# How Credential Revocation Works¶

This doc aims to explain credential revocation at a conceptual level. If this doc still feels too low-level, you might consider watching this introductory video from time offset 0:30 to 4:30.

## Background: Cryptographic Accumulators¶

Before explaining the mechanism in detail, it’s necessary to understand cryptographic accumulators at a very high level. We will try to avoid daunting math in our explanation.

You can think of an accumulator as the product of multiplying many numbers together. In the equation `a * b * c * d =` `e`, the accumulator would be `e`; it accumulates a value as each new factor is multiplied in. We could plug in numbers; if `a`=2 and `b`=3 and `c`=5 and `d`=7, then our accumulator `e` has a value of 210. If `e` has this value, we say that 3 is “in” `e` because it is a factor. If we want to take 3 out of the accumulator, we divide 210 by 3 and get 70 (=2 * 5 * 7); 3 has now been “removed”.

Notice that you can also produce `e` by multiplying any single factor such as `a` by the product of all the other factors (`b * c * d`).

The product of the other factors contributing to the accumulator (all factors except the private one for this credential) is called a witness.

This is a useful characteristic; it means you can tell someone else the value of `a` and the product of all the other inputs to the accumulator, but not the other inputs themselves, and they can produce the output.

## Background: Tails Files¶

In our simple example above, we only have 4 factors, and we are using small numbers. We are also using standard arithmetic, where you can reverse multiplication by dividing. In such a system, the contents of an accumulator can be reverse-engineered by simple prime factorization.

To be useful for revocation, Indy’s accumulators can’t be reversible; that is, it must be the case that the only way to derive the accumulator value is to know the factors. We accomplish this by using modular arithmetic (where division is undefined), and by using massive prime numbers for factors, resulting in a very long integer witness.

A tails file is associated with an accumulator and its factors. It is a binary file that contains an array of randomly generated factors for an accumulator. Instead of small numbers like 2 and 3 and 7, these factors are massive numbers, far too big to display conveniently on a screen. Typically the quantity of these numeric factors in a tails file is large–hundreds of thousands to tens of millions.

A tails file is not secret; it is published as plain text to the world and freely downloadable by anyone. The contents of this file never change.

Each potential or actual credential issued by a particular issuer is assigned an index to an accumulator factor in a tails file. However, only credentials that have not been revoked contribute to the value of the accumulator. We will see how this works, below.

## Setup¶

Before revocable credentials can be issued, a number of things must be true about the ecosystem:

1. A schema for each credential type must be written to the ledger. For example, if companies wish to issue proof of employment, then a “Employee Credential” schema would need to be published. Similarly, before birth certificate credentials can be issued, a “Birth Certificate” schema would need to be defined and made available to the public. Any number of issuers can reference the same schema. Schemas can be versioned and evolved over time. Any individual or institution can write a schema to the ledger; it does not require special privileges.
2. Each issuer must publish on the ledger one credential definition for each credential type they intend to create. The definition announces the issuer’s intention to create credentials that match a particular schema, and specifies the keys that the issuer will use to sign such credentials. (The verkey+ signing key pair used to authenticate the issuer’s DID should be kept separate from the keys used to sign credentials, so that each key pair can be rotated independently; it would be bad if a sysadmin rotated a DID keypair and accidentally invalidated all credentials issued by an institution…)
3. Each issuer must also publish on the ledger a revocation registry. This metadata references a credential definition and specifies how revocation for that credential type will be handled. The revocation registry tells which cryptographic accumulator can be used to test revocation, and gives the URI and hash of the associated tails file.
4. Each issuer must publish on the ledger an accumulator value that describes the revocation status for all associated credentials. This accumulator must be updated on a periodic or as-needed basis. For example, if a driver’s license division revokes 3 licenses during a given work day, then when they close their doors at 5 pm, they might issue a ledger transaction that updates the accumulator value for their driver’s license credentials, removing the 3 revoked credentials from the accumulator. What we mean by “removing” is as described above– the factors listed in the tails file for the indexes associated with the 3 revoked credentials are no longer multiplied into the accumulator.

## How Revocation Will Be Tested¶

Let us now skip ahead to think about what needs to happen much later. When a prover gives proof to a verifier, we normally think about the proof as focusing on core information demands: What is your birthdate? Please disclose your address. This is primary proof.

But there is another dimension of proof that’s also necessary: The prover must demonstrate that the credentials behind the primary proof have not been revoked. This is called proof of non-revocation.

In Indy, proof of non-revocation is accomplished by having provers show that they can derive the value of the accumulator for their credential using a factor for the accumulator that they know, plus the product of all other factors. The verifier can see that the prover produces the right answer (because the answer is on the ledger), but does not know certain details of how the prover derived it. The issuer can revoke by changing the answer to the math problem in a way that defeats the prover.

## Preparing for Revocation at Issuance¶

When a credential is issued, the actual credential file is transmitted to the holder (who will later become a prover). In addition, the issuer communicates two other pieces of vital information:

• The index corresponding to this credential, in the tails file. This lets the holder look up their private factor, which we could map to `a` in the simple equation from the accumulator background section at the top of the doc.
• The witness.

## Presenting Proof of Non-Revocation¶

When the prover needs to demonstrate that her credential is not revoked, she shows that she can provide math that derives the accumulator value on the ledger using her private factor times the witness. She does this without actually disclosing what her private value is; this is important to avoid correlation.

But there is a complication: what if the accumulator has changed value since the time the credential was issued? In this case, the private factor times the witness will not equal the accumulator…

This is handled by requiring accumulator updates to also publish a witness delta as part of the same transaction. This tells provers how to adjust their witness (referencing other indexes in the public tails file) to bring it back into harmony with the current value of the accumulator. Updating witnesses requires the prover (but not the verifier) to download the tails file.

## Putting It All Together¶

This discussion has suppressed some details. The math has been simplified, and we haven’t discussed how an issuer copes with multiple tails files and revocation registries, or why that might be desirable. However, the broad flow of the mechanism should be apparent, and its features are now easy to summarize:

• Issuers revoke by changing a number on the ledger. They can revoke as many credentials as they want in a single transaction, since they are just changing the answer to a math problem that either does or doesn’t include the factors they choose. Issuers do not have to contact anybody–provers or verifiers–to revoke. Changes take place globally, the instant the accumulator update transaction appears on the ledger.
• Revocation is reversible.
• Provers demonstrate proof of non-revocation in a privacy-preserving way. They cannot be correlated by something like a credential ID or a tails index. This is radically different from a revocation list approach, which requires correlation to test.
• Verification of proof of non-revocation is extremely easy and cheap. No tails files are needed by verifiers, and computation is trivial. Proving non-revocation is somewhat more expensive for provers, but is also not overly complex.
• Verifiers do not need to contact issuers or consult a revocation list to test revocation.