You might have noticed that the word “cryptocurrency” starts with “crypto”, which is also often used as a term for anything related to the matter, even as an umbrella term for all cryptocurrencies. Why do you think that is? Is it related to crypts, or perhaps — kryptonite? In a way — yes to both — since all come from the word “kryptos” which is the Greek word for hiding, and which also gave its name to the fascinating, brilliant and mysterious science of cryptography. While the direct translation from ancient Greek would be “hidden writing”, in very broad sense cryptography is the science and practice of secure communication.
Virtually all modern forms of cryptography are based on mathematical theory and the practicalities of computer science and they usually (but not always, we will get into that later) rely on a mathematical problem that is very hard to solve in a reasonable amount of time. This makes the science ever-changing, as new methods for solving those problems are invented every now and then, and the algorithms are updated to become more and more secure and new ones are invented. For quite some time cryptography has been an integral part of our life, in its typical ever-present but non-obvious ways — you cannot log in in your favorite social network, email or even your own phone without some cryptographic algorithm to prove that you have the necessary authentication and nobody else can access your data. With the advent of the cryptocurrencies and the myriad of possibilities of their technology cryptography found another welcome home for its powers. Actually, the science is so integral into building a cryptocurrency, that its presence is even part of any formal definition of the term — if something is to be declared a cryptocurrency, its ownership can be proven exclusively cryptographically.
So, cryptography is essential. But where does it come in? The first and most obvious use of cryptography in building a cryptocurrency is providing a secure signature scheme. Only the rightful owner of the funds should be able to spend them, so every transaction is signed by the owner’s private key. There is no way around it, every cryptocurrency should have a cryptography-based signature scheme. For example, the most famous currency — Bitcoin — uses the Elliptic Curve Digital Signature Algorithm (ECDSA) which relies on the hardness of the Discrete Logarithm Problem on elliptic curves. Monero uses a form of ring signature, in which a group of possible signers is merged together to produce a distinctive signature that can authorize a transaction. There are many other varieties of signatures or clever proposals, for example, the idea that one can use a tree of one-time signatures which provides absolute forward secrecy. The topic is so fascinating, that would do a separate blog post comparing the various digital signature options with their advantages and disadvantages.
However, some other ingenious uses of cryptography can be invented. We are particularly interested in the following scenario — imagine that your currency already has a secure digital signature, but someone observes the accounts carefully (as everyone should be able to verify the transactions). With enough time, this careful observer can make some deduction about the accounts — for example who tend to receive more and who tend to spend more, who gets big sums and who gets small sums and — in theory — can even try to relate an account to real-world people and organisations which defeats the purpose of one of the pillars of the currency — the secrecy. Thus, a big innovation in the cryptocurrency concept is the use of a secure cryptosystem to encrypt the amounts transferred between the accounts, and in this way, no one can make the dangerous deductions described above.
We will get into more details of how that can be achieved later. Because, just as we have so many established currencies and new ones emerging every so often, a developed market, the use of well-researched cryptosystems and powerful digital signatures — a new development in the world of cryptography might change all those things forever.
Cryptography is a fast-changing science, where new algorithms are discovered and old ones become obsolete every year. But to everyone even vaguely familiar with the current topics of cryptographic debates it is clear, that a great challenge looms ahead — the advent of Quantum computers. The concept of quantum computers have existed for a long time, but in recent years some of the tech giants have started to finally make practical progress on them. And while the advent of a practical, usable, functioning, well-programmed quantum computer might be decades in the future, it already stirs the waters of the cryptographic community.
As usual, humanity’s ideas go way ahead of the practical implementation and years before anything related to quantum computers became a reality, Peter Shor invented an algorithm that slowly changed the field of cryptography forever. Shor’s algorithm uses the suspected power of a quantum computer to solve the factorization problem (if you have a number, how to find its prime factors, — especially hard when the number is the product of the multiplication of two very big prime numbers). Many of the cryptosystems currently used, like the all-prevalent RSA are directly based on factorization, many others like ElGamal and most of the elliptic curve cryptography can be reduced to a similar problem and is also solved theoretically using Shor’s algorithm. Almost all digital signatures are also not secure in the long run.
And now when quantum computers are slowly but surely becoming a reality — the world needs to change. It does not actually matter if they will come in 10 years (as the boldest predictions see it) or in 15–20 (the more realistic prognosis), and it does not matter that the change will come slowly and that even with state of the art quantum computer it will take a considerable time for it to decode any particular data, anyone who wants to stay ahead of those developments must act now. Thus, we have decided, that in order to provide the highest quality standard of encryption and to create an enduring system, we must use cryptography that is quantum secure.
In a world of technological competition and innovation, we strive to be at the top level of modernization and advancement and provide a product, technically strong and secure enough to endure into the future. The cryptographical aspects of the currency are no exception to this and extensive research was put into the properties of quantum-secure cryptography. Several cryptosystems are currently considered quantum secure, and several digital signature schemes also aim to tackle the problem.
In a series of blog posts we will have a look at them and their implications and limitations and the applications we, or others, might have for them. Among those cryptosystems, one of the most well-developed and widely used cryptosystems and pretty much-considered state of the art in the post-quantum cryptography is called NTRU and this is what we will tackle in our next cryptography blog post.