circuits with other results of lightweight block cipher implementations in quantum circuits. Finally, quantum resources of PRESENT and GIFT block ciphers required for the oracle of the Grover search algorithm were estimated.
The Grover search algorithm reduces the security level of symmetric key cryptography with n-bit security level to O(2n/2). In order to evaluate the Grover search algorithm, the target block cipher should be efficiently implemented in quantum circuits. Recently, many research works evaluated required quantum resources of AES block ciphers by optimizing the expensive substitute layer. However, few works were devoted to the lightweight block ciphers, even though it is an active research area, nowadays. In this paper, we present optimized implementations of every Korean made lightweight block ciphers for quantum computers, which include HIGHT, CHAM, and LEA, and NSA made lightweight block ciphers, namely SPECK. Primitive operations for block ciphers, including addition, rotation, and exclusive-or, are finely optimized to achieve the optimal quantum circuit, in terms of qubits, Toffoli gate, CNOT gate, and X gate. To the best of our knowledge, this is the first implementation of ARX-based Korean lightweight block ciphers in quantum circuits.
The emergence of quantum computers is threatening the security of cryptography through various quantum algorithms. Among them, the Grover search algorithm is known to be efficient in accelerating brute force attacks on block cipher algorithms. To utilize the Grover’s algorithm for brute force attacks, block ciphers must be implemented in quantum circuits. In this paper, we present optimized quantum circuits of the SPN (Substitution Permutation Network) structured lightweight block cipher, namely the PIPO block cipher. In particular, the compact design of quantum circuits for the 8-bit Sbox is investigated. These optimization techniques are used to implement other cryptographic operations as quantum circuits. Finally, we evaluate quantum resources of Grover search algorithm for the PIPO block cipher in ProejctQ, a quantum simulator provided by IBM.
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.
A quantum computer capable of running the Grover search algorithm, which reduces the complexity of brute-force attacks by a square root, has the potential to undermine the security strength of symmetric-key cryptography and hash functions. Recently, studies on quantum approaches have proposed analyzing potential quantum attacks using the Grover search algorithm in conjunction with optimized quantum circuit implementations for symmetric-key cryptography and hash functions. Analyzing quantum attacks on a cipher (i.e., quantum cryptanalysis) and estimating the necessary quantum resources are related to evaluating post-quantum security for the target cryptography algorithms. In this paper, we revisit quantum implementations of CHAM block cipher, an ultra lightweight cipher, with a focus on optimizing the linear operations in its key schedule. We optimized the linear equations of CHAM as matrices by applying novel optimized decomposition techniques. Using the improved CHAM quantum circuits, we estimate the cost of Grover’s key search and evaluate the post-quantum security strength with further reduced costs.
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.
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.