As networks of computers grew through the 1970's and '80s, a big problem with password verification remained unsolved. Computers became more powerful, minimal cryptographic key sizes got longer, and researchers found that older methods for verifying a typical password over a network were broken. This is an essential problem for password verification between untrusted parties. With classical password verification, whoever goes first gives away the secret. Worse still, across an open channel, anyone listening in can get it too.
Attackers have powerful computers.
In the failed attempts to solve the problem, people tried using the password as a key. But most cryptographic methods, whether symmetric as in DES, or asymmetric as in RSA, require very large keys. Ordinary encryption methods and one-way hash functions cannot solve this problem. Even when zero-knowledge proofs of knowledge were developed, they were not designed to work with a small secret. There were also many efforts to encourage people to memorize larger, more random passwords, with notably little success.