2 research outputs found
Quantum Speed-Up for Multidimensional (Zero Correlation) Linear Distinguishers
This paper shows how to achieve a quantum speed-up for multidimensional (zero correlation) linear distinguishers.
A previous work by Kaplan et al. has already shown a quantum quadratic speed-up for one-dimensional linear distinguishers.
However, classical linear cryptanalysis often exploits multidimensional approximations to achieve more efficient attacks, and in fact it is highly non-trivial whether Kaplan et al.\u27s technique can be extended into the multidimensional case.
To remedy this, we investigate a new quantum technique to speed-up multidimensional linear distinguishers.
Firstly, we observe that there is a close relationship between the subroutine of Simon\u27s algorithm and linear correlations via Fourier transform.
Specifically, a slightly modified version of Simon\u27s subroutine, which we call Correlation Extraction Algorithm (CEA), can be used to speed-up multidimensional linear distinguishers.
CEA also leads to a speed-up for multidimensional zero correlation distinguishers, as well as some integral distinguishers through the correspondence of zero correlation and integral properties shown by Bogdanov et al.~and Sun et al.
Furthermore, we observe possibility of a more than quadratic speed-ups for some special types of integral distinguishers when multiple integral properties exist.
Especially, we show a single-query distinguisher on a 4-bit cell SPN cipher with the same integral property as 2.5-round AES.
Our attacks are the first to observe such a speed-up for classical cryptanalytic techniques without relying on hidden periods or shifts.
By replacing the Hadamard transform in CEA with the general quantum Fourier transform, our technique also speeds-up generalized linear distinguishers on an arbitrary finite abelian group