One Key To Rule Them All - ECC Math Tricks

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Come and listen to a tale in which we build upon basics about Elliptic Curves to discover how we could have One Key To Rule Them All, in order to do SSH key management or even build a Wireguard PKI.

Among the novelties developed for Bitcoin, one can find a very interesting scheme for asymmetric key derivation introduced in BIP32 (“Bitcoin Improvement Proposals”). The principle is to be able to derive child keys in a deterministic way from their parents’ keys.

This is a “feature” which is already available in straight ECC, since one can simply exploit the distributivity of the scalar multiplication over the elliptic curve addition law.

No need for any blockchain, and I'm thus explaining in this talk some basic EC maths, before explaining how this key derivation works, and I'll finally be showcasing a few examples.