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The third edition is a substantive extension, with new topics, including new sections or chapters: a description of the new SHA-3 standard for cryptographic hash functions, Keccak, and the underlying sponge construction; Paillier encryption; an introduction to elliptic curve cryptosystems including Diffie-Hellman key exchange, ElGamal encryption and the elliptic curve digital signature standard ECDSA; the basics of plane curves and elliptic curves; basic concepts of interactive proof systems, such as the special honest-verifier zero-knowledge property; unconditionally secure schemes; and an introduction to quantum cryptography.§