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Quantum implementation and resource estimates for Rectangle and Knot

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Abstract

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 Authenticated 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. The implementations reported here are simulated on classical computer (as long as it is feasible).

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Notes

  1. Except for measurement, see Sect.  2.3.

  2. https://github.com/starj1023/KNOT-QC/.

  3. We indicate the SBoxes by the shorthand string-based notation, as opposed to the more common table-based notation, to save space.

  4. https://csrc.nist.gov/Projects/lightweight-cryptography/round-2-candidates.

  5. It may be noted that, \(c = b - r\) is the capacity.

  6. https://competitions.cr.yp.to/caesar.html.

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Authors and Affiliations

  1. Nanyang Technological University, Singapore, Singapore

    Anubhab Baksi

  2. Division of IT Convergence Engineering, Hansung University, Seoul, South Korea

    Kyungbae Jang, Gyeongju Song & Hwajeong Seo

  3. Faculty of Mathematics and Statistics, Hubei Key Laboratory of Applied Mathematics, Hubei University, Wuhan, People’s Republic of China

    Zejun Xiang

Authors
  1. Anubhab Baksi
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  2. Kyungbae Jang
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  3. Gyeongju Song
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  4. Hwajeong Seo
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  5. Zejun Xiang
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Correspondence to Anubhab Baksi.

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Baksi, A., Jang, K., Song, G. et al. Quantum implementation and resource estimates for Rectangle and Knot. Quantum Inf Process 20, 395 (2021). https://doi.org/10.1007/s11128-021-03307-6

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