The concept of a time-memory trade-off was first introduced by M. Hellman in 1980, providing an algorithm for conducting brute-force attacks more efficiently. This method consists of an intensive precomputation phase, the results of which are stored in tables and subsequently used to significantly reduce the time required for brute-force attacks. A notable advancement is the introduction of rainbow tables by Oechslin in 2003. However, the process of precomputing rainbow tables is marked by inefficiency, primarily due to the large proportion of computed values that are ultimately discarded. In 2023, descending stepped rainbow tables were introduced by Avoine et al., which consists of recycling chains during the precomputation phase. This paper introduces and evaluates ascending stepped rainbow tables, unlike traditional rainbow tables, which use uniform chains, this variant adds new, distinct chains during the precomputation phase. The paper presents a detailed analysis of the ascending stepped rainbow tables, including formulas to predict attack time, precomputation time, memory requirements, and coverage. Through theoretical results and implementation, the analysis demonstrates that this new variant offers significant improvements over both descending stepped rainbow tables and traditional rainbow tables for high coverage. Specifically, for the typical 99.5% coverage, ascending stepped rainbow tables achieve up to 30% faster precomputation time compared to descending stepped tables, and up to 45% compared to traditional rainbow tables, while also reducing attack times by up to 15% and 11% respectively. For lower coverages, although the precomputation times are higher, the attacks remain faster.