I gave two educational talks at the second iteration of Bitcoin Edge Dev++ at Keio university in Tokyo, immediately preceeding the Scaling Bitcoin Conference.

I covered the following topics:

#### Digital signatures - finite fields, elliptic curves, Schnorr signatures and ECDSA

Erratum:

- The slide on Cyclic Groups said “The integers modulo p for any number p is a cyclic group”. It should say “The integers modulo p for any
*prime*p is a cyclic group”. (If p is composite, ie p = ab, then the order of a in G is b, so G is not cyclic). - during the talk, I was asked
*“how does the verifier know*I said that`K`

in the non-interactive schnorr identification protocol?”`K`

can be provided by the prover. That’s wrong. In fact, the verifier calculates`K`

himself and then checks that`e`

is the hash of`K`

. The verification step is checking that`e`

does in fact commit to`K`

.

The slides above are corrected.