In The Mathematics of Secrets: Cryptography from Caesar Ciphers to Digital Encryption, Joshua Holden provides the mathematical principles behind ancient and modern cryptic codes and ciphers.
The Mathematics of Secrets kicks off with a pretty decent chunk of introductory linear algebra in the service of basic substitution ciphers, preceded by a few pages of terminology. This is introduced apologetically as an unfortunate necessity, but some of the explanation could be handled better.
The seemingly-impossible shenanigans of public-key encryption, where the two parties can concoct some secret numbers that only the two of them know despite all their communication being entirely public, is well-explained. As are the newfangled elliptic-curve-based systems that might one day replace all that current mucking about with massive semiprimes, and the exciting world of quantum cryptography, where the preposterous properties of protons are corralled into a fundamentally unbreakable code system.
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