Elliptical Curve CryptologyWhat and Why of ECC?Elliptic Curve Cryptology (ECC) is a public key cryptography technique that makes use of the properties of the elliptic curve and of their algebraic structure of finite fields. It is one of the most effective ways to provide encryption of cryptographic keys. Elliptic curves as algebraic/geometric entities have been studied extensively over the past 150 years, and from these studies a rich and profound theory has emerged. Elliptic curve systems applied to cryptography were first proposed in 1985 independently by Neal Koblitz of the University of Washington and Victor Miller, then working at IBM, Yorktown Heights.[1]These curves allowed the creation of a new generation of asymmetric cryptographic systems. algorithms. ECC's big win, compared to other public key algorithms, is key size. A fairly typical key size for RSA is 1024 bits - it would take about 10^11 MIPs per year to crack. A simple 160-bit ECC key offers the same level of security. This advantage only increases with the level of security, something that will be important as the power of computers continually grows. A 2048-bit RSA key and a 210-bit ECC key are equivalent. Furthermore, ECC has a lower computational load than RSA, mainly because it does not have to analyze prime numbers, a rather expensive operation.[1] ECC can be used with SSL scheme, certificates, Diffie-Hellman key agreement, El-Gamal and protocols such as ECDSA (elliptic curve digital signature algorithm). This could lead to ECC being an important tool/element of tomorrow's cryptography. Although ECC has not been studied as extensively as RSA, all research to date has confirmed that ECC is safe. ..pute u1 = h(m)w mod n and u2 = rw mod n.5. Calculate u1 P + u2 Q = (x0 , y0 ) and v = x0 mod n.6. Accept the signature if and only if v = r .[2]References[1] www.certicom.com[2] Neal Koblitz, Alfred Menezes, Scott Vanstone “The State of Elliptic Curve Cryptography”[3] Nick Sullivan “http: //arstechnica.com/security/2013/10/a-relatively-easy-to-understand-primer-on-elliptic-curve-cryptography/"[4] P.Kocher", Timing Attacks on Implementations of Diffe-Hellman, RSA, DSS, and Other Systems,”Advances in Cryptology-CRYPTO'96 Proceedings, Springer-Verlag, 1996, pp. 104-113[5] Darrel Hankerson, Julio Lopez Hernandez and Alfred Menezes, “Software Implementation of Elliptic Curve Cryptography Over Binary Fields", Cryptographic Hardware and Embedded Systems, 2000.[6] Don Johnson and Alfred Menezes, “The Algorithm of elliptic curve digital signature (ECDSA)”, 1999.