Accessible Requires Authentication Published by De Gruyter October 22, 2019

Combining a quantum random number generator and quantum-resistant algorithms into the GnuGPG open-source software

Francesco Raffaelli, Robert Denman, Richard Collins, Jean-Charles Faugere, Gaetano De Martino, Charles Shaw, Jake Kennard, Philip Sibson, Ludovic Perret and Chris Erven ORCID logo

Abstract

The “quantum threat” to our current, convenient cryptographic algorithms is getting closer, with demonstrable progress by commercial quantum computing efforts. It is now more important than ever that we combine all of our tools into a new quantum-safe toolbox to develop the next generation of quantum-safe networking solutions. Here we combine an integrated quantum entropy source with quantum-resistant algorithms in the GnuGPG open-source software; leading to a fully quantum-safe version of GnuGPG. The quantum entropy source itself is capable of a raw rate of randomness in excess of 10 Gbps. After post-processing, quantum random numbers are used by the quantum-resistant algorithms to allow GnuGPG to perform its usual public-key cryptographic tasks, such as digitally signing documents, but now in a secure quantum-safe way.


Corresponding author: Chris Erven, KETS Quantum Security Ltd., Unit DX, St. Philips Central, Albert Road, St. Philips, Bristol, BS2 0XJ, UK; and H. H. Wills Physics Laboratory and Department of Electrical and Electronic Engineering, Quantum Engineering Technology Labs, University of Bristol, Nanoscience and Quantum Information Building, Tyndall Avenue, Bristol, BS8 1FD, UK, E-mail:

  1. Author contribution: All the authors have accepted responsibility for the entire content of this submitted manuscript and approved submission.

  2. Research funding: None declared.

  3. Conflict of interest statement: The authors declare that they are employed at 2 start-ups which produce commercial QRNG and QR solutions.

References

[1] P. W. Shor, “Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer,” SIAM J. Comput., vol. 26, no. 5, pp. 1484–1509, 1997, https://doi.org/10.1137/s0097539795293172. Search in Google Scholar

[2] V. Gheorghiu and M. Mosca, Benchmarking the Quantum Cryptanalysis of Symmetric, Public-Key and Hash-Based Cryptographic Schemes, arXiv:1902.02332 [quant-ph], 2019. Search in Google Scholar

[3] E. Anschuetz, J. Olson, A. Aspuru-Guzik, and Y. Cao, “Variational quantum factoring,” in Quantum Technology and Optimization Problems Cham, S. Feld and C. Linnhoff-Popien, Eds., New York, Springer International Publishing, 2019, pp. 74–85. Search in Google Scholar

[4] D. J. Bernstein and T. Lange, “Post-quantum cryptography,” Nature, vol. 549, pp. 188–194, Sept 2017, https://doi.org/10.1038/nature23461. Search in Google Scholar

[5] S. Pirandola, U. L. Andersen, L. Banchi, et al.., Advances in Quantum Cryptography, arXiv:1906.01645 [quant-ph], 2019. Search in Google Scholar

[6] M. Herrero-Collantes and J. C. Garcia-Escartin, “Quantum random number generators,” Rev. Mod. Phys., vol. 89, p. 015004, Feb 2017, https://doi.org/10.1103/revmodphys.89.015004. Search in Google Scholar

[7] I. Reidler, Y. Aviad, M. Rosenbluh, and I. Kanter, “Ultrahigh-speed random number generation based on a chaotic semiconductor laser,” Phys. Rev. Lett., vol. 103, p. 024102, Jul 2009, https://doi.org/10.1103/physrevlett.103.024102. Search in Google Scholar

[8] T. Stojanovski, J. Pihl, and L. Kocarev, “Chaos-based random number generators. Part II: practical realization,” IEEE Trans. Circ. Syst. Fund. Theor. Appl., vol. 48, pp. 382–385, March 2001, https://doi.org/10.1109/81.915396. Search in Google Scholar

[9] J. Szczepanski, E. Wajnryb, J. Amigo, M. V. Sanchez-Vives, and M. Slater, “Biometric random number generators,” Comput. Secur., vol. 23, no. 1, pp. 77–84, 2004, https://doi.org/10.1016/s0167-4048(04)00064-1. Search in Google Scholar

[10] C. S. Petrie and J. A. Connelly, “A noise-based IC random number generator for applications in cryptography,” IEEE Trans. Circ. Syst. Fund. Theor. Appl., vol. 47, pp. 615–621, May 2000, https://doi.org/10.1109/81.847868. Search in Google Scholar

[11] J. Rarity, P. Owens, and P. Tapster, “Quantum random-number generation and key sharing,” J. Mod. Optic., vol. 41, no. 12, pp. 2435–2444, 1994, https://doi.org/10.1080/09500349414552281. Search in Google Scholar

[12] T. Jennewein, U. Achleitner, G. Weihs, H. Weinfurter, and A. Zeilinger, “A fast and compact quantum random number generator,” Rev. Sci. Instrum., vol. 71, no. 4, pp. 1675–1680, 2000, https://doi.org/10.1063/1.1150518. Search in Google Scholar

[13] M. A. Wayne, E. R. Jeffrey, G. M. Akselrod, and P. G. Kwiat, “Photon arrival time quantum random number generation,” J. Mod. Optic., vol. 56, no. 4, pp. 516–522, 2009, https://doi.org/10.1080/09500340802553244. Search in Google Scholar

[14] M. Wahl, M. Leifgen, M. Berlin, T. Röhlicke, H.-J. Rahn, and O. Benson, “An ultrafast quantum random number generator with provably bounded output bias based on photon arrival time measurements,” Appl. Phys. Lett., vol. 98, no. 17, p. 171105, 2011, https://doi.org/10.1063/1.3578456. Search in Google Scholar

[15] M. Stipčević and B. M. Rogina, “Quantum random number generator based on photonic emission in semiconductors,” Rev. Sci. Instrum., vol. 78, no. 4, p. 045104, 2007, https://doi.org/10.1063/1.2720728. Search in Google Scholar

[16] B. Qi, Y.-M. Chi, H.-K. Lo, and L. Qian, “High-speed quantum random number generation by measuring phase noise of a single-mode laser,” Optic. Lett., vol. 35, pp. 312–314, Feb 2010, https://doi.org/10.1364/ol.35.000312. Search in Google Scholar

[17] F. Xu, B. Qi, X. Ma, H. Xu, H. Zheng, and H.-K. Lo, “Ultrafast quantum random number generation based on quantum phase fluctuations,” Optic. Express, vol. 20, pp. 12366–12377, May 2012, https://doi.org/10.1364/oe.20.012366. Search in Google Scholar

[18] Y.-Q. Nie, L. Huang, Y. Liu, F. Payne, J. Zhang, and J.-W. Pan, “The generation of 68 Gbps quantum random number by measuring laser phase fluctuations,” Rev. Sci. Instrum., vol. 86, no. 6, pp. 063105, 2015, https://doi.org/10.1063/1.4922417. Search in Google Scholar

[19] J. Liu, J. Yang, Z. Li, et al.., “117 gbits/s quantum random number generation with simple structure,” IEEE Photon. Technol. Lett., vol. 29, pp. 283–286, Feb 2017, https://doi.org/10.1109/lpt.2016.2639562. Search in Google Scholar

[20] M. Jofre, M. Curty, F. Steinlechner, et al.., “True random numbers from amplified quantum vacuum,” Optic. Express, vol. 19, pp. 20665–20672, Oct 2011, https://doi.org/10.1364/oe.19.020665. Search in Google Scholar

[21] C. Abellán, W. Amaya, M. Jofre, et al.., “Ultra-fast quantum randomness generation by accelerated phase diffusion in a pulsed laser diode,” Optic. Express, vol. 22, pp. 1645–1654, Jan 2014, https://doi.org/10.1364/oe.22.001645. Search in Google Scholar

[22] C. Gabriel, C. Wittmann, D. Sych, et al.., “A generator for unique quantum random numbers based on vacuum states,” Nat. Photon., vol. 4, pp. 711–715, Oct 2010, https://doi.org/10.1038/nphoton.2010.197. Search in Google Scholar

[23] M. Avesani, D. G. Marangon, G. Vallone, and P. Villoresi, Secure Heterodyne-Based Quantum Random Number Generator at 17 Gbps, arXiv:1709.00685v1 [quant-ph], 2017. Search in Google Scholar

[24] B. Xu, Z. Li, J. Yang, et al.., High Speed Continuous Variable Source-independent Quantum Random Number Generation, arXiv:1709.00685v1 [quant-ph], 2017. Search in Google Scholar

[25] Z. Zheng, Y.-C. Zhang, W. Huang, S. Yu, and H. Guo, 6 Gbps Real-Time Optical Quantum Random Number Generator Based on Vacuum Fluctuation, arXiv:1805.08935 [quant-ph], 2018. Search in Google Scholar

[26] F. Raffaelli, G. Ferranti, D. H. Mahler, et al.., “A homodyne detector integrated onto a photonic chip for measuring quantum states and generating random numbers,” Quant. Sci. Technol., vol. 3, no. 2, p. 025003, 2018, https://doi.org/10.1088/2058-9565/aaa38f. Search in Google Scholar

[27] F. Raffaelli, P. Sibson, J. E. Kennard, D. H. Mahler, M. G. Thompson, and J. C. F. Matthews, “Generation of random numbers by measuring phase fluctuations from a laser diode with a silicon-on-insulator chip,” Optic. Express, vol. 26, pp. 19730–19741, Aug 2018, https://doi.org/10.1364/oe.26.019730. Search in Google Scholar

[28] M. Rude, C. Abellan, A. Capdevila, et al.., Phase Diffusion Quantum Entropy Source on a Silicon Chip, arXiv:1804.04482 [quant-ph], 2018. Search in Google Scholar

[29] C. Abellan, W. Amaya, D. Domenech, et al.., “Quantum entropy source on an photonic integrated circuit for random number generation,” Optica, vol. 3, pp. 989–994, Sep 2016, https://doi.org/10.1364/optica.3.000989. Search in Google Scholar

[30] P. Sibson, C. Erven, M. Godfrey, et al.., “Chip-based quantum key distribution,” Nat. Commun., vol. 8, p. 13984, Feb 2017, https://doi.org/10.1038/ncomms13984. Search in Google Scholar

[31] P. Sibson, J. E. Kennard, S. Stanisic, C. Erven, J. L. O’Brien, and M. G. Thompson, “Integrated silicon photonics for high-speed quantum key distribution,” Optica, vol. 4, pp. 172–177, Feb 2017, https://doi.org/10.1364/optica.4.000172. Search in Google Scholar

[32] Quantis QRNG chip, 2020. Available at: https://www.idquantique.com/random-number-generation/products/quantis-qrng-chip. Search in Google Scholar

[33] A. I. Lvovsky and M. G. Raymer, “Continuous-variable optical quantum-state tomography,” Rev. Mod. Phys., vol. 81, pp. 299–332, Mar 2009, https://doi.org/10.1103/revmodphys.81.299. Search in Google Scholar

[34] X. Ma, F. Xu, H. Xu, X. Tan, B. Qi, and H.-K. Lo, “Postprocessing for quantum random-number generators: entropy evaluation and randomness extraction,” Phys. Rev., vol. 87, p. 062327, Jun 2013, https://doi.org/10.1103/physreva.87.062327. Search in Google Scholar

[35] B. Chor and O. Goldreich, “Unbiased bits from sources of weak randomness and probabilistic communication complexity,” SIAM J. Comput., vol. 17, no. 2, pp. 230–261, 1988, https://doi.org/10.1137/0217015. Search in Google Scholar

[36] D. Zuckerman, “General weak random sources,” in Proceedings [1990] 31st Annual Symposium on Foundations of Computer Science, St. Louis, MO, USA, IEEE Institute of Electrical and Electronics Engineers, 1990, pp. 534–543. Search in Google Scholar

[37] C. H. Bennett, E. Bernstein, G. Brassard, and U. V. Vazirani, “Strengths and weaknesses of quantum computing,” SIAM J. Comput., vol. 26, no. 5, pp. 1510–1523, 1997, https://doi.org/10.1137/s0097539796300933. Search in Google Scholar

[38] A. Rukhin, J. Soto, J. Nechvatal, et al.., A Statistical Test Suite for Random and Pseudorandom Number Generators for Cryptographic Applications, Gaithersburg, MD, USA: National Institute of Technology, 2010. Search in Google Scholar

[39] N. Bindel, U. Herath, M. McKague, and D. Stebila, “Transitioning to a quantum-resistant public key infrastructure,” in PQCrypto 2017. Lecture Notes in Computer Science, vol. 10346, T. Lange and T. Tsuyoshi, Eds., Cham, Springer, 2017, pp. 384–405. Search in Google Scholar

[40] P. Kampanakis, P. Panburana, E. Daw, and D. V. Geest, The viability of post-quantum x.509 certificates, Cryptology ePrint Archive, Report 2018/063, 2018. Available at: https://eprint.iacr.org/2018/063. Search in Google Scholar

[41] D. Sikeridis, P. Kampanakis, and M. Devetsikiotis, “Post-quantum authentication in tls 1.3: a performance study,” in Network and Distributed Systems Security (NDSS) Symposium 2020. St. Louis, USA: NDSS; 2020. Search in Google Scholar

[42] N. Bindel, J. Braun, L. Gladiator, T. Stöckert, and J. Wirth, “X.509-compliant hybrid certificates for the post-quantum transition,” J. Open Source Software, vol. 4, no. 40, p. 1606, 2019, https://doi.org/10.21105/joss.01606. Search in Google Scholar

[43] Composite keys and signatures for use in internet PKI, 2020. Available at: https://tools.ietf.org/html/draft-ounsworth-pq-composite-sigs-02. Search in Google Scholar

[44] ISARA catalyst agile digital certificate technology, 2020. Available at: https://www.isara.com/products/isara-catalyst-agile-digital-certificate-technology.html. Search in Google Scholar

Received: 2020-05-29
Accepted: 2020-09-14
Published Online: 2019-10-22
Published in Print: 2020-11-26

© 2020 Walter de Gruyter GmbH, Berlin/Boston