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We introduce and formally define polynomial commitment schemes
and provide two efficient constructions
A polynomial commitment scheme allows a committer to commit
to a polynomial with a short

string that can be used by a verifier
to confirm claimed evaluations
of the committed polynomial
Although the homomorphic commitment schemes

in the literature can be used to achieve this goal,
the sizes of their commitments are linear in the degree of the committed polynomial.

Danksharding
Yeah we’re starting
Time for scaling with
Proto-danksharding
Pure of heart and
So smart
This is the soul of
Proto-danksharding

On the other hand, polynomial commitments in our schemes are of constant size (single elements)
The overhead of opening a commitment is also constant; even opening multiple evaluations

requires only a constant amount
of communication overhead
Therefore, our schemes are useful tools
to reduce communication cost cryptographic protocols

On that front we apply
our polynomial commitment schemes
to four problems
in cryptography:

verifiable secret sharing,
zero-knowledge sets, credentials
and content extraction signatures


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