Quantum Cryptography Algorithms Implementations

Question

The Post Quantum Cryptography is a type of cryptography that lies on physics properties instead of mathematics , it has many algorithms and implementations like NTRU , McEliece , SIDH ... etc

But there is a difference between Post Quantum Cryptography and Quantum Cryptography , i'd like to know some algorithms of that and also if they have implementations for example on Github or any thing like that

Thank you

Answer 1

The Post Quantum Cryptography is a type of cryptography that lies on physics properties instead of mathematics , it has many algorithms and implementations like NTRU , McEliece , SIDH ... etc. But there is a difference between Post Quantum Cryptography and Quantum Cryptography

Let's try to classify this:

1. Quantum Privacy Amplification, which is the honest name of the better known Quantum Key Distribution. It was formerly the meat of Quantum Cryptography, and has become a sub-field of that. It matches “(re)lies on physics properties instead of mathematics” well. More precisely, the aim is establishing a trusted shared secret key between parties, with security relying on:
   • a Quantum physics model of the devices used;
   • mathematical facts (contrast with other cryptography, which additionally relies on a few mathematical conjectures);
   • a shorter trusted shared secret¹ key (hence Privacy Amplification).
2. Quantum Computing, which aims at performing useful² computing tasks that today's ordinary computers can't do. It uses physical devices directly relying on Quantum physics effects, without the abstraction/limitation of Boolean logic as today's computers do. There are many burgeoning and hopefully cross-fertilizing sub-fields, in which I vaguely distinguish three levels:
   • Experimental+theoretical³ physics to get these things going at the atomic scale and avoid the accumulation of errors; this subdivides according to technology and level of abstraction.
   • Study and even development of quantum algorithms to run on hypothesized quantum computers, with a subfield Quantum Cryptanalysis aiming at attack of cryptographic algorithms (not to be confused with attack of cryptographic hardware using quantum sensors)
   • Development of classical software tools running on classical computers to support development and simulation of quantum algorithms.
3. Post-Quantum cryptography, which develops cryptographic algorithms that run on ordinary computers and hopefully would resist Quantum Cryptanalysis. This field has “many algorithms and implementations like NTRU, McEliece, SIDH…”.

Sticking to the three disjoint things on-topic for crypto.SE, there is a lot of software involved in Quantum Privacy Amplification, Quantum Cryptanalysis, and Post-Quantum Cryptography. Some is on Github or similar. But as a matter of policy we generally do not recommend software.

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¹ In some KPA/KQD setups, that initial key would only need to be kept secret until first used by the first party doing so, and could be public in the part of the plot where some old-fashioned courier then carries it to the second party by a process insuring its integrity. However, because couriers are slow, practice is to send the initial key in advance. In that case it must be secret while the courier moves it, else we loose security reducible to having a valid quantum model of the devices used.

² There are recent well-substantiated claims that we can do things with today's bleeding edge quantum computers that today's classical computers struggle at. However these things are not, yet, the kind of things ordinary heavy users of computing want to do. In particular, these things are as far as can be from cryptanalysis and “big data”. To caricature, today's bleeding edge quantum computers excel in the study of quantum phenomenons, by implementing them.

³ The two are hard to distinguish these days. Before 2020, “wear protective gear” did quite well, for guys in experimental mode need to protect themselves from liquefied gaz, laser, acid and other toxics… and protect their work and tools from the contamination their body generates.

Answer 2

I've looked quite a bit into post-quantum cryptography, so I could tell you plenty of algorithms for that. Post-quantum cryptography is secure against a quantum computer, but can be executed on a classical system.

Quantum cryptography on the other hand would need to be executed on a quantum computer, so even if you could find an implementation on GitHub or anywhere else, you unfortunately wouldn't be able to run it for a while yet. There are certainly plenty of quantum cryptography ideas and techniques, but I'm not aware of any actual concrete algorithms. Hell, we've barely standardised post-quantum algorithms, it'll be a while yet I think before we get standardisation on actual quantum techniques.

In the meantime, as Stephen Ullrich suggested, check out the Wikipedia page on quantum cryptography. It'll give you a good starting point for checking out some of these techniques. Sorry I couldn't provide a more useful answer.