Multi-party Signatures/Group Signatures/Threshold Signatures in Blockchain (2024)

Multi-party signatures are a type of digital signature scheme where multiple parties jointly sign a message. The signature is valid only if a sufficient number of parties participate in the signing process. Multi-party signatures are useful in situations where multiple parties need to sign a message, but it is not practical or desirable for all parties to be present and participate in the signing process. Threshold signatures are a common approach to multi-party signatures. In threshold signatures, each signing party generates a share of a secret key, and the signature is computed by combining a sufficient number of these shares. The number of shares required to generate a valid signature is determined by a threshold parameter, which can be set to any value less than the total number of parties. Threshold signatures provide increased security compared to traditional digital signatures, as an attacker would need to compromise multiple parties in order to forge a signature. Threshold signatures can also be used to provide additional privacy, as the identity of the signing parties can be kept anonymous. Multi-party signatures have important applications in fields such as distributed systems, blockchain technology, and secure multiparty computation.

Table 1 below provides comparison of four famous threshold signature schemes based on properties like Key generation, Signing, Signature Aggregation and Blockchains where that scheme is implemented-

Shamir’s Secret Sharing

Shamir's Secret Sharing is a cryptographic algorithm used to split a secret into multiple parts, called shares, which can be distributed among different parties. The algorithm was developed by Adi Shamir, an Israeli cryptographer, in 1979.

The basic idea behind Shamir's Secret Sharing is that a secret can be divided into n shares in such a way that any k of the shares (where k is less than or equal to n) can be combined to reconstruct the secret, but fewer than k shares reveal no information about the secret. This is known as a (k, n) threshold scheme. The following flowcharts explain Shamir's Secret Sharing with an example.

As mentioned in the above table, Cardano uses a modified version of Shamir's secret sharing scheme to secure its network in the following manner-

• The original secret is hashed using a cryptographic hash function to produce a random value, which is used as the seed to generate a sequence of public-private key pairs.
• Each private key is then used to generate a transaction output that is publicly recorded on the blockchain.
• These transaction outputs are randomly distributed among a set of participants, who each hold a single output.
• To recover the original secret, a threshold number of participants must come together to reveal their transaction outputs and re-derive the private keys using the seed value.
• This method provides a high level of security, as an attacker would need to compromise a threshold number of participants to recover the original secret.
• This modified scheme is used to secure Cardano's network by ensuring that the private keys necessary to perform critical operations, such as confirming transactions and minting new coins, are securely distributed and protected from attack.

In the next article, we will talk about BLS Signatures.