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Signature verification

As explained in Elliptic Curve Cryptography for Developers

The cryptographic procedure that checks whether a signature satisfies the verification equation for specified data and public keys.

Signature verification checks whether an aggregate signature satisfies the pairing equation e(σ, g₂) = e(H₀(m), A). Recompute H₀(m) for every attempt so a changed message fails verification; mismatched messages likewise invalidate the aggregate. section 18.3.4

A practical multi-signature verification flow is:

  • For subgroup signatures, hash the aggregate public key with the message and node indices, calculate three pairings, and compare w₁·w₂ with w₃. section 18.5

Verification output

A test signs the same 200-byte message with each node, aggregates the individual points, and calls multisig_verify(). Successful output reports that e(sigma, g2) matches e(H0, apk); verification can be performed by anyone holding the public keys, aggregate signature, and message. section 18.6.3

How Elliptic Curve Cryptography for Developers covers it

How deep it goes
Descends to pairing calls, group conversion, equality testing, memory cleanup, and subgroup-specific hash construction, while delegating pairing internals.
Examples
Demonstrates node-level signing, point aggregation, pairing comparison, and successful verification output in a single-machine simulation.
What it assumes
Assumes signatures, public keys, aggregate points, message hashing, elliptic-curve groups, and pairing routines are available.
What you can do after
Diagnose/debug with it by detecting changed messages, inconsistent node inputs, failed pairing equality, and incorrect public-key membership.
How it connects
Connects aggregate signatures, public-key aggregation, hash functions, elliptic-curve groups, Weil pairing, and subgroup signatures.

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