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This PR adds verification key 'summaries' to the snarky verifiers.
Basically we construct a (non-deterministic, non-total) function
summary : G1.t list * G2.t list * Fqk.Unitary.t list -> bool list
which is injective (if it doesn't throw). ByFqk.Unitary.t
I mean Fqk elements which are unitary.a + b beta : Fqk.t
is unitary if(a + b beta)(a - b beta) = 1
.The summary works element-wise as follows:
a + b beta
are mapped toa
and the parity of the 'real part' ofb
, assuming the real part is non-zero.b
is determined up to sign bya
by unitary-ness.The point of this is for making hashing more efficient.
summary
shrinks the size of its input, so you can get away with hashing fewer bits.