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Digital signature -
how signing works. key ideas: asymmetric (public key) cryptography, hard to compute but easy to verify.
Merkle tree -
important data structure optimizing the storage of hashes in a blockchain
Distributed consensus
Practical Byzantine Fault Tolerance (Castro and Liskov, 1999) -
a seminal algorithm for state machine replication / transaction ordering in a distributed system with up to 1/3 malicious nodes
Distributed Systems -
excellent 101-level lecture notes. presumes some comfort with math notation, particularly predicate logic.
distributed systems concepts can help answer questions like "why is Solana's "Proof of History" an innovation?"
CAP Theorem -
fundamental trade-off between staying consistent vs. staying available when there's a network partition, i.e. nodes can't communicate
FLP Result -
why distributed consensus is not guaranteed when a node goes down. in practice, this is solved by relaxing the constraints of their model
Proof of useful work -
using collective computing power to search for prime number chains. an academic application but interesting concept
Bonus
P vs. NP -
deep theoretical question on the very nature of computation: whether easy to verify implies (=>) easy to solve
Elliptic curve cryptography -
in-depth blog post with plenty of diagrams on how elliptic curve cryptography works