The post-quantum security of the SHA-3 hash function standard

Project Details

Layman's description

Quantum computers will pose a major challenge for cryptography. There are two types of cryptography, namely public-key and symmetric-key. It has been known for a long time that attackers with quantum computers will be able to break most public-key cryptography currently in use due to the high computational power of quantum computers. Cryptographers have been concentrating on searching for alternative public-key cryptography primitives because of this fact. Recently, it became clear that symmetric-key cryptography primitives, like hash functions and block ciphers, are also affected by surprisingly efficient quantum attacks. These primitives are used to secure the integrity of the data used in password verification, message authentication, digital signatures, and so on. They are crucial for almost every digital piece of infrastructure, from military communications all the way to digital public administration (e-governance) and online shopping. If quantum attacks are successful on these primitives, it means that your bank account is in danger because someone else can pretend to be you in the digital world. Therefore, proving that these primitives will remain secure upon the arrival of quantum computers is a problem of utmost importance to our society. The solution to this problem requires expertise in cryptography, quantum computing, and mathematics.

In this project, we want to prove the security of the hash functions against attackers with quantum computers. When using these functions in complex protocols, researchers often resort to idealized models where they can make security proofs, such as the random oracle model (ROM). Here, the functions are modeled as random objects that all parties have black-box access to. Quantum at-tackers can implement these on their quantum computers. Taking this into account has led to the introduction of the quantum random oracle model (QROM). Here, adversaries have quantum black-box access to the idealized models. Quantum-accessible idealized models share many of the advantages of their classical counterparts. However, analyzing the post-quantum security in idealized models is very challenging, with difficulties arising from fundamental features of quantum theory like the fact that measurement will irreversibly disturb a quantum state, the existence of the no-cloning principle, and so on. In our project, we are concerned with the SHA-3 hash function standard, which is the most recent addition to the SHA family of standards. This standard hash function makes use of permutations, which are functions satisfying certain properties; hence, we switch to the permutation version of the above idealized models. The complex structure of permutations causes more difficulties to overcome in addition to the ones caused by quantum theory. Our goal is to develop a powerful tool for the security analysis of constructions based on cryptographic permutations using group representation theory.
StatusActive
Effective start/end date01/02/202431/01/2027

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