I would hypothesize, that a number of factors, perhaps interacting with each other, contributed:
- Formation of theoretical computer science. The ACM chapter SIGACT for theoretical computer science was founded in 1968. The first regular conference Symposium on Theory of Computing (STOC) was launched in 1969.
- Increasingly broad availability of hardware. Intels first commercial microcomputer based on microprocessor design was released in 1971. Diffie & Hellmann's paper opens noting the transformative nature of the change in computer miniaturization and availability.
- Emergence of non-military cryptographic needs. The first ATM launched in 1967. In fact Diffie-Hellmann gives "remote cash dispensers" as an application area of cryptograpy. This application also drove early attempts around the NBS/NIST standard DES.