[link to summary excised because it uses cross-host redirect tricks to retain tracking ids] [some commentary lost during system misbehavior] The following is taken from a paper I submitted for the MSc Applied Cryptography module [https://www.napier.ac.uk/courses/msc-advanced-security-and-digital-forensics...] The full code listing and PDF can be found on GitHub at https://github.com/leedale1981/msc-applied-crypto-coursework # Introduction Currently the world of cryptography is solely based on what classical computers can achieve with well know Turing machine based algorithms. Quantum computers don’t come into the picture when it comes to general use encryption. This is set to change as quantum computers start to gain enough Qubits to successfully implement general use quantum algorithms that can break the encryption of our current state of the art public key exchange mechanisms [Bel+21]. Once this happens there will be a need for robust quantum key exchange methods that allow privacy of message exchange to be maintained, even when subjected to a quantum computing algorithms. Quantum computers with new quantum based algorithms will also make it possible to brute force current encryption keys in polynomial time. This puts any data that is currently encrypted with todays state of the art encryption algorithms in jeopardy of being cracked and made available for anyone with a quantum computer to view. Once a quantum computer with enough Qubits becomes available for general use it will mean they can also be used to keep communications between two parties secret. This paper outlines the current weaknesses in todays cryptography schemes including public key exchange methods that rely on the a mathematically hard to compute private key, and why these will be vulnerable to quantum computers in the future. It will then outline some key solutions to this problem that will be robust in a post quantum world. ...[the internals of the paper review classical and quantum cryptography and go through example quantum code. a good cypherpunk would include them so people would learn all these things. i'm not including them for personal reasons, to pressure myself to read such things a little rather than just copypaste.] ## Results When Eve interfered with the Qubits the result of the difference measurement was 65%. When no eavesdropping occurred the differences percentage dropped to only 25%. This shows that the amount of difference in bases comparisons increases when there is an eavesdropper interfering with the qubits. A percentage threshold can be set to determine when Alice and Bob should retry their communication based on a set percentage of difference of measurements. # Conclusions I have outlined the problems with cryptography that relies on hard to compute mathematical properties and the issues this creates for current asymmetric public key exchange 11 mechanisms such as RSA and elliptic curves. The current state of post quantum cryptography includes new methods of encryption such as lattice based cryptography and new public key exchange methods such as quantum key distribution. I showed that a protocol called BB84 can be used to share bits that can be later used to encrypt messages and which crucially doesn’t rely on a key that is hard to crack computationally. BB84 relies on the properties of quantum mechanics that allow two actors to know if their communication channel has been compromised. I showed an example of the BB84 protocol using a 6 bit key, due to the nature of the protocol this means that we would need a quantum computer that can support 24 qubits. Scaling this up to larger keys would means a larger amount of qubits. A 128 bit key for example would need 512 qubits and as of November 2022 the largest quantum computer produced by IBM has 433 qubits [22], falling short of the required amount for even a 128 bit key. For generating encryption keys it seems that lattice based cryptography methods are showing the most promise as protection against the computation power of quantum computers and this is most likely the area where the most benefits will be shown in the early stages of a post quantum world. In terms of communications channels then QKD methods will likely be adopted with more advanced methods like using Muons or other sources of quantum randomness to generate secret keys being used when methods become more refined and hardware is able to support the methods. # References [Deu85] D Deutsch. “Quantum theory, the Church–Turing principle and the universal quantum computer”. In: Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences 400.1818 (Apr. 1985), pp. 97–117. issn: 00804630. doi: 10.1098/RSPA.1985.0070. url: https://royalsocietypublishing. org/doi/10.1098/rspa.1985.0070. [Mon94] Peter L Montgomery. “A Survey of Modern Integer Factorization Algorithms”. In: 7.4 (1994), pp. 337–365. [Sho94] Peter W. Shor. “Algorithms for quantum computation: Discrete logarithms and factoring”. In: Proceedings — Annual IEEE Symposium on Foundations of Computer Science, FOCS (1994), pp. 124–134. issn: 02725428. doi: 10. 1109/SFCS.1994.365700. [MR08] Daniele Micciancio and Oded Regev. “Lattice-based Cryptography *”. In: (2008). [Gus+09] Julia Guskind et al. “Controlling passively quenched single photon detectors by bright light Circular Semi-Quantum Secret Sharing Using Single Particles This content was downloaded from IP address New Journal of Physics Controlling passively quenched single photon detectors by bright light”. In: New Journal of Physics 11.18pp (2009), p. 65003. doi: 10.1088/1367–2630/11/ 6/065003. url: http://www.idquantique.com/;. [And20] Ross Anderson. “Security engineering: a guide to building dependable distributed systems”. In: 2020, pp. 170–170. [BB20] Charles H. Bennett and Gilles Brassard. “Quantum cryptography: Public key distribution and coin tossing”. In: Theoretical Computer Science 560.P1 (Mar. 2020), pp. 7–11. doi: 10.1016/j.tcs.2014.05.025. url: http://arxiv. org/abs/2003.06557%20http://dx.doi.org/10.1016/j.tcs.2014.05. 025. 12 [Bel+21] Davide Bellizia et al. “Post-Quantum Cryptography: Challenges and Opportunities for Robust and Secure HW Design”. In: Proceedings — IEEE International Symposium on Defect and Fault Tolerance in VLSI and Nanotechnology Systems, DFT 2021-October (2021). issn: 2765933X. doi: 10.1109/ DFT52944.2021.9568301. [KG21] Ajay Kumar and Sunita Garhwal. “State-of-the-Art Survey of Quantum Cryptography”. In: Archives of Computational Methods in Engineering 2021 28:5 28.5 (Apr. 2021), pp. 3831–3868. issn: 1886–1784. doi: 10.1007/S11831–021- 09561–2. url: https://link.springer.com/article/10.1007/s11831- 021–09561–2. [22] IBM unveils world’s largest quantum computer at 433 qubits — New Scientist. 2022. url: https : / / www . newscientist . com / article / 2346074 — ibm — unveils-worlds-largest-quantum-computer-at-433-qubits/. [CCE23] Edwin Cartlidge, Cartlidge, and Edwin. “Muons used for cryptography system”. In: PhyW 36.3 (Mar. 2023), pp. 5–5. issn: 0953–8585. doi: 10.1088/ 2058–7058 / 36 / 03 / 05. url: https : / / ui . adsabs . harvard . edu / abs / 2023PhyW…36….5C/abstract. [Dal23] Lee Dale. leedale1981/msc-applied-crypto-coursework: Coursework repository for MSc Applied Cryptography document and code. 2023. url: https : / / github.com/leedale1981/msc-applied-crypto-coursework.