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• Zentralblatt MATH, by Juan Tena Ayuso.
  
  "the book gathers the main mathematical topics related to public key cryptography and provides an excellent source of information for both students and researchers interested in the field"
  
  
• MAA Reviews, by Darren Glass.
  
  "I enjoy Galbraith's exposition, and am very happy to have a copy of this book on my shelf"
  
  

• Table of notation
• Hints and Solutions to Exercises

• Section 5.2, page 73. Part 1 of Lemma 5.2.20: varphi_i^{-1}^* is not a k-algebra homomorphism (consider the sum of two polynomials of different total degree). Part 6 of Lemma 5.2.20: f should be homogeneous. Also proof of part 2 of Lemma 5.2.25: f should be homogeneous. (Error noticed by Parinaz Shahabi.)
• Section 7.7, page 113, Proof of Lemma 7.7.10 (second line): "\iota(P) = \iota(P) = " should just be "\iota(P) = ". (Error noticed by Parinaz Shahabi.)
• Section 8.1, page 122, Definition 8.1.6: A field F between phi^*( k( C_2 )) and k( C_1 ) with those properties does not necessarily exist if the extension is not normal. The treatment should be the other way around: k(C_1)/F purely inseparable and F/phi^*( k( C_2 )) separable. (Error noticed by Alexander Schiller.)
• Section 12.2.1, page 241, line -5: The standard definition of a Sophie Germain prime is a prime p such that 2p+1 is prime. The book defines 2p+1 to be the Sophie Germain prime, which is not standard. (Error noticed by Florian Weingarten.)
• Section 18.2, page 371, line 1: According to the definition used in the book, [7/2] = [3.5] = 4 and so the correct vector should be 4 b_1 + 2 b_2 = (10, 8, 6). But this ruins the moral of Example 18.2.4 (pages 372-373) that Babai nearest plane and Babai rounding can give different results (which is true in general, just not in this case). (Error noticed by Bart Coppens.)
• Section 25.2, page 523, line -3: It is not true that Phi_{ell}( j(E), j( tilde{E} ) = 0 implies there is an isogeny from E to tilde{E}, as the isogeny might be to a twist of tilde{E}. Correct wording would be to replace "cyclic kernel from E to tilde{E}" to "cyclic kernel from E to a twist of tilde{E}". (Error noticed by Drew Sutherland.)