This paper presents a new side channel attack to recover a block cipher key. No plaintext and no ciphertext are required, no tem- plates are built. Only the leakage measurements collected in many different rounds of the algorithm are exploited. The leakage is considered as a Hamming weight with a Gaussian noise. The chosen target is the Advanced Encryption Standard (AES). Bayesian inference is used to score all guesses on several consecutive round-key bytes. From these scores a Belief Propagation algorithm is used, based on the relations of the Key-Expansion, to discriminate the unique correct guess. Theoretical results according to various noise models are obtained with simulations.