Rivest denies that these names have any relation to the 1969 movie Bob & Carol & Ted & Alice, as occasionally suggested by others.
Before the publication of Rivest's paper in 1998 other people brought to his attention a 1965 novel, Rex Stout's The Doorbell Rang, which describes the same concept and was thus included in the paper's references.
He invented the widely used encryption algorithm now commonly known as RSA, about three years before it was independently developed by Rivest, Shamir, and Adleman at MIT.
When, a few years later, Diffie and Hellman published their 1976 paper, and shortly after that Rivest, Shamir, and Adleman announced their algorithm, Cocks, Ellis, and Williamson suggested that GCHQ announce that they had previously developed both.
It was the need to synchronize the scramblers that suggested to James H. Ellis the idea for non-secret encryption which ultimately led to the invention of both the RSA encryption algorithm and Diffie-Hellman key exchange well before either was reinvented publicly by Rivest, Shamir, and Adleman, or by Diffie and Hellman.
After the re-discovery and commercial use of PKI by Rivest, Shamir, Diffie and others, the British government considered releasing the records of GCHQ's successes in this field.