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Elliptic Curve Cryptosystems

Neal Koblitz — Published

This paper, along with Use of Elliptic Curves in Cryptography, independently proposed the use of elliptic curves in cryptography.

Unlike other public-key cryptosystems — like RSA, which relies on the fact that factoring large integers is slow and multiplication is fast (the Prime Factorization Problem) — elliptic curve cryptography (ECC) depends on the difficulty of the Elliptic Curve Discrete Logarithm Problem: given two points, P and Q, on an elliptic curve, find the integer n, if it exists, such that Q = nP.

ECC provides similar security guarantees compared to RSA, but with significantly reduced key sizes and more efficient computation. ECC — specifically, Elliptic Curve Diffie-Hellman (ECDH) — is now the preferred authentication mechanism for secure web browsing over SSL/TLS.

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