Finance, Insurance, Healthcare, all rely on leaky proof in their operations, leading to the bigger horror stories, from perso info leaked, CCard number,
Self sovereign Identity requires a mean of proving one identity or [nym], without giving away critical information which can be malinianly reuse by corrupted individuals
a proof can be
 an age range proof
 a degree possession proof, (degree signed by University)
 a proof of solvency (balance > X) (certified by financial institution)
 a statement of ID attribute certified by institution or gov)
 a solution to an equation proof f(x) = 0
 a proof of membership
 a proof of trust
Proofs property:
 completeness (if both honest can’t convince it is false)
 soundness (if false can’t convince it is true)
 zeroknowledge
Zero Knowledge Proof
Example : interactive ZK Proof Riddles
 Where is Waldo ?
 Easter Egg Hunt (single egg left)
 Leaves on a tree superpower
 Alibaba cave with special key

Sudoku Solution
 Swapping 2 different objects (color balls)
 key to door lock (tunnel)

range proof of salary
 Yao’s Millionaire’s Problem
 chocola te bars
 The Knowledge Complexite of Interactive ProofSystems
 A physical zeroknowledge objectcomparison system
 …
Homomorphism (arithmetically conservative)
 F(x+y) = F(x) + F(y)
commitement (bet in future)
msg [commit]> H(msg) [open]> msg (msg revealed)
homomorphic commitment + range inner product proofs
This is where zeroknowledge proof are powerful
Cryptography give us a way to secure pointtopoint communication,
Pseudo anonymous blockchain try to solve the “pointtomany” security permission blockchain are simply using the pointtopoint i.e. the security problem disappear when intermediary are removed