What is an Adaptor Signature and how does it enable "Scriptless Scripts"?

An Adaptor Signature is an incomplete "pre-signature" encrypted under a cryptographic statement (such as a discrete logarithm Y = y*G). It allows a party to prove that revealing a valid signature on a message will reveal the secret witness y, and vice versa. Because the final signature published on the blockchain is a completely standard Schnorr or ECDSA signature indistinguishable from normal single-key payments, smart contract logic (like atomic swaps and payment channels) executes with zero on-chain scripts, achieving maximum privacy, minimal transaction fees, and cross-chain interoperability.

How does discrete log witness extraction work mathematically in Schnorr adaptors?

Let signer have private key x and public key P = x*G. The statement is Y = y*G. The signer generates an adaptor pre-signature s_tilde = k + e*x mod q where e = H(P, R + Y, m). The receiver verifies that s_tilde*G = R + e*P. When the signer later completes and publishes the valid signature s = s_tilde + y mod q to claim funds on-chain, the receiver simply computes y = s - s_tilde mod q, instantly obtaining the private witness y needed to unlock funds on the counterpart blockchain.

Why are Adaptor Signatures superior to Hash Time-Locked Contracts (HTLCs) in Lightning networks?

HTLCs require publishing a cryptographic preimage hash H(R) on-chain and sharing that identical hash across every hop in a multi-hop Lightning payment route. This allows intermediate nodes to correlate the sender and receiver. Point Time-Locked Contracts (PTLCs) based on Adaptor Signatures use randomized point re-blinding at each hop, making payment hops cryptographically uncorrelated and completely preventing route tracking.

Can Adaptor Signatures be implemented with ECDSA as well as Schnorr?

Yes. While Schnorr adaptors (used in Bitcoin Taproot, BIP 340) have linear equations that make adaptor signatures mathematically elegant, ECDSA adaptor protocols (developed by Lindell, Fournier, and Komlo) also exist. They require additional zero-knowledge proofs (such as Paillier encryption proofs or Class Group proofs) to handle ECDSA's non-linear inversion k^(-1), but achieve the exact same scriptless atomic swap guarantees on legacy ECDSA blockchains like Ethereum and Bitcoin SegWit.

Schnorr Adaptor Signatures Studio | Scriptless Scripts & Atomic Swaps

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Scriptless Scripts Architecture BIP 340 Schnorr Compatible

Schnorr Adaptor Signatures Studio

Simulate off-chain adaptor pre-signatures and atomic cross-chain settlements. Step through statement generation, adaptor verification, on-chain signature release, and automatic discrete log witness extraction.

1. Cryptographic Setup & Witness Statement

            Elliptic Curve Group: secp256k1 (q = prime order, G = base generator)
          

Alice Private Key (x): Atomic Swap Secret Witness (y ∈ ℤ_q): Transaction Message (m):

2. Adaptor Pre-Signature State

Adaptor Point R_hat (R + Y)

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Pre-Signature Scalar s_tilde

-

On-Chain Signature s

-

Bob Extracted Witness y

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3. Step 4: Bob Witness Extraction

Once Alice broadcasts the valid on-chain Schnorr signature (s), Bob subtracts his known pre-signature scalar: y = s - s_tilde (mod q).

AWAITING ON-CHAIN SIGNATURE

Complete Steps 1-3 to unlock witness extraction

4. Protocol Execution Trace Log

            Click "Step 1: Alice Generates Adaptor Pre-Signature" to begin protocol run...
          

5. Atomic Swap & Payment Channel Mechanisms Compared

Mechanism	On-Chain Footprint	Privacy & Fungibility	Cross-Route Unlinkability	Smart Contract VM Required?
Schnorr Adaptor Signatures	Standard 64-byte signature	100% Indistinguishable from simple transfer	Complete (Random point blinding)	No (Scriptless Scripts)
Hash Time-Locked Contracts (HTLCs)	Exposes SHA256 preimage script	Identical hash public on both chains	Zero (Vulnerable to route tracking)	Requires OP_SHA256 & OP_CHECKLOCKTIMEVERIFY
Cross-Chain Bridges (Lock/Mint)	Large multi-sig contract calls	Custodian addresses visible	Vulnerable to central censorship	Heavy Solidity / EVM contracts

Schnorr Adaptor Signatures Studio

1. Cryptographic Setup & Witness Statement

2. Adaptor Pre-Signature State

3. Step 4: Bob Witness Extraction

4. Protocol Execution Trace Log

5. Atomic Swap & Payment Channel Mechanisms Compared

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