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Journal of Experimental and Theoretical Physics

Application of Grover’s Quantum Algorithm for SDES Key Searching

Д. Денисенко, M. V. Nikitenkova

Published Jan 1, 2019• 13 citations
Publisher

Abstract

Abstract The problem of finding the key of Simplified-DES (SDES)—a model of a block cipher DES—by Grover’s quantum algorithm is considered. Examples of application of Grover’s algorithm are presented. A quantum system with the minimum number of qubits is constructed that implements SDES key searching by a single pair of plaintext and ciphertext and requires only 19 qubits. This quantum circuit is simulated by using a Quipper quantum simulator.

DOI
10.1134/s1063776118120142

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Abstract The problem of finding the key of Simplified-DES (SDES)—a model of a block cipher DES—by Grover’s quantum algorithm is considered. Examples of application of Grover’s algorithm are presented. A quantum system with the minimum number of qubits is constructed that implements SDES key searching by a single pair of plaintext and ciphertext and requires only 19 qubits. This quantum circuit is simulated by using a Quipper quantum simulator.
To evaluate the security of a symmetric cryptosystem against any quantum attack, the symmetric algorithm must be first implemented on a quantum platform. In this study, a quantum implementation of a classical block cipher is presented. A quantum circuit for a classical block cipher of a polynomial size of quantum gates is proposed. The entire work has been tested on a quantum mechanics simulator called libquantum. First, the functionality of the proposed quantum cipher is verified and the experimental results are compared with those of the original classical version. Then, quantum attacks are conducted by using Grover's algorithm to recover the secret key. The proposed quantum cipher is used as a black box for the quantum search. The quantum oracle is then queried over the produced ciphertext to mark the quantum state, which consists of plaintext and key qubits. The experimental results show that for a key of n-bit size and key space of N such that [Formula: see text], the key can be recovered in [Formula: see text] computational steps.
In this study, we present in detail the application of Grover's quantum algorithm to the searching problem of the secret key of a simple SPN (Substitution–permutation network) block cipher called Yo-yo. The main goal of the paper is to clarify the construction of the quantum circuit and the operation phases of Grover's algorithm to find the secret key with the condition of knowing at least 1 pair of plaintext-ciphertext. To achieve this goal, we consider 2 cases: the case where there is a unique key that satisfies and the case where there are 2 keys that satisfy at the same time. As a result, our implementation technique, implemented in the Qiskit programming language, requires only 17 qubits to find the key of the Yo-yo block cipher correctly. This technique can be effectively applied on IBM quantum computers for large-scale SPN block ciphers, such as AES and GOST R.34.10.2015, which are widely used today.
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.
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.
Abstract Quantum Algorithms reduce the computational complexity or solve certain difficult problems that were originally impossible to solve with classical computers. Grover's search algorithm is a Quantum computation algorithm that can find target elements from a set of unstructured data with the best possible, O(√ N) queries. Grover's search Quantum circuits implemented accurately can be used to successfully search and find the keys of Symmetric ciphers. However, very few demonstrations of such practical cryptanalysis are available. In this paper, practical Quantum cryptanalysis circuits for Affine Cipher are proposed and demonstrated, that successfully break the cipher by finding the keys.