Improving protection of falcon electronic signature software implementations against attacks based on floating point noise

The object of this study is digital signatures. The Falcon digital signature scheme is one of the finalists in the NIST post-quantum cryptography competition. Its distinctive feature is the use of floating-point arithmetic, which leads to the possibility of a key recovery attack with two non-matching signatures formed under special conditions. The work considers the task to improve the Falcon in order to prevent such attacks, as well as the use of fixed-point calculations instead of floating-point calculations in the Falcon scheme. The main results of the work are proposals for methods on improving Falcon's security against attacks based on the use of floating-point calculations. These methods for improving security differ from others in the use of fixed-point calculations with specific experimentally determined orders of magnitude in one case and proposals for modifying procedures during the execution of which the conditions for performing an attack on implementation level arise in the second case. As a result of the analysis, the probability of a successful attack on the recovery of the secret key for the reference implementation of the Falcon was clarified. Specific places in the code that make the attack possible have been localized and code modifications have been suggested that make the attack impossible. In addition, the necessary scale for fixed-point calculations was determined, at which it is possible to completely get rid of floating-point calculations. The results could be used to qualitatively improve the security of existing digital signatures. This will make it possible to design more reliable and secure information systems using digital signatures. In addition, the results could be implemented in existing systems to ensure their resistance to modern threats