In this paper methods of forming cryptographic keys from biometric images using fuzzy extractors are considered. A new scheme of a fuzzy extractor based on the McEliece cryptosystem is proposed. It is shown that the new design of the fuzzy extractor allows forming cryptographic passwords from biometric images even without the use of non-secret helper string. When using helper string, the proportion of corrected distortions of biometric images increases significantly. In addition, the proposed design relates to a class of post-quantum information security methods, i.e. it is expected to be safely used even for solving cryptanalysis problems with universal quantum computers.