Theoretically secure cryptographic algorithms can be vulnerable to attacks due to their implementation flaws. Bernstein's attack is a well-known cache-timing attack that uses execution times as the side-channel. The major drawback of this attack is that it needs an identical target machine to perform its profiling phase where the attacker models the cache timing-behavior of the target machine. This assumption makes the attack unrealistic in many circumstances. In this work, we present an effective method to eliminate the profiling phase. We propose a methodology to model the cache timing-behavior of the target machine by trying hypothetical cache behaviors exhaustively. Our implementation results show that the proposed nonprofiled Bernstein's attack has comparable (and better in some test instances) performance to the original attack with the profiling phase.