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Cryptography

Primitives

Cardano uses asymmetric key and certification primitives to secure the interactions between network participants:

img_3.png
Source: https://docs.cardano.org/core-concepts/cardano-keys

Asymmetric Keys

Asymmetric keys are used by nodes and addresses:

  • Node Keys:
    • Stake pool key pair (cold): used to create operational certificates for each KES period, granting stake rights
    • Key Evolving Signature (KES) key pair (hot): key used to authenticate node and for signing blocks, which expires periodically (90 days)
    • VRF key pair: signing verification key, used to verify a slot leader and stored within operational certificate
  • Address Keys:
    • Payment key pair: used for generating UTXO addresses
    • Staking key pair: generating stake account/reward addresses

Certifications

Cardano uses certifications in two places:

  • Operational certificates:
    • Used by staking pools, generated offline before being copied to node to validate KES keys used to sign blocks
    • link between offline key and operational key, which verifies stake pool has authority to run
    • include an issue counter number, higher number replaces existing if compromised
    • included in header of each block node generates
  • Delegation certificates:
    • Staking address registration certificate: creates a staking address by a user looking to delegate block-signing rights to a stake pool
    • Delegation certificate: details stake being delegated to a particular stake pool

Exotic Primitives

Additive Homomorphic Encryption

Post-Voting: enables generation of the seed for the next round, which can be decrypted by t of n committee members. An implementation can be found here.

Non-Interactive Zero Knowledge (NIZK's)

Voting and Post-Voting: the world's first honest ZK verifier, which is used to tally votes.

Pederson Commitments

Voting: used to anonymize votes for a proposal.

Sealed Glass Proofs

Sealed Glass Proofs are proposed in the Cardano Computation Layer, which are a form of zero knowledge proof on a secure enclave.1

Verifiable Random Functions

Cardano uses the ECVRF-ED25519-SHA512-Elligator2* verifiable random function via the verifyVrf function, during block production:

  • Used by Ouroboros Praos consensus mechanism for private slot leader selection. Leader selection was public in previous versions of the protocol, so anyone could determine which node had the right to produce a block.
  • Using VRFs keeps the slot leader schedule private until a leader is selected. The slot leader can then prove to everyone that they are using the VRF key and produce a block.

Digital Signatures

The chain currently only supports EdDSA and Curve25519 for signing and verification (with added support for HD wallets), but ECDSA SECP256k1 and Schnorr Ed25519 are due imminently for improved interoperability2.

Other signatures maybe added through soft forks (in particular BLISS-B for anti-quantum).

Key evolving signatures (KES)

Key evolving signatures (KES) according to the MMM scheme. These type of signature schemes provide forward cryptographic security, meaning that a compromised key does not make it easier for an adversary to forge a signature that allegedly had been signed in the past. In KES, the public verification key stays constant, but the corresponding private key evolves incrementally.

For this reason, KES signing keys are indexed by integers representing the step in the key’s evolution. This evolution step parameter is also an additional parameter needed for the signing (denoted by sign ev) and verification (denoted by verify ev) functions. Since the private key evolves incrementally in a KES scheme, the ledger rules require the pool operators to evolve their keys every time a certain number of slots have passed, as determined by the global constant SlotsPerKESPeriod.

Multi-Signatures

Cardano allows multi-signatures via multi-signature scripts. The terms form a tree like structure and are evaluated via the evalMultiSigScript function. The parameters are a script and a set of key hashes. The function returns True when the supplied key hashes are a valid combination for the script, otherwise it returns False.

Hashing

The hashing algorithm for all verification keys and multi-signature scripts is BLAKE2b-224 (64 bit). Explicitly, this is the payment and stake credentials, the genesis keys and their delegates, stake pool verification keys, and VRF verification keys.

BLAKE2b-256 (also 64bit) is used everywhere else (e.g. block headers, block bodies, block transactions, epochs, transaction and pool metadata).

Hash-Based Data Structures

Cardano uses an Extended UTXO3 model and due to its stateless nature (in comparison to the account-based model), no explicit descriptions of the usage of hash-based data structures were found in the literature. Further research into the underlying codebase did indeed show the current usage of merkle trees in UTXO transaction proofs and the block body hash4. More widespread use of merkle trees is planned in the upcoming Hydra implementation of the protocol (instead of Merkle Patricia Tries which were deemed to be too expensive to use on-chain).

Pros/Cons

Pros

  1. Usage of additive homomorphic encryption to encrypt the random seed for voting. This enables the seed to be decrypted with only a threshold of signers.
  2. Usage of NIZKs to hide the vote from each voter

Cons

  1. The dependence on Sealed Glass Proofs to power the CCL increases the barrier of entry for regular validators who don't have machines with secure enclaves.
  2. Computational overhead due to the use of so many exotic cryptographic primitives.

Commonly used primitives in Governance

  • Digital signatures
    • [Pre-Voting] Signing keys are freshly generated to vote for each proposal
  • One way hash functions
    • [Pre-Voting] To generate the voter ID, and expert ID, which are hashes of the signing key generated for each proposal
  • Public-key cryptography
    • [All-stages] Are used to sign transactions that are broadcasted onto the network
  • Commitment scheme
    • [Pre-Voting] The seed which is used to select a random group of committee members to tally and execute votes is committed in the previous voting round, and revealed at the start of the new voting round

Footnotes

Footnotes

  1. Sealed Glass Proofs - https://eprint.iacr.org/2016/635.pdf ↩

  2. https://iohk.io/en/blog/posts/2022/07/08/bridges-and-sidechains-wanchain-making-cardano-interoperable/ ↩

  3. https://docs.cardano.org/plutus/eutxo-explainer ↩

  4. https://github.com/input-output-hk/cardano-ledger/blob/ac51494e151af0ad99b937a787458ce71db0aaea/eras/byron/ledger/impl/src/Cardano/Chain/UTxO/TxProof.hs and https://github.com/input-output-hk/cardano-ledger/blob/28632ee614b76ae189f140889f4722c35a81bb5e/libs/cardano-ledger-core/src/Cardano/Ledger/Era.hs ↩