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Why the full r-torsion group contains r^2 many elements and consists of r+1 subgroups

Only if $r$ is prime. Let $E[r] = \langle P,Q \rangle$ be the $r$-torsion subgroup. Its cyclic subgroup is defined by a generator of the form $[a]P + [b]Q$, but up to a (non-zero) scalar multiple: ...
Fractalice's user avatar
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Where can I find 2 of the steps/proofs described in Dan Boneh's video on PLONK in the PLONK Paper? The 2 don't seem to match

In the talk, Boneh shows how to obtain an "arithmetization" from an arithmetic circuit, which represents a specific computation. In the paper, Gabizon does provide a proof system, given a ...
Seminal Worker's user avatar
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which zero knowledge proof technique is suitable for identity verification system?

There are many instances of implementing ZKP for anonymous authentication, such as $\Sigma$ protocol(interactive ZKP), classical Fiat-Shamir transformer by assuming random oracle and Groth-Sahai ...
ming alex's user avatar
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What do we know about the relationship between IP, ZKP?

unconditionally IP = PSPACE [Because of shamir] Now NP contianed in ZK (if OWF exist). This is essential since to prove the zero knowledge aspect of the protocol you need commitment schemes that imply ...
bagheera's user avatar

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