This paper provides a new approach to perform Correlation Power Analysis (CPA) attack. Power analysis attacks are side channel attacks based on power consumption measures on a device running a cryptographic algorithm with a CMOS technology based circuitry. Unlike most of CPA attacks that are based on statistical attacks, this paper proposes a new approach based on spectral analysis. The interest lies in the reduction of the attack complexity. The complexity is quasi linear in the size of the table of values of the S-box whereas it is quadratic with statistical attacks. It is shown that it can be easily extended to a so-called multidimensional attack. The attack is experimented on a AES S-box.