In cryptography, the security of algorithms is typically proven in a security model. The so-called random probing model has become established for analysing the security of masking methods against side-channel attacks. In this model, it is assumed that each intermediate value of a calculation is disclosed to the attacker with a certain probability. The probability depends on the one hand on the protection mechanisms used and on the other hand on the noise present in physical measurements.

Today's science assumes that a system that is secure in the random probing model should also be secure against side-channel attacks in the real world as long as the physical noise in a measurement is large enough. Previous methods with security in the random probing model require a high degree of physical noise to guarantee provable security. In the research work presented here, it was possible to show how cryptographic methods can guarantee security through additional randomisation steps even if there is significantly less noise in the physical measurement. This is particularly important for cryptographic systems that work with large fields, such as the AES encryption standard or newer post-quantum methods.