The hash extension technique used to generate an ECGA may be used to increase the strength of one-way hash functions and/or decrease the number of bits in any situation where some external requirement limits the number of hash bits, and that limit is below what is (or may be in the future) considered secure against brute-force attacks. For example, to decrease the length of human entered security codes (and maintain the same security), and/or to increase the strength of a human entered security code (and maintain the length of the security code), the security code may be generated and/or authenticated using an extended hash method.