A British mathematician, working on code decryption, unexpectedly falls in love with another decrypter. This leads them to a complicated intrigue within the codebreakers.
Sebastian, a former Oxford professor, heads the all-female decoding staff of British Intelligence. One day he has a chance meeting with young Becky Howard and is so impressed by her mental agility that he offers her a job deciphering codes used by foreign agents. A crisis develops when Elsa Shahn, a former Communist and one of Sebastian's most trusted associates, is accused of being a poor security risk by the brutish Inspector Phillips. But Sebastian persuades the Head of Intelligence that Elsa is vital to his operation. During all of this the headstrong Becky seduces Sebastian, thereby irritating his longtime mistress, Carol Fancy, a former pop singer. Elsa then betrays the trust placed in her by giving decoded information to a left-wing political organization. Obligated to resign, Sebastian leaves London and returns to his professorship at Oxford. Sometime later he is summoned back to his post by Head of Intelligence to help decode the signals emanating from a newly-launched Russian satellite. While looking for Becky (who has left the department), he runs into Carol and is lured to a party at her flat and drugged with LSD. He is saved from killing himself while hallucinating by the timely intervention of Inspector Phillips, who has been trailing him. Eventually, Sebastian locates Becky and learns that he is the father of her baby. A noise from the child's rattle provides Sebastian with the clue to the Russian signals; and, aided by his still-faithful team of girls, he breaks the sputnik code.
