Nullifiers

• Nullifiers are used to prevent things from happening more than once
• UniRep uses two different nullifiers

Epoch key nullifiers

• Epoch key nullifiers are used to prevent users from using the same epoch key twice and prevent users from double user state transition.
• If an epoch key nullifier is seen before, then drop the second user state transition proof.
• Nullifier of an epoch key is computed by

hash2([
    epoch, 
    identityNullifier + nonce
])

caution

It would be better to be expressed as

hash3([
    epoch,
    identityNullifier,
    nonce
]) % BigInt(2 ** epochTreeDepth)

But to save circuit constraints, we put identityNullifier and nonce in one input field.
NOTE: It is similar but not the same as epoch key.

Reputation nullifiers

• Reputation nullifiers are used to prevent users from double spending the reputation if an action requires users to spend reputation.
• If a reputation nullifier is seen before, then the second reputation proof is recognized invalid.
• Nullifier of a reputation spent is computed by

hash4([
    identityNullifier, 
    epoch, 
    nonce, 
    attesterId
])

• The nonce can only be within 0 to posRep-negRep-1 with the given attesterID.