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NIST's primary post-quantum signature standard works by signing, checking your own signature against a size limit, and throwing it away and starting over if it's too big. Learn how 'Fiat-Shamir with Aborts' turns a leaky lattice proof into a secure signature.
Falcon produces the smallest signatures of any NIST post-quantum standard. It does that by solving a problem that broke the leading lattice signature schemes of the late 1990s/early 2000s. Learn the hash-and-sign paradigm, and why the naive version of it is fatally insecure.
Rainbow signed messages using polynomial equations so tangled that solving them looks impossible. Then, in 2022, someone found a shortcut and broke it in a weekend on a laptop. Learn how it worked, and how it fell.
Every other post-quantum signature scheme bets on a new hard math problem holding up. SPHINCS+ makes almost no new bet at all: its security rests on nothing but hash functions. Learn how a tree of one-time signatures becomes a full signature scheme.
