[docs] Add zk token proof program description (solana-labs#32011)

docs/sidebars.js

@@ -301,6 +301,11 @@ module.exports = {
           id: "developing/runtime-facilities/sysvars",
           label: "Sysvar Cluster Data",
         },
+        {
+          type: "doc",
+          label: "ZK Token Proof Program",
+          id: "developing/runtime-facilities/zk-token-proof",
+        }
       ],
     },
     {

docs/src/developing/runtime-facilities/zk-token-proof.md

@@ -0,0 +1,122 @@
+---
+title: ZK Token Proof Program
+---
+
+The native Solana ZK Token proof program verifies a number of zero-knowledge
+proofs that are tailored to work with Pedersen commitments and ElGamal
+encryption over the elliptic curve
+[curve25519](https://www.rfc-editor.org/rfc/rfc7748#section-4.1). The program
+was originally designed to verify the zero-knowledge proofs that are required
+for the [SPL Token 2022](https://spl.solana.com/token-2022) program. However,
+the zero-knowledge proofs in the proof program can be used in more general
+contexts outside of SPL Token 2022 as well.
+
+- Program id: `ZkTokenProof1111111111111111111111111111111`
+- Instructions:
+  [ProofInstruction](https://github.com/solana-labs/solana/blob/master/zk-token-sdk/src/zk_token_proof_instruction.rs)
+
+### Pedersen commitments and ElGamal encryption
+
+The ZK Token proof program verifies zero-knowledge proofs for Pedersen
+commitments and ElGamal encryption, which are common cryptographic primitives
+that are incorporated in many existing cryptographic protocols.
+
+ElGamal encryption is a popular instantiation of a public-key encryption scheme.
+An ElGamal keypair consists of an ElGamal public key and an ElGamal secret key.
+Messages can be encrypted under a public key to produce a ciphertext. A
+ciphertext can then be decrypted using a corresponding ElGamal secret key. The
+variant that is used in the proof program is the
+[twisted ElGamal encryption](https://eprint.iacr.org/2019/319) over the elliptic
+curve [curve25519](https://www.rfc-editor.org/rfc/rfc7748#section-4.1).
+
+The Pedersen commitment scheme is a popular instantiation of a cryptographic
+commitment scheme. A commitment scheme allows a user to wrap a message into a
+commitment with a purpose of revealing the committed message later on. Like a
+ciphertext, the resulting commitment does not reveal any information about the
+containing message. At the same time, the commitment is binding in that the user
+cannot change the original value that is contained in a commitment.
+
+Interested readers can refer to the following resources for a more in-depth
+treatment of Pedersen commitment and the (twisted) ElGamal encryption schemes.
+
+- [Notes](./zk-docs/twisted_elgamal.pdf) on the twisted ElGamal encryption
+- A technical
+  [overview](https://github.com/solana-labs/solana-program-library/blob/master/token/zk-token-protocol-paper/part1.pdf)
+  of the SPL Token 2022 confidential extension
+- Pretty Good Confidentiality [research paper](https://eprint.iacr.org/2019/319)
+
+The ZK Token proof program contains proof verification instructions on various
+zero-knowledge proofs for working with the Pedersen commitment and ElGamal
+encryption schemes. For example, the `VerifyRangeProofU64` instruction verifies
+a zero-knowledge proof certifying that a Pedersen commitment contains an
+unsigned 64-bit number as the message. The `VerifyPubkeyValidity` instruction
+verifies a zero-knowledge proof certifying that an ElGamal public key is a
+properly formed public key.
+
+### Context Data
+
+The proof data associated with each of the ZK Token proof instructions are
+logically divided into two parts:
+
+- The <em>context</em> component contains the data that a zero-knowledge proof
+  is certifying. For example, context component for a `VerifyRangeProofU64`
+  instruction data is the Pedersen commitment that holds an unsigned 64-bit
+  number. The context component for a `VerifyPubkeyValidity` instruction data is
+  the ElGamal public key that is properly formed.
+- The <em>proof</em> component contains the actual mathematical pieces that
+  certify different properties of the context data.
+
+The ZK Token proof program processes a proof instruction in two steps:
+
+1. Verify the zero-knowledge proof data associated with the proof instruction.
+2. If specified in the instruction, the program stores the context data in a
+   dedicated context state account.
+
+The simplest way to use a proof instruction is to execute it without producing a
+context state account. In this case, the proof instruction can be included as
+part of a larger Solana transaction that contains instructions of other Solana
+programs. Programs should directly access the context data from the proof
+instruction data and use it in its program logic.
+
+Alternatively, a proof instruction can be executed to produce a context state
+account. In this case, the context data associated with a proof instruction
+persists even after the transaction containing the proof instruction is finished
+with its execution. The creation of context state accounts can be useful in
+settings where ZK proofs are required from PDAs or when proof data is too large
+to fit inside a single transaction.
+
+## Proof Instructions
+
+The ZK Token proof program supports the following list of zero-knowledge proofs.
+
+#### Proofs on ElGamal encryption
+
+- `VerifyPubkeyValidity`:
+
+  - The ElGamal public-key validity proof instruction certifies that an ElGamal
+    public-key is a properly formed public key.
+  - Mathematical description and proof of security:
+    [[Notes]](./zk-docs/pubkey_proof.pdf)
+
+- `VerifyZeroBalance`:
+
+  - The zero-balance proof certifies that an ElGamal ciphertext encrypts the
+    number zero.
+  - Mathematical description and proof of security:
+    [[Notes]](./zk-docs/zero_proof.pdf)
+
+#### Equality proofs
+
+- `VerifyCiphertextCommitmentEquality`:
+
+  - The ciphertext-commitment equality proof certifies that an ElGamal
+    ciphertext and a Pedersen commitment encode the same message.
+  - Mathematical description and proof of security:
+    [[Notes]](./zk-docs/ciphertext_commitment_equality.pdf)
+
+- `VerifyCiphertextCiphertextEquality`:
+
+  - The ciphertext-ciphertext equality proof certifies that two ElGamal
+    ciphertexts encrypt the same message.
+  - Mathematical description and proof of security:
+    [[Notes]](./zk-docs/ciphertext_ciphertext_equality.pdf)