Then, he combines the previously recorded identity signatures of the signers and aggregates it to the signature he has already created. The generated signature can be verified with public keys and identities of the signers.
Later, when she wants to sign a message, she signs it with her private key and add the identity signature she has recorded. She sends it to the combiner. The combiner aggregates the signatures he receives.
3. ASMwCA:
Each potential signer in the organization signs the others' public identities individually with their private key and sends them to the combiner. She stores her own identity signature.
Multi-signature is produced by aggregating the signatures of all signers by the combiner. The generated signature can be verified with public keys of the signers and signers' public identities.
Later, when she wants to sign a message, she creates a subgroup membership key by combining the identity signatures she has already generated and stored for everyone who signs with her, and adds this subgroup membership key to the signature she has created.
2. ASMwSA:
Each potential signer in the organization generates and stores signatures on the public identity of each potential signer by signing them one by one with her private key.
A signature with this membership key(s) can only be verified with the group commitment set and the public identity of the signer(s). This public identity requirement naturally brings accountability to the signature scheme.
Each user creates her own unique membership key by summing the shares that she receives, and aggregates the commitment sets she receives into the group commitment set.
1. vASM:
Each potential signer in an organization shares her private key with all users in the group, including herself, through a verifiable secret sharing scheme (VSS). In addition to this share, she sends a commitment set for its consistency.
We have proposed 3 novel pairing-based Accountable Subgroup Multi-signature (ASM) Schemes:
1. vASM
2. ASMwSA
3. ASMwCA
in a joint work with @oguzyayla.
The definitions of the schemes can be found here: https://t.co/NEf8MIrP1a
#Cryptography#Multisignature#Accountability