An introduction to Elliptic Curve Cryptography (ECC) aimed at FPGA and embedded systems designers. Covers the GF(2^n) finite field math underlying point addition and doubling, how scalar multiplication is built from these operations, and how Diffie-Hellman key exchange works over elliptic curves to produce shared AES keys. Includes a concrete GF(2^226) curve example illustrating curve selection, base-point order, and the security argument based on the Elliptic Curve Discrete Logarithm Problem. Also touches on NIST curve choices, binary extension field trade-offs, and Weil descent attacks.
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