scholarly journals Grover on Korean Block Ciphers

2020 ◽  
Vol 10 (18) ◽  
pp. 6407
Author(s):  
Kyoungbae Jang ◽  
Seungju Choi ◽  
Hyeokdong Kwon ◽  
Hyunji Kim ◽  
Jaehoon Park ◽  
...  
Keyword(s):  
Search Algorithm ◽  
Quantum Circuit ◽  
Block Ciphers ◽  
Research Area ◽  
Quantum Circuits ◽  
Security Level ◽  
Toffoli Gate ◽  
Grover Search ◽  
Target Block ◽  
Grover Search Algorithm

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.

scholarly journals Efficient Implementation of PRESENT and GIFT on Quantum Computers

2021 ◽  
Vol 11 (11) ◽  
pp. 4776
Author(s):  
Kyungbae Jang ◽  
Gyeongju Song ◽  
Hyunjun Kim ◽  
Hyeokdong Kwon ◽  
Hyunji Kim ◽  
...  
Keyword(s):  
Block Cipher ◽  
Search Algorithm ◽  
Block Ciphers ◽  
Quantum Circuits ◽  
Security Level ◽  
Symmetric Key ◽  
Grover Search ◽  
Target Block ◽  
Symmetric Key Cryptography ◽  
Grover Search Algorithm

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.

scholarly journals Grover on PIPO

Electronics ◽  
2021 ◽  
Vol 10 (10) ◽  
pp. 1194
Author(s):  
Kyungbae Jang ◽  
Gyeongju Song ◽  
Hyeokdong Kwon ◽  
Siwoo Uhm ◽  
Hyunji Kim ◽  
...  
Keyword(s):  
Block Cipher ◽  
Search Algorithm ◽  
Quantum Algorithms ◽  
Optimization Techniques ◽  
Quantum Circuits ◽  
Brute Force ◽  
Grover Search ◽  
Quantum Simulator ◽  
Compact Design ◽  
Grover Search Algorithm

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.

Entanglement in the Grover search algorithm

2005 ◽  
Vol 345 (4-6) ◽  
pp. 265-272 ◽  
Author(s):  
Yiyuan Fang ◽  
Dagomir Kaszlikowski ◽  
Chunming Chin ◽  
Ken Tay ◽  
L.C. Kwek ◽  
...  
Keyword(s):  
Search Algorithm ◽  
Grover Search ◽  
Grover Search Algorithm

scholarly journals Quantum Implementation of Powell’s Conjugate Direction Method

2019 ◽  
Vol 23 (4) ◽  
pp. 726-734
Author(s):  
Kehan Chen ◽  
Fei Yan ◽  
Kaoru Hirota ◽  
Jianping Zhao ◽  
◽  
...  
Keyword(s):  
Search Algorithm ◽  
Quantum Circuit ◽  
Data Fitting ◽  
Quadratic Equation ◽  
Quantum Circuits ◽  
Quantum Gates ◽  
Circuit Implementation ◽  
One Dimensional ◽  
Conjugate Direction ◽  
Conjugate Direction Method

A quantum circuit implementation of Powell’s conjugate direction method (“Powell’s method”) is proposed based on quantum basic transformations in this study. Powell’s method intends to find the minimum of a function, including a sequence of parameters, by changing one parameter at a time. The quantum circuits that implement Powell’s method are logically built by combining quantum computing units and basic quantum gates. The main contributions of this study are the quantum realization of a quadratic equation, the proposal of a quantum one-dimensional search algorithm, the quantum implementation of updating the searching direction array (SDA), and the quantum judgment of stopping the Powell’s iteration. A simulation demonstrates the execution of Powell’s method, and future applications, such as data fitting and image registration, are discussed.

scholarly journals Quantum Image Steganography Protocol Based on Quantum Image Expansion and Grover Search Algorithm

IEEE Access ◽  
2019 ◽  
Vol 7 ◽  
pp. 50849-50857 ◽  
Author(s):  
Zhiguo Qu ◽  
Zhengyan Li ◽  
Gang Xu ◽  
Shengyao Wu ◽  
Xiaojun Wang
Keyword(s):  
Search Algorithm ◽  
Image Steganography ◽  
Quantum Image ◽  
Grover Search ◽  
Quantum Image Steganography ◽  
Grover Search Algorithm ◽  
Image Expansion

QUANTUM SEARCH ALGORITHMS

2009 ◽  
Vol 23 (31) ◽  
pp. 5727-5758 ◽  
Author(s):  
VLADIMIR E. KOREPIN ◽  
YING XU
Keyword(s):  
Target Item ◽  
Search Algorithm ◽  
Search Algorithms ◽  
Quantum Search ◽  
Large Database ◽  
Grover Algorithm ◽  
Speed Up ◽  
The Subject ◽  
Grover Search ◽  
Target Block

This article reviews recent progress in quantum database search algorithms. The subject is presented in a self-contained and pedagogical way. The problem of searching a large database (a Hilbert space) for a target item is performed by the famous Grover algorithm which locates the target item with high probability and a quadratic speed-up compared with the corresponding classical algorithm. If the database is partitioned into blocks and one is searching for the block containing the target item instead of the target item itself, then the problem is referred to as partial search. Partial search trades accuracy for speed and the most efficient version is the Grover–Radhakrishnan–Korepin (GRK) algorithm. The target block can be further partitioned into sub-blocks so that GRK's can be performed in a sequence called a hierarchy. We study the Grover search and GRK partial search in detail and prove that a GRK hierarchy is less efficient than a direct GRK partial search. Both the Grover search and the GRK partial search can be generalized to the case with several target items (or target blocks for a GRK). The GRK partial search algorithm can also be represented in terms of group theory.

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