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’s search algorithm is a generic attack against symmetric key cryptographic primitives, that can reduce the search complexity to square root. To apply the Grover’s 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 AuA. Baksi Nanyang Technological University, Singapore E-mail: anubhab001@e.ntu.edu.sg Corresponding author K. Jang Division of IT Convergence Engineering, Hansung University, Seoul, South Korea E-mail: starj1023@gmail.com Corresponding author G. Song Division of IT Convergence Engineering, Hansung University, Seoul, South Korea E-mail: thdrudwn98@gmail.com H. Seo Division of IT Convergence Engineering, Hansung University, Seoul, South Korea E-mail: hwajeong84@gmail.com Z. Xiang Faculty of Mathematics and Statistics, Hubei Key Laboratory of Applied Mathematics, Hubei University, Wuhan, PR China E-mail: xiangzejun@hubu.edu.cn thenticated 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.