Welcome to our first blog post in the series on elliptic curve cryptography. With the following posts, you will get an overview of the world of elliptic curves, starting with a brief history and some thoughts on what the future holds. Without further ado, let us begin.
The need to exchange information and, at the same time, keep it partially secret is as old as human civilization. The first signs of deliberately shifting away from well-known spelling traditions date back to Ancient Egypt, to ca. 1900 BC (although, at that time, the goal was probably more artistic-religious). Hints to secret coding can be found from the Bible, the book of Jeremiah, where the word “Babel” is replaced with “Sheshak” twice, which is derived from the world “Babel” through replacing characters.
It did not take long before leaders and commanders understood the potential benefits that stem from the art of secret coding and how it could help them achieve their strategic goals. This was followed by a centuries-long race between cryptographers (writers of secret code) and cryptoanalysts (breakers of secret code). The winner of that race was the one who could invent smarter methods than his enemy.
The history of creating and cracking ciphers has shown that the more complex the structure of a cryptosystem, the harder it is to keep it a secret from the enemy. That is why, at the end of the 19th century, a Dutch cryptographer, Auguste Kerckhoffs, laid down a principle, according to which, the security of a cryptogram should rely on a secret as solid as possible (and, therefore, as protected as possible), also known as the key1.2
How large the possible size of the keys (so called key space) should be depends on the capability of the enemy. Cryptoanalysis made a huge step forward during World War II with the development of electronic computers (one goal of the development of which was to actually break the enemy’s ciphers). It took several decades before computers reached a wide audience, but by around the 1960s/70s, it was clear that secret coding could no longer rely on the fact that the enemy is not strong enough to go through a few million possible key combinations. The need to widen the search space increased remarkably and it screamed for a more systematic approach.
Another problem regarding the use of historic cryptosystems was key symmetry. This means that for both creating and reading of the secret code you needed the same key. By doing so, you must solve the problem of key distribution – how to ensure that the recipient of the secret message has the necessary key to understand it. On the other hand, it is not possible to send the key over an unsecure channel in order to create a secure one, because the attacker can track the key and later open the encrypted communication using the same key. To solve this, you’ll have to read on as we look at asymmetric keys in this series of blog posts.
Written by Jan Willemson
1 Auguste Kerckhoffs. La cryptographie militaire. Journal des sciences militaires, IX:5–38, 1883.
2 Not to confuse Auguste Kerckhoffs with the German physicist Gustav Kirchhoff, who phrased the principles of electric charge and energy conservation in electric circuits.