Incorrect usage of the singular possessive?

One of the author’s purposes in the code book is to explain different types of codebreaking to his readers. which line best demonstrates this purpose? a theoretical breakthrough would be a fundamentally new way of finding alice's private key mathematicians have been studying factoring for centuries, and modern factoring techniques are not significantly better than ancient techniques a more recent development is the so-called tempest attack, which aims to detect the electromagnetic signals emitted . . in a computer's display unit if scientists could build a quantum computer, it would be able to perform calculations with . . enormous speed