Threshold Signature

In this chapter, we give an overview of threshold signatures and describe the threshold ECDSA construction of Canetti et al in [CGGMP21] and the FROST threshold signature scheme in [KG20], which is a threshold version of Schnorr signature scheme, including its EdDSA (or ed25519) instatiation. The chapter is separated into \(5\) major parts below:

  • First, we give a brief introduction to threshold signatures and state its syntax and security properties in Introduction.

  • Second, we state the syntax and security properties of threshold signatures in Definition and Security.

  • Third, we describe the threshold ECDSA construction of [CGGMP21] in Canetti's Construction to support the threshold ECDSA version for the curve secp256k1.

  • Fourth, we describe the FROST threshold signature construction of [KG20] in FROST Construction to support the threshold signature version of ed25519 and sr25519.

  • Finally, we briefly specify our instatiation and analyse the security for the threshold ECDSA construction of Canetti et al using secp256k1 parameters and FROST threshold signature construction using ed25519 and sr25519 parameters as follows:

    • In Threhold signature for secp256k1, we discuss and analyse the security of the threshold ECDSA signature of Canneti et al. when instatiated using the parameters of secp256k1.

    • In Threhold signature for ed25519 we discuss and analyse the security of the FROST threshold signature when instatiated using the parameters of ed25519.

    • In Threhold signature for sr25519 we discuss and analyse the security of the FROST threshold signature when instatiated using the parameters of sr25519.