Two methods for random number generation are modified to make them more resistant to attacks by current measurements. The methods are particularly designed to be implemented in electronic devices such as smart cards, PCMCIA, badges, contactless cards or any other portable device. The DES algorithm is encrypted using a key K having a value D representing date information, to generate an integer variable I. For j ranging from 1 to m, the following steps are carried out: substituting s with s XOR I; introducing in the integer variable y the result of the encryption of s with the DES algorithm using the key K; introducing in x.sub.j the result of y or s; substituting s with y XOR I; and introducing in s the result of the encryption of s with the DES algorithm using the key K. The sequence (x.sub.1, x.sub.2, x.sub.m) is then restored in the output.