Enhanced QSimon Algorithm for Attacking the Offset Two-Round Scheme

Abstract

QSimon algorithm (a full quantum version of Simon's algorithm) is used to find periods in commitment functions and does not require classical calculations. However, QSimon algorithm circuit is incomplete, and the implementation of an essential component (solving boolean linear equations) has high resource consumption. This work further studies QSimon algorithm and applies QSimon algorithm to attack the offset two-round (OTR) scheme. QSimon algorithm is established by quantum boolean linear equations solving algorithm and general quantum truncation technique, which can obtain the period of any truncated function with overwhelming probability. The confidentiality and integrity of the OTR scheme are compromised by employing QSimon algorithm. The attacks ensure a high success rate and realize exponential speedup compared with classical versions.