Nigel Smart made available a draft of the third edition of Cryptography: An Introduction for free on his page. The book contains a very gentle introduction into elliptic curves (the author doesn't assume any prior knowledge of number therory). Smart also provides very interesting historical background (like how the Enigma machine was developed and used by Germans and eventually broken by the Turing algorithm.)

Nigel Smart made available a draft of the third edition of Cryptography: An Introduction for free on his page. The book contains a very gentle introduction into elliptic curves (the author doesn't assume any prior knowledge of number theory). Smart also provides very interesting historical background (e.g. how the Enigma machine was developed and used by Germans and eventually broken by the Turing algorithm.)

Another great introductory text is Elliptic curves: number theory and cryptography by Washington. It puts a stronger emphasis on number-theoretic applications but the exposition is clear and mostly elementary.

Nigel Smart made available a draft of the third edition of Cryptography: An Introduction for free on his page. The book contains a very gentle introduction into elliptic curves (the author doesn't assume any prior knowledge of number therory).

Nigel Smart made available a draft of the third edition of Cryptography: An Introduction for free on his page. The book contains a very gentle introduction into elliptic curves (the author doesn't assume any prior knowledge of number therory). Smart also provides very interesting historical background (like how the Enigma machine was developed and used by Germans and eventually broken by the Turing algorithm.)