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Crypto

Updated: 2023/2/27 bybjartekbjartek
12 min read

Hashing

The built-in enum HashAlgorithm provides the set of hashing algorithms that are supported by the language natively.

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pub enum HashAlgorithm: UInt8 {
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    /// SHA2_256 is SHA-2 with a 256-bit digest (also referred to as SHA256).
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    pub case SHA2_256 = 1
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    /// SHA2_384 is SHA-2 with a 384-bit digest (also referred to as  SHA384).
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    pub case SHA2_384 = 2
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    /// SHA3_256 is SHA-3 with a 256-bit digest.
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    pub case SHA3_256 = 3
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    /// SHA3_384 is SHA-3 with a 384-bit digest.
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    pub case SHA3_384 = 4
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    /// KMAC128_BLS_BLS12_381 is an instance of KECCAK Message Authentication Code (KMAC128) mac algorithm.
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    /// Although this is a MAC algorithm, KMAC is included in this list as it can be used hash 
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    /// when the key is used a non-public customizer.
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    /// KMAC128_BLS_BLS12_381 is used in particular as the hashing algorithm for the BLS signature scheme on the curve BLS12-381.
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    /// It is a customized version of KMAC128 that is compatible with the hashing to curve
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    /// used in BLS signatures. 
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    /// It is the same hasher used by signatures in the internal Flow protocol. 
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    pub case KMAC128_BLS_BLS12_381 = 5
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    /// KECCAK_256 is the legacy Keccak algorithm with a 256-bits digest, as per the original submission to the NIST SHA3 competition.
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    /// KECCAK_256 is different than SHA3 and is used by Ethereum.  
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    pub case KECCAK_256 = 6
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    /// Returns the hash of the given data
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    pub fun hash(_ data: [UInt8]): [UInt8]
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    /// Returns the hash of the given data and tag
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    pub fun hashWithTag(_ data: [UInt8], tag: string): [UInt8]
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}

The hash algorithms provide two ways to hash input data into digests, hash and hashWithTag.

Hashing

hash hashes the input data using the chosen hashing algorithm. KMAC is the only MAC algorithm on the list and configured with specific parameters (detailed in KMAC128 for BLS)

For example, to compute a SHA3-256 digest:

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let data: [UInt8] = [1, 2, 3]
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let digest = HashAlgorithm.SHA3_256.hash(data)

Hashing with a domain tag

hashWithTag hashes the input data along with an input tag. It allows instanciating independent hashing functions customized with a domain separation tag (DST). For most of the hashing algorithms, mixing the data with the tag is done by pre-fixing the data with the tag and hashing the result.

  • SHA2_256, SHA2_384, SHA3_256, SHA3_384, KECCAK_256: If the tag is non-empty, the hashed message is bytes(tag) || data where bytes() is the UTF-8 encoding of the input string, padded with zeros till 32 bytes. Therefore tags must not exceed 32 bytes. If the tag used is empty, no data prefix is applied, and the hashed message is simply data (same as hash output).
  • KMAC128_BLS_BLS12_381: refer to KMAC128 for BLS for details.

KMAC128 for BLS

KMAC128_BLS_BLS12_381 is an instance of the cSHAKE-based KMAC128. Although this is a MAC algorithm, KMAC can be used as a hash when the key is used as a non-private customizer. KMAC128_BLS_BLS12_381 is used in particular as the hashing algorithm for the BLS signature scheme on the curve BLS12-381. It is a customized instance of KMAC128 and is compatible with the hashing to curve used by BLS signatures. It is the same hasher used by the internal Flow protocol, and can be used to verify Flow protocol signatures on-chain.

To define the MAC instance, KMAC128(customizer, key, data, length) is instanciated with the following parameters (as referred to by the NIST SHA-3 Derived Functions):

  • customizer is the UTF-8 encoding of "H2C".
  • key is the UTF-8 encoding of "FLOW--V00-CS00-with-BLS_SIG_BLS12381G1_XOF:KMAC128_SSWU_RO_POP_" when hash is used. It includes the input tag when hashWithTag is used and key becomes the UTF-8 encoding of "FLOW-" || tag || "-V00-CS00-with-BLS_SIG_BLS12381G1_XOF:KMAC128_SSWU_RO_POP_".
  • data is the input data to hash.
  • length is 1024 bytes.

Signing Algorithms

The built-in enum SignatureAlgorithm provides the set of signing algorithms that are supported by the language natively.

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pub enum SignatureAlgorithm: UInt8 {
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    /// ECDSA_P256 is ECDSA on the NIST P-256 curve.
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    pub case ECDSA_P256 = 1
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    /// ECDSA_secp256k1 is ECDSA on the secp256k1 curve.
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    pub case ECDSA_secp256k1 = 2
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    /// BLS_BLS12_381 is BLS signature scheme on the BLS12-381 curve.
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    /// The scheme is set-up so that signatures are in G_1 (subgroup of the curve over the prime field)
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    /// while public keys are in G_2 (subgroup of the curve over the prime field extension).
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    pub case BLS_BLS12_381 = 3
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}

PublicKey

PublicKey is a built-in structure that represents a cryptographic public key of a signature scheme.

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struct PublicKey {
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    let publicKey: [UInt8]
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    let signatureAlgorithm: SignatureAlgorithm
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    /// Verifies a signature under the given tag, data and public key.
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    /// It uses the given hash algorithm to hash the tag and data.
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    pub fun verify(
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        signature: [UInt8],
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        signedData: [UInt8],
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        domainSeparationTag: String,
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        hashAlgorithm: HashAlgorithm
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    ): Bool
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    /// Verifies the proof of possession of the private key.
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    /// This function is only implemented if the signature algorithm
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    /// of the public key is BLS (BLS_BLS12_381).
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    /// If called with any other signature algorithm, the program aborts
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    pub fun verifyPoP(_ proof: [UInt8]): Bool
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}

PublicKey supports two methods verify and verifyPoP. verifyPoP will be covered under BLS multi-signature.

Public Key construction

A PublicKey can be constructed using the raw key and the signing algorithm.

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let publicKey = PublicKey(
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    publicKey: "010203".decodeHex(),
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    signatureAlgorithm: SignatureAlgorithm.ECDSA_P256
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)

The raw key value depends on the supported signature scheme:

  • ECDSA_P256 and ECDSA_secp256k1: The public key is an uncompressed curve point (X,Y) where X and Y are two prime field elements. The raw key is represented as bytes(X) || bytes(Y), where || is the concatenation operation, and bytes() is the bytes big-endian encoding left padded by zeros to the byte-length of the field prime. The raw public key is 64-bytes long.

  • BLS_BLS_12_381: The public key is a G_2 (curve over the prime field extension) element. The encoding follows the compressed serialization defined in the IETF draft-irtf-cfrg-pairing-friendly-curves-08. A public key is 96-bytes long.

Public Key validation

A public key is validated at the time of creation. Only valid public keys can be created. The validation of the public key depends on the supported signature scheme:

  • ECDSA_P256 and ECDSA_secp256k1: The given X and Y coordinates are correctly serialized, represent valid prime field elements, and the resulting point is on the correct curve (no subgroup check needed since the cofactor of both supported curves is 1).

  • BLS_BLS_12_381: The given key is correctly serialized following the compressed serialization in IETF draft-irtf-cfrg-pairing-friendly-curves-08. The coordinates represent valid prime field extension elemnents. The resulting point is on the curve, and is on the correct subgroup G_2.

Since the validation happen only at the time of creation, public keys are immutable.

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publicKey.signatureAlgorithm = SignatureAlgorithm.ECDSA_secp256k1   // Not allowed
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publicKey.publicKey = []                                            // Not allowed
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publicKey.publicKey[2] = 4      // No effect

Invalid public keys cannot be constructed so public keys are always valid.

Signature verification

A signature can be verified using the verify function of the PublicKey:

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let pk = PublicKey(
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    publicKey: "96142CE0C5ECD869DC88C8960E286AF1CE1B29F329BA4964213934731E65A1DE480FD43EF123B9633F0A90434C6ACE0A98BB9A999231DB3F477F9D3623A6A4ED".decodeHex(),
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    signatureAlgorithm: SignatureAlgorithm.ECDSA_P256
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)
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let signature = "108EF718F153CFDC516D8040ABF2C8CC7AECF37C6F6EF357C31DFE1F7AC79C9D0145D1A2F08A48F1A2489A84C725D6A7AB3E842D9DC5F8FE8E659FFF5982310D".decodeHex()
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let message : [UInt8] = [1, 2, 3]
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let isValid = pk.verify(
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    signature: signature,
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    signedData: message,
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    domainSeparationTag: "",
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    hashAlgorithm: HashAlgorithm.SHA2_256
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)
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// `isValid` is false

The inputs to verify depend on the signature scheme used:

  • ECDSA (ECDSA_P256 and ECDSA_secp256k1):
    • signature expects the couple (r,s). It is serialized as bytes(r) || bytes(s), where || is the concatenation operation, and bytes() is the bytes big-endian encoding left padded by zeros to the byte-length of the curve order. The signature is 64 bytes-long for both curves.
    • signedData is the arbitrary message to verify the signature against.
    • domainSeparationTag is the expected domain tag. Multiple valid tag values can be used (check hashWithTag for more details).
    • hashAlgorithm is either SHA2_256, SHA3_256 or KECCAK_256. It is the algorithm used to hash the message along with the given tag (check the hashWithTagfunction for more details).

As noted in hashWithTag for SHA2_256, SHA3_256 and KECCAK_256, using an empty tag results in hashing the input data only. If a signature verification needs to be done against data without any domain tag, this can be done by using an empty domain tag "".

ECDSA verification is implemented as defined in ANS X9.62 (also referred by FIPS 186-4 and SEC 1, Version 2.0). A valid signature would be generated using the expected signedData, domainSeparationTag and hashAlgorithm used to verify.

  • BLS (BLS_BLS_12_381):
    • signature expects a G_1 (subgroup of the curve over the prime field) point. The encoding follows the compressed serialization defined in the IETF draft-irtf-cfrg-pairing-friendly-curves-08. A signature is 48-bytes long.
    • signedData is the arbitrary message to verify the signature against.
    • domainSeparationTag is the expected domain tag. All tags are accepted (check KMAC128 for BLS).
    • hashAlgorithm only accepts KMAC128_BLS_BLS12_381. It is the algorithm used to hash the message along with the given tag (check KMAC128 for BLS).

BLS verification performs the necessary membership check of the signature while the membership check of the public key is performed at the creation of the PublicKey object and not repeated during the signature verification.

The verificaction uses a hash-to-curve algorithm to hash the signedData into a G_1 point, following the hash_to_curve method described in the draft-irtf-cfrg-hash-to-curve-14. While KMAC128 is used as a hash-to-field method resulting in two field elements, the mapping to curve is implemented using the simplified SWU.

A valid signature would be generated using the expected signedData and domainSeparationTag, as well the same hashing to curve process.

BLS multi-signature

BLS signature scheme allows efficient multi-signature features. Multiple signatures can be aggregated into a single signature which can be verified against an aggregated public key. This allows authenticating multiple signers with a single signature verification. While BLS provides multiple aggregation techniques, Cadence supports basic aggregation tools that cover a wide list of use-cases. These tools are defined in the built-in BLS contract, which does not need to be imported.

Proof of Possession (PoP)

Multi-signature verification in BLS requires a defense against rogue public-key attacks. Multiple ways are available to protect BLS verification. The language provides the proof of possession of private key as a defense tool. The proof of possession of private key is a BLS signature over the public key itself. The PoP signature follows the same requirements of a BLS signature (detailed in Signature verification), except it uses a special domain separation tag. The key expected to be used in KMAC128 is the UTF-8 encoding of "BLS_POP_BLS12381G1_XOF:KMAC128_SSWU_RO_POP_". The expected message to be signed by the PoP is the serialization of the BLS public key corresponding to the signing private key (serialization details). The PoP can only be verified using the PublicKey method verifyPoP.

BLS signature aggregation

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fun aggregateSignatures(_ signatures: [[UInt8]]): [UInt8]?

Aggregates multiple BLS signatures into one. Signatures could be generated from the same or distinct messages, they could also be the aggregation of other signatures. The order of the signatures in the slice does not matter since the aggregation is commutative. There is no subgroup membership check performed on the input signatures. If the array is empty or if decoding one of the signature fails, the program aborts

The output signature can be verified against an aggregated public key to authenticate multiple signers at once. Since the verify method accepts a single data to verify against, it is only possible to verfiy multiple signatures of the same message.

BLS public key aggregation

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fun aggregatePublicKeys(_ publicKeys: [PublicKey]): PublicKey?

Aggregates multiple BLS public keys into one.

The order of the public keys in the slice does not matter since the aggregation is commutative. The input keys are guaranteed to be in the correct subgroup since subgroup membership is checked at the key creation time. If the array is empty or any of the input keys is not a BLS key, the program aborts

The output public key can be used to verify aggregated signatures to authenticate multiple signers at once. Since the verify method accepts a single data to verify against, it is only possible to verfiy multiple signatures of the same message.

Crypto Contract

The built-in contract Crypto can be used to perform cryptographic operations. The contract can be imported using import Crypto.

Key Lists

The crypto contract also allows creating key lists to be used for multi-signature verification. For example, to verify two signatures with equal weights for some signed data:

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import Crypto
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pub fun test main() {
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    let keyList = Crypto.KeyList()
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    let publicKeyA = PublicKey(
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        publicKey:
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            "db04940e18ec414664ccfd31d5d2d4ece3985acb8cb17a2025b2f1673427267968e52e2bbf3599059649d4b2cce98fdb8a3048e68abf5abe3e710129e90696ca".decodeHex(),
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        signatureAlgorithm: SignatureAlgorithm.ECDSA_P256
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    )
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    keyList.add(
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        publicKeyA,
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        hashAlgorithm: HashAlgorithm.SHA3_256,
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        weight: 0.5
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    )
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    let publicKeyB = PublicKey(
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        publicKey:
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            "df9609ee588dd4a6f7789df8d56f03f545d4516f0c99b200d73b9a3afafc14de5d21a4fc7a2a2015719dc95c9e756cfa44f2a445151aaf42479e7120d83df956".decodeHex(),
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        signatureAlgorithm: SignatureAlgorithm.ECDSA_P256
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    )
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    keyList.add(
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        publicKeyB,
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        hashAlgorithm: HashAlgorithm.SHA3_256,
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        weight: 0.5
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    )
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    let signatureSet = [
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        Crypto.KeyListSignature(
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            keyIndex: 0,
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            signature:
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                "8870a8cbe6f44932ba59e0d15a706214cc4ad2538deb12c0cf718d86f32c47765462a92ce2da15d4a29eb4e2b6fa05d08c7db5d5b2a2cd8c2cb98ded73da31f6".decodeHex()
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        ),
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        Crypto.KeyListSignature(
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            keyIndex: 1,
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            signature:
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                "bbdc5591c3f937a730d4f6c0a6fde61a0a6ceaa531ccb367c3559335ab9734f4f2b9da8adbe371f1f7da913b5a3fdd96a871e04f078928ca89a83d841c72fadf".decodeHex()
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        )
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    ]
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    // "foo", encoded as UTF-8, in hex representation
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    let signedData = "666f6f".decodeHex()
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    let isValid = keyList.verify(
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        signatureSet: signatureSet,
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        signedData: signedData
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    )
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}

The API of the Crypto contract related to key lists is:

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pub struct KeyListEntry {
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    pub let keyIndex: Int
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    pub let publicKey: PublicKey
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    pub let hashAlgorithm: HashAlgorithm
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    pub let weight: UFix64
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    pub let isRevoked: Bool
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    init(
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        keyIndex: Int,
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        publicKey: PublicKey,
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        hashAlgorithm: HashAlgorithm,
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        weight: UFix64,
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        isRevoked: Bool
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    )
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}
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pub struct KeyList {
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    init()
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    /// Adds a new key with the given weight
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    pub fun add(
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        _ publicKey: PublicKey,
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        hashAlgorithm: HashAlgorithm,
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        weight: UFix64
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    )
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    /// Returns the key at the given index, if it exists.
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    /// Revoked keys are always returned, but they have `isRevoked` field set to true
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    pub fun get(keyIndex: Int): KeyListEntry?
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    /// Marks the key at the given index revoked, but does not delete it
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    pub fun revoke(keyIndex: Int)
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    /// Returns true if the given signatures are valid for the given signed data
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    pub fun verify(
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        signatureSet: [KeyListSignature],
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        signedData: [UInt8]
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    ): Bool
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}
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pub struct KeyListSignature {
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    pub let keyIndex: Int
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    pub let signature: [UInt8]
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    pub init(keyIndex: Int, signature: [UInt8])
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}
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