ALGEBRAIC CRYPTANALYSIS OF SYMMETRIC CIPHERS: MODELING AND MULTISTEP SOLVING STRATEGIES

This paper presents a systematic study of algebraic cryptanalysis for symmetric ciphers. It explains how encryption algorithms can be expressed as systems of polynomial equations over finite fields and analyzed using algebraic and logical solvers. The study begins by detailing block and stream ciphers through the lens of difference algebra, interpreting state up-dates and key additions as polynomial mappings. It then outlines the main solving strategies used in algebraic cryptanalysis, starting from Gröbner-basis and SAT approaches and progressing to hybrid solving. It next focuses on multistep and oracle-based strategies, which adjust variable guessing according to the hardness of each instance. These strategies extend classical hybrid attacks and make the solving process more efficient. Four case studies on Bluetooth E0, Bivium, Trivium, and Aradi illustrate these ideas. Each example shows how algebraic modeling and adaptive solving reveal structural properties and solvability thresholds intrinsic to the considered cipher. The results show that multistep reasoning reduces computational effort compared with the static hybrid solving and provides a unified way to understand algebraic complexity in both stream and block ciphers.