Algebraic side-channel attacks are a type of side-channel analysis which can recover the secret information with a small number of samples (e.g., power traces). However, this type of side-channel analysis is sensitive to measurement errors which may make the attacks fail.
In this paper, we propose a new method of algebraic side-channel attacks which considers noisy leakages as integers restricted to intervls and finds out the secret information with a constraint programming solver named BEE. To demonstrate the efficiency of this new method in algebraic side-channel attacks, we analyze some popular implementations of block ciphers---PRESENT, AES, and SIMON under the Hamming weight or Hamming distance leakage model. For AES, our method requires the least leakages compared with existing works under the same error model. For both PRESENT and SIMON, we provide the first analytical results of them under algebraic side-channel attacks in the presence of errors. To further demonstrate the wide applicability of this new method, we also extend it to cold boot attacks. In the cold boot attacks against AES, our method increases the success rate by over $25\\%$ than previous works.