KolmoCrypt (101142322)

  https://cordis.europa.eu/project/id/101142322

  Horizon Europe (2021-2027)

  Cryptography from Unstructured Hardness

  ERC ADVANCED GRANTS (ERC-2023-ADG)

  linear algebra  ·  internet  ·  cryptography  ·  logarithmic functions

  2025-03-01 Start Date (YY-MM-DD)

  2030-02-28 End Date (YY-MM-DD)

  € 2,496,250

  Description

Cryptography—and its basic tasks such as encryption, authentication and key exchange—is essential for ensuring privacy and security on the Internet. The question of whether “unbreakable” encryption methods exist has fascinated mathematicians and cryptographers for thousands of years, and is closely related to the famous NP vs. P problem. This question is still wide open and consequently, Internet security today relies on cryptographic constructions based on the *conjectured* hardness of some computational problems (such as e.g., the factoring problem, the discrete logarithms problem or various noisy linear algebra problems). However, these conjectured hard problems all contain significant (e.g., algebraic) *structure*, that may make them vulnerable to attacks. Furthermore, for tasks such as key exchange and public-key encryption, only a *handful* of candidate hard problems are known on which these tasks can be based. As a result, some unexpected algorithmic developments for structured problems could upend the whole infrastructure we rely on for communicating and transacting on the Internet. In this project, we propose to develop an alternative approach: a foundation for provably-secure Cryptography from *unstructured hardness* assumptions. Towards resolving this long-standing challenge, we will leverage our recently-discovered connection between Cryptography and the seemingly unrelated area of Kolmogorov Complexity. Specifically, we will develop new hardness assumptions rooted in Kolmogorov Complexity on which the cryptographic tasks (e.g., private-key encryption, key-exchange, public-key encryption) can be based. Critically, these assumptions will lack algebraic and other computational structure that may make them vulnerable to attacks. Overall, KolmoCrypt will provide a new theoretical foundation for the hardness assumptions on which Cryptography is based, and ultimately, a more secure foundation for the Internet (and beyond).

  Complicit Organisations

1 Israeli organisation participates in KolmoCrypt.