Quantum Cryptography, Blockchain, and Post-Quantum Security Analysis

This discussion post explores the application of quantum cryptography in blockchain technology, focusing on the use of algorithms such as Grover's and Shor's. It delves into the vulnerabilities of blockchain systems to quantum attacks and the implications of post-quantum cryptography. The post references research on quantum key distribution, including experiments on secure three-user network communication and the DARPA quantum network. It also covers code-based and lattice-based cryptosystems, as well as the advantages and formulas related to quantum key distribution using photons. The discussion highlights the ongoing efforts to secure cryptographic systems in the face of advancing quantum computing capabilities and the importance of post-quantum cryptography. The references provide further context for the topics discussed.

Discussion 1-
Blockchain used in bitcoin was a type of quantum computational cryptography and quantum
enhanced attacks and is based on Grover’s algorithm and Shor’s algorithm (Li et al., 2019). It
consists of core blocks that are attached and are stored on and copied between public servers.
It was first used in bitcoin. Each block consists of 4 fundamental elements-
The hash of the preceding block, its data content, the hash of that block and the nounce. The
algorithms used to make blockchain can be used to destroy them also. The hash used in the
blockchains can be searched by the Grover’s algorithm and can be changed to different
hashes. Besides hash any of the blockchain that uses public key or private key can be
destroyed with the help of Shor’s algorithm (Rajan and Visser, 2019), (Haney, 2019).
Discussion 2-
In an article by (Chen et al., 2009) they have experimentally showed a safe three - user
network communication system with the help of decoy state quantum cryptography. With the
help of the experiments it was possible to make 3 secure quantum keys on a request by USTC
(University of Science and Technology
Of China), Binhu, and Xinglin that are located in Hefei city of China. The keys were to be
used among these 3 institutions. The basis of the experiment is purely on DARPA (The
Defense Advanced Research Projects Agency) (Elliott et al., 2005). The DARPA quantum
network was the first quantum network with the first QKD deployment in the history (.
Sergienko, 2005). Basically, the DARPA security model is based on VPN (Virtual Private
Network) a model by (Sharbaf, 2009) in which the authors could also find out the errors in
the quantum by Quantum Bit Error Rate.
Discussion 3-
Post quantum cryptography is basically code-based signatures or cryptography which was
first done in 1978 by McEliece. The cryptosystems were first developed had a problem of
large amount of storage or memory requirements (Lange and Steinwandt, n.d.). GRS codes
are used as cryptosystems instead of Goppa codes because of smaller key sizes of the GRS
codes. Pairing based key exchange is based on public key cryptography in which one key is
shared between 3 or more participants with the help of cryptosystems (Gu et al., 2011). Code
based and lattice based cryptosystems have believed to achieve security level up to 2k with
the help of polynomial size public keys and polynomial time encryption and decryption
(Buchmann et al., 2009).
Discussion 4-
Quantum key distribution uses photons as information carriers. One of the major advantage
with this is that the catcher of the information will be able to track the information and get it

but he cannot change the information (Kiktenko et al., 2016). In a paper by (Lütkenhaus,
2000) he has mentioned a formula for the gain of secure bits per signal which is sent to the
receiver. He has showed security against singular attack for only one single photon for
different photons sources, for multiple photons sources with ideal polarisations. He derived
different formulas for different type of photons and photons sources used (Jouguet et al.,
2013),(Symul et al., 2007).

References
Buchmann, J., Lindner, R., Rückert, M. and Schneider, M. (2009). Post-quantum
cryptography: lattice signatures. Computing, 85(1-2), pp.105-125.
Elliott, C., Colvin, A., Pearson, D., Pikalo, O., Schlafer, J. and Yeh, H. (2005). <title>Current
status of the DARPA quantum network (Invited Paper)</title>. Quantum
Information and Computation III.
Gu, and Bleumer, et al,(2011). Post-Quantum Cryptography. Encyclopedia of Cryptography
and Security, pp.949-950.
Haney, B. (2019). Blockchain: Post-Quantum Security &amp; Legal Economics. SSRN
Electronic Journal.
Jouguet, P., Kunz-Jacques, S., Leverrier, A., Grangier, P. and Diamanti, E. (2013).
Experimental demonstration of long-distance continuous-variable quantum key
distribution. Nature Photonics, 7(5), pp.378-381.
Kiktenko, E., Trushechkin, A., Kurochkin, Y. and Fedorov, A. (2016). Post-processing
procedure for industrial quantum key distribution systems. Journal of Physics:
Conference Series, 741, p.012081.
Lange, T. and Steinwandt, R. (n.d.). Post-Quantum Cryptography. Springer International
Publishing.
Li, C., Xu, Y., Tang, J. and Liu, W. (2019). Quantum Blockchain: A Decentralized,
Encrypted and Distributed Database Based on Quantum Mechanics. Journal of Quantum
Computing, 1(2), pp.49-63.
Lütkenhaus, N. (2000). Security against individual attacks for realistic quantum key
distribution. Physical Review A, 61(5).
Rajan, D. and Visser, M. (2019). Quantum Blockchain Using Entanglement in
Time. Quantum Reports, 1(1), pp.3-11.

Sergienko, A. (2005). Quantum Communications and Cryptography. 1st ed.
Symul, T., Alton, D., Assad, S., Lance, A., Weedbrook, C., Ralph, T. and Lam, P. (2007).
Experimental demonstration of post-selection-based continuous-variable quantum key
distribution in the presence of Gaussian noise. Physical Review A, 76(3).