Cryptology is a foundation of information security in the digital world. Today's internet is protected by a form of cryptography based on complexity theoretic hardness assumptions. Ideally, they should be strong to ensure security and versatile to offer a wide range of functionalities and allow efficient implementations. However, these assumptions are largely untested and internet security could be built on sand. This issue is becoming even more sensitive due to the possible emergence of general purpose quantum computers in the mid-term future.
The main ambition of Almacrypt is to remedy this issue by challenging the assumptions through an advanced algorithmic analysis.
In particular, the scope of proposal includes the status of the two current pillars of public-key encryption: factoring and discrete logarithms. It is already known that they would be vulnerable to quantum computers. In addition, recent progress showed that in some cases, the discrete logarithm problem is considerably weaker than previously assumed against classical computers. A main objective is to ponder the security of other cases of the discrete logarithm problem, including elliptic curves, and of factoring. We are studying the generalization of the recent techniques and searching for new algorithmic options with comparable or better efficiency. Concerning elliptic curves, we are also interested by the related issue of isogeny between curves.
We also study hardness assumptions based on codes, subset-sum and polynomial systems, which are candidates hard problems for post-quantum cryptographic schemes. Essentially, we are considering the applicability of recent algorithmic and mathematical techniques, in order to discover more about the corresponding complexity classes, to refine the analysis of the algorithms, and to design new algorithm tools.
Cryptology is not limited to the above assumptions: other hard problems can be proposed to aim at post-quantum security or to offer extra functionalities. Using these other problems as testbeds to demonstrate other applications of our algorithmic progress is also within the scope of Almacrypt.
In addition to its scientific goal, Almacrypt also aims at seeding a strengthened research community dedicated to algorithmic and mathematical cryptology.
