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Elliptic Curve Cryptography

This overview of Elliptic Curve Cryptography (ECC) introduces the fundamental concepts of elliptic curves and their application in cryptographic protocols. Learn how ECC enables secure key agreement through the Elliptic Curve Diffie-Hellman method and ensures data integrity via the Elliptic Curve Digital Signature Algorithm. We explore the efficiency of ECC compared to traditional systems like RSA, highlighting the shorter key lengths for equivalent security levels. Finally, we compare performance in terms of signing and decryption versus signature verification and encryption.

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Elliptic Curve Cryptography

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  1. Elliptic Curve Cryptography

  2. Outline • Introduction to elliptic curves • Elliptic curve Diffie-Hellman key agreement • Elliptic curve Digital Signature Algorithm

  3. Q=(x,-y)

  4. How do elliptic curve cryptosystemscompare with other cryptosystems? • Roughly speaking, elliptic curve cryptosystems with a 160-bit key offer about the same security as RSA and discrete logarithm based systems with a 1024-bit key. As a result, the length of the public key and private key is much shorter in elliptic curve cryptosystems. • Elliptic curve cryptosystems are faster than the RSA system in signing and decryption, but slower in signature verification and encryption. • Reference: http://www.rsa.com/rsalabs/node.asp?id=2245

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