Efficient Implementation of PRESENT and GIFT on Quantum Computers

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 on PIPO

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.

Grover on Korean Block Ciphers

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.