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# Smart Signature Update 2025

> "Today’s simplistic signatures are just the start; they can be improved, to create more powerful and more complex signatures that can truly be better and smarter." -- Christopher Allen, 2016

Here’s the streamlined revision, reducing repetition in the **Introduction** while maintaining the key points:

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# Smart Signature Update 2025

> "Today’s simplistic signatures are just the start; they can be improved, to create more powerful and more complex signatures that can truly be better and smarter." — Christopher Allen, 2016

Digital signatures have been a cornerstone of online security, providing identity verification for activities like signing documents or approving transactions. However, traditional signatures are limited to verifying authenticity. Over the past decade, smart signatures have evolved to overcome these limitations by embedding programmable rules, conditions, and approvals into the signing process. These advancements enhance security for online transactions, streamline business operations, improve privacy, and support the foundation of blockchain-based systems.

In recent years, emerging **cryptographic smart signatures** are reaching a new level of maturity. Leveraging advanced techniques available with Schnorr signatures, including multi-party computation, adaptor signatures, and more, these systems encode complex conditions directly into cryptographic processes. As an alternative to computational scripts, they offer greater security and privacy while addressing complex authorization requirements.

This update explores how cryptographic smart signatures can transforming trust in the digital world through enhanced efficiency, security, and privacy.

## What is a Smart Signature?

A **smart signature** enhances traditional digital signatures by incorporating programmable logic, conditional checks, and predicates. Early concepts focused on using logical statements within constrained scripting languages to enforce specific rules, such as multiple signatures, co-signing, time-locked approvals, or conditional execution. This approach allowed smart signatures to automate workflows, enable trustless transactions, and meet the demands of decentralized systems.

The emergence of new **cryptographic smart signatures** takes this concept further. By embedding logic directly into cryptographic operations, such as through Schnorr-based aggregation or adaptor signatures, they eliminate reliance on external scripts or computational logic. Instead, cryptographic smart signatures use unforgeable mathematical guarantees to ensure that conditions like multisig thresholds or other constraints are met securely and efficiently.

These innovations enable smart signatures to achieve not only greater flexibility but also improved security and efficiency. Cryptographic smart signatures minimize the risks of manipulation, enhance privacy through aggregation, and reduce computational overhead—making them ideal for modern enterprise and financial applications.

## Types of Smart Signatures

First, it's crucial to distinguish smart signatures from smart contract languages. Smart contract languages, like Solidity for Ethereum, are Turing-complete, meaning they can theoretically perform any computation. This flexibility comes at a cost: complexity and potential security vulnerabilities.

Smart signatures, on the other hand, are designed for specific purposes and can offer a more secure and efficient approach to certain tasks. Bitcoin's Script is a example of a constrained smart signature language with its FORTH-like stack and operators. The execution of the script results in one of 2 choices: either TRUE and the transaction is valid and can proceed, or FALSE and must be ignored.

Within the realm of smart signatures scripting languages, we can further categorize them into two main types:

* **Computational smart signatures:** These signatures rely on logical statements and conditional expressions to define their execution logic. They are often implemented using constrained scripting languages that allow for complex computations and conditional branching. Bitcoin's Script falls into this category.
* **Cryptographic smart signatures:** These signatures leverage the mathematical properties of cryptographic primitives, such as Schnorr signatures and adaptor signatures, to achieve their functionality. They rely on cryptographic proofs and verification mechanisms to ensure the integrity and security of the signature. Atomic Cross-Chain Swaps fall into this category.
  
The key difference lies in how the logic is encoded and enforced. Computational smart signatures rely on the correct interpretation and execution of computation logic predicate statements in the script itself, which can be vulnerable to manipulation or exploitation. Cryptographic smart signatures, on the other hand, rely on the unforgeability of cryptographic operations to function as predicates, making them significantly more resistant to attacks.


## Schnorr: The Engine of Cryptographic Smart Signatures

To truly grasp the transformative potential of cryptographic smart signatures, we need to delve into the underlying [magic of Schnorr signatures](https://www.blockchaincommons.com/musings/Schnorr-Intro/)[^Allen-Schnorr-Intro-2023]. What sets Schnorr signatures apart from other schemes, such as ECDSA, is their unique mathematical property: **linearity**. 

Linearity, in this context, refers to the signature scheme's adherence to the principles of additivity and homogeneity. These properties allow multiple Schnorr signatures to be aggregated into a single compact signature that remains just as valid as the individual signatures it replaces. Additivity ensures that the sum of individual signatures corresponds to the sum of their respective public keys, while homogeneity guarantees that scalar multiplication distributes consistently across these sums. Together, these traits make it possible to verify an aggregated signature using an aggregated public key, all without requiring the original signatures to be separated.

This linearity not only enhances efficiency by saving space and reducing transaction fees but also improves privacy. For example, in a multi-signature transaction, the aggregated signature obfuscates the number of participants, making it virtually impossible to determine how many signers contributed. This boost in confidentiality is a critical advantage for privacy-focused applications.

But linearity enables more than just aggregation—it provides **crucial flexibility**. A Schnorr signature can be combined with a secret or random value, altering it in a reversible manner to create what is known as an "Adaptor Signature." To validate a signature, the same adaptor value must be subtracted during the verification process. This seemingly simple mechanism underpins Schnorr's versatility and its suitability for advanced cryptographic constructs.

Adaptor signatures pave the way for building sophisticated tools like atomic swaps, escrow systems, and payment channels—all without relying on cumbersome on-chain scripts. By acting as programmable predicates in cryptographic smart contracts, adaptor signatures can embed conditions directly into the signature process itself.

This lightweight and secure alternative to traditional script-based systems underscores the simplicity, efficiency, and security of Schnorr signatures, positioning them as the ideal foundation for the next generation of cryptographic innovations.

## The Power of Cryptographic Predicates

Imagine a scenario where a smart signature needs to enforce a threshold requirement, such as requiring approval from at least two out of three parties. Using legacy signature technology, a "computational smart signature", this would typically be implemented using a logical AND statement. However, an attacker could potentially manipulate the script to change the AND to an OR, thereby bypassing the threshold requirement.

With these new "cryptographic smart signatures", this attack vector is effectively eliminated. The threshold condition is encoded within the cryptographic construction itself, ensuring that the signature is only valid if the cryptographic result satisfies the predicate. This reliance on mathematical proofs rather than computational logic significantly enhances security by preventing unauthorized modifications, and can enhance privacy though anti-correlation.

## Adaptor Signatures: Expanding the Possibilities

Adaptor signatures are a crucial building block for cryptographic smart signatures. They allow for the creation of "scriptless scripts," which are essentially smart contracts that can be executed off-chain without relying on complex on-chain scripts.

This offers several advantages, including:   

* Enhanced efficiency: Leveraging adapter signatures, cryptographic smart signatures reduce the size of transactions and the computational resources required for verification.
* Improved privacy: By aggregating signatures and concealing the details of the contract, cryptographic smart signatures enhance privacy for the parties involved.
* Increased fungibility: cryptographic smart signatures make it challenging to distinguish between transactions involved in different types of contracts.

The value of adaptor signatures is just beginning to be explored. The secret value that "adapts" the partial signature into a full signature can be sourced from various places, unlocking a wide range of possibilities:

* **Atomic Swaps:** Perhaps the most well-known use of adaptor signatures is in atomic swaps, which allow two parties to exchange cryptocurrencies on different blockchains without relying on a trusted intermediary. In an atomic swap, each party creates a transaction that is conditional on the other party revealing a secret value. This secret is embedded within the adaptor signature, ensuring that both parties either receive their desired assets or the entire transaction is canceled . This eliminates counterparty risk and enables trustless cross-chain trading, fostering interoperability and liquidity across different blockchain ecosystems. Atomic swaps based on adaptor signatures offer several advantages over traditional Hash Time-Locked Contracts (HTLCs), including reduced on-chain space utilization and improved efficiency. These also can be used to enable encrypted data to be decrypted only after a payment is made, or to make "single-use" tokens with limited authority.
* **Discreet Log Contracts (DLCs):** DLCs allow parties to create contracts that are settled based on the outcome of a future event, as determined by an oracle.Adaptor signatures are used in DLCs to encrypt a signature for a specific contract execution transaction, which can be decrypted and used once the oracle reveals the corresponding secret value . This enables secure and trustless execution of contracts based on real-world events, such as financial derivatives, insurance claims, or even the outcome of elections.
* **Anti-correlation using blind signatures:** Two parties can generate adaptor signatures based on secret values that are anti-correlated, meaning that one value can be used to derive the other. This enables secure and private exchange of information or assets without revealing the underlying values. Useful for more sophisticated atomic swaps, but also useful other anti-correlation measures. 
* **Predicate blind signatures:** Blind signatures allow a user to obtain a signature on a message without revealing the message content to the signer. There is a variant, predicate blind signatures that add their own conditions to this process, ensuring that the signature is only valid if the message satisfies a specific predicate.
* **Offline zk-proofs:** Zero-knowledge proofs (ZKPs) allow one party to prove to another that they possess certain information without revealing the information itself. Offline ZKPs can be used to generate adaptor signature secrets, enabling the creation of scriptless scripts that enforce complex conditions without requiring on-chain verification. For example, the paper "Bitcoin PIPEs: Covenants and ZKPs on Bitcoin Without Soft Fork" explores how ZKPs can be used to implement covenants and other advanced features on Bitcoin today.   
* **Threshold keys:** A threshold key, generated using schemes like MuSig2 or FROST, can be used as the secret value in an adaptor signature. This allows a group of parties to collectively control the execution of a scriptless script, ensuring that a certain threshold of approvals is met before the contract can be finalized.
* **Recursive structures**: Adaptor signatures can be nested within each other, creating complex and dynamic scripts that can adapt to changing conditions. This opens up possibilities for more sophisticated smart contracts and decentralized applications.

## Conclusion: A Secure Foundation for the Future
Cryptographic smart signatures, built on the foundation of Schnorr signatures and adaptor signatures, offer a powerful and secure approach to building the next generation of smart contracts and decentralized applications. By encoding logic within cryptographic operations, they provide a higher level of security and resistance to attacks compared to traditional computational approaches.

The versatility of adaptor signatures, with their ability to incorporate secret values from various sources, further expands the possibilities for cryptographic smart signatures. This opens up exciting new avenues for innovation in areas like decentralized finance, supply chain management, and digital identity.

As we continue to explore the potential of cryptographic smart signatures, we are laying the groundwork for a more secure, efficient, and privacy-preserving digital future.

## Appendix 1: History

The concept of smart signatures was conceived[^Allen-Smart-Signatures-2015] almost 10 years ago, in 2015, at the first [Rebooting Web of Trust Workshop](https://github.com/WebOfTrustInfo/rwot1-sf). Joining me were notable co-authors, Greg Maxwell (Bitcoin Core Contributor, co-founder of Blockstream), Peter Todd (Bitcoin Core Contributor), Ryan Shea (Co-Founder of Blockstack), Pieter Wuille (Bitcoin Core Contributor, co-founder of Blockstream, inventor of Segregated Witness), Joseph Bonneau (cryptographer, professor at NYU), Joseph Poon (co-inventor of the Lightning Network), and Tyler Close (cryptographer and author of WebKey cryptographic standards).

> ABSTRACT: Traditional cryptographic signature systems are based on strictly-defined authentication and authorization mechanisms that assume a single private key can be used to produce a given signature and that a single public key can be used to verify it. Given the evident limitations of this design, we propose an alternative with more powerful capabities, based on the ability to explicitly outline and fully program conditions for verification. These conditions would then be used to determine when a signature or set of signatures can be considered valid.
>
>Our inspiration for this authorization system is the bitcoin scripting language, where the authorization to spend funds is explicitly defined within a script, rather than being implicitly defined through the reference to an authorized public key. The largest benefit of explicit specification of authorization conditions is that the system is fully extensible, so new operations can be defined at any time, with the only limitation being the set of operations that the authorization interpreters
understand.

In 2016, my long-time co-author Shannon Appelcline and I, in *Smarter Signatures: Experiments in Verifications* [^Allen-Smarter-Signatures-2016], expanded on the initial concept. This included defining six key requirements for implementation, including:

- **Composability**: Building complexity from simple operations.  
- **Provability**: Enabling logical analysis of signature logic.  
- **Determinism**: Ensuring consistent behavior across platforms.  
- **Efficiency**: Minimizing computational overhead.  
- **Boundedness**: Preventing resource exhaustion.  
- **Inspectability**: Ensuring human readability and understanding of signature logic.

It also established a range of use cases, such as:

- **Multifactor authentication**: Combining multiple elements like biometric verification and hardware tokens.  
- **Delegation of signing authority**: Supporting time-limited, use-specific, and content-restricted delegations.
- **Multisignature schemes**: Enabling N-of-N, M-of-N, and logical combinations like AND/OR signatures.  
- **Transactional workflows**: Verifying and chaining signatures across complex processes.  
- **Internal and external depth**: Allowing for layered (synchronous) and chained (asynchronous) validation in complex systems.  

The update also emphasized privacy considerations, shared examples of early language experiments with systems like Dex and Crypto-Conditions, and introducing concept of layered validation to support complex workflows. It highlighted the importance of transactional history, deterministic behavior for cross-platform consistency, and scalable design using mechanisms like Merkle trees. Drawing lessons from failures like the Ethereum DAO exploit, it stressed the need for secure language design and raised open questions about revocation, oracles, and hierarchical deterministic keys to guide future developments.

I presented this paper (with minor updates) at Stanford's BPASE conference in 2018:[^Allen-Smart-Signatures-Video-2018]:

[![Smart Signatures: Experiments in Verification(Stanford BPASE '18)](https://img.youtube.com/vi/E9sbWKbfyJU/hqdefault.jpg)](https://youtu.be/E9sbWKbfyJU)

A parallel term for "cryptographic smart signatures" is "scriptless scripts", coined in 2017 by Andrew Poelstra (Director of Research at Blockstream), as a way to enable complex smart contract functionality without relying on a blockchain's native scripting language. He first presented this concept at Scaling Bitcoin in 2017 [Video](https://www.youtube.com/watch?v=3pd6xHjLbhs&t=5759s), [Transcript](https://btctranscripts.com/scalingbitcoin/stanford-2017/using-the-chain-for-what-chains-are-good-for), [Presentation PDF](https://stanford2017.scalingbitcoin.org/files/Day2/Using-the-Chain-for-what-Chains-are-Good-For.pdf), as a consequence of his research[^Poestra-Mimblewimble](https://github.com/BlockstreamResearch/scriptless-scripts/blob/master/md/atomic-swap.md) on MimbleWimble[^Jedusor-Mimblewimble](https://docs.beam.mw/Mimblewimble.pdf).

I'm not sure who first coined the term "adapter signature", but the first use that I've been able to find is also by Andrew Poelstra as part of his May 2017 work on Scriptless Scripts for Atomic Swaps[^Poelstra-Atomic-Swap](https://github.com/BlockstreamResearch/scriptless-scripts/blob/master/md/atomic-swap.md).

### Citations

[^Allen-Schnorr-Intro-2023]: _**A Layperson’s Intro to Schnorr**_ (2023-10-24). [web article]. _Allen, Christopher._ Retrieved 2024-12-12 from Blockchain Commons: <https://www.BlockchainCommons.com/musings/Schnorr-Intro/>. Cross-posted at Life With Alacrity: <https://www.LifeWithAlacrity.com/article/musings-schnorr/>.

[^Allen-Smart-Signatures-2015]: _**Smart Signatures**_ (2015). [white paper]. _Allen, Christopher; Maxwell, Greg; Todd, Peter; Shea, Ryan; Wuille, Pieter; Bonneau, Joseph; Poon, Joseph; Close, Tyler._ Produced as part of "_Rebooting the Web of Trust Workshop_," November 3-4, 2015, San Francisco, CA. Version 1.0.1. Retrieved 2024-12-12 from GitHub/WebOfTrustInfo [PDF]: <https://github.com/WebOfTrustInfo/rwot1-sf/blob/master/final-documents/smart-signatures.pdf>. _([fully annotated citation](https://hackmd.io/fPkq0LA8QpSdkc6rPlgjOw#Allen-Smart-Signatures-2015))_

[^Allen-Smarter-Signatures-2016]: _**Smarter Signatures: Experiments in Verifications**_ (2024). [web article]. _Allen, Christopher; Appelcline, Shannon._ Retrieved 2024-12-12 from Life With Alacrity: <https://www.lifewithalacrity.com/article/smarter-signatures-experiments-in-verifications/>. _([fully annotated citation](https://hackmd.io/fPkq0LA8QpSdkc6rPlgjOw#Allen---Smarter-Signatures-2016))_

[^Allen-Smart-Signatures-Video-2018]: _**Smart Signatures: Experiments in Authorization**_ (2016-06-29). [YouTube video; transcript]. _Allen, Christopher._ Presented at the Stanfor BPASE '18 Conference. Video available on YouTube: <https://www.youtube.com/watch?v=E9sbWKbfyJU>. Transcript available from BTC Transcripts: <https://btctranscripts.com/w3-blockchain-workshop-2016/smart-signatures>, [PDF](TBD) of presentation. _([fully annotated citation](https://hackmd.io/fPkq0LA8QpSdkc6rPlgjOw#Allen-Smart-Signatures-Video-2016))_
