Threshold Signatures (TSS) are a cryptographic method that enhances the security of private keys by splitting them among multiple participants. Instead of storing the entire private key in one place, TSS divides it into shares held by n participants. To produce a valid digital signature, at least t of those participants (the threshold) must collaborate. Fewer than t shares cannot reconstruct the key or generate a signature.
Basics of Public-Key Cryptography
-
Public Key (PK) is used to verify signatures, and Private Key (SK) is used to create them.
-
In a traditional wallet, the entire SK is stored in one location (e.g., a hardware wallet or software wallet), which becomes a single point of failure if breached.
How TSS Works
-
Key Generation via MPC
-
Rather than generating a single SK, participants run a Multi-Party Computation (MPC) protocol.
-
Each of the n participants receives a secret share of the SK. No single share reveals the full key.
-
The combined shares implicitly define the public key (PK), which is publicly known for verification purposes.
-
-
Signature Creation
-
To sign a message or transaction, at least t participants engage in an interactive MPC protocol.
-
They use their individual shares to collaboratively compute a single signature.
-
The output is one standard digital signature, compatible with ECDSA or Schnorr verification.
-
-
Signature Verification
-
Any verifier uses PK and the produced signature to confirm authenticity.
-
Verification is identical to traditional schemes:
Verify(PK, message, signature) → valid/invalid.
-
Role of MPC
Multi-Party Computation is a subfield of cryptography where multiple parties jointly compute a function without revealing their inputs. In TSS:
-
Privacy: Each participant’s share remains secret.
-
Security: SK never exists in a single location.
-
Threshold: Only when t shares cooperate does the protocol output a valid signature.
Main Advantages of TSS
-
Enhanced Security: An attacker must compromise at least t out of n shares to forge a signature or reconstruct SK.
-
No Single Point of Failure: Even if up to n–t participants go offline or are compromised, the remaining t can still sign transactions.
-
Share Privacy: Individual shares never reveal any information about SK.
-
Single Signature Output: Only one compact signature is produced per transaction, avoiding the overhead of combining multiple independent signatures.
Alternatives to TSS
-
Multi-Signature (Multi-Sig): Requires multiple independent signatures on-chain. The number of required signers is visible publicly, and every signer must broadcast their partial signature, increasing on-chain footprint.
-
Shamir Secret Sharing Scheme (SSSS): A dealer splits SK into shares. To sign, shares are recombined off-chain to reconstruct SK, which briefly exists in full—introducing a single point of failure during reconstruction.
Summary
Threshold Signatures combine the security of distributed key storage with the efficiency of a single digital signature. By using MPC, SK stays split among n participants, and only any t of them can create a valid signature. This reduces single-point risks and keeps shares private. TSS is increasingly used in institutional wallets, multisig replacements, and other high-security environments to protect digital assets on blockchain networks.
