Borromean Rules

Introduction

These rules apply to all ringCT types that use Borromean ring signatures to prove an output amount is in the correct range.

Rules

Number Of Borromean Range Proofs

The amount of Borromean range proofs must be the same as the number of outputs.1

Ci Valid Points

Each Ci (bit commitment) must be canonically encoded points.2

Sum Ci

For a range proof at a certain index the sum of each Ci must equal the outPK at that index.3

Borromean Scalar Encoding

Monero does not check that the scalars s0 and s1 are reduced this leads to them, if not reduced, being interpreted as a different scalar by the slide function which calculates the 5-NAF of the number. The slide function restricts it's output to 256 bytes however if the last bit is set on the input this could lead to the 5-NAF of the scalar being 257 bytes long. There are scalars on the chain which have this behavior.4

The scalar ee must be a fully reduced scalar as it is compared against the raw bytes of an output from the hash_to_scalar function.5

The Borromean Ring Must Be Valid

To verify a Borromean ring signature is valid you must first set up the public keys that the ring will be verified with, one member of the ring will be a Ci the other will be (\(Ci - H * 2^X \)), where X is the index of the Ci. By setting up the ring like this the prover will only know the discreet log of a ring member if either the Ci is a commitment to 0 or \(2^X\)6.

After setting up the public keys the actual borromean rings must be valid.7