Designing cryptographic protocols and proving these rigorously secure is an arduous and challenging task. Among the methods commonly used to prove security of cryptographic protocols, formalizing it in Canneti's Universal Composability (UC) Framework offers several benefits: (1) Modular design, (2) demonstrating that security remains under arbitrary composition and concurrent execution, (3) the security against any computationally polynomially bound adversary. However, working within the UC Framework can be cumbersome, requires a long time commitment by the prover, and it is prone to errors. While utilization of proof assistants in Cryptography and IT Security is a prominent research area, proof assistants for UC are still in their infancy. Here we show our ongoing work to utilize model checking for verification of proofs in the UC Framework, which to the best of our knowledge is the first attempt to do so. In this work we (1) formally create a Markov Decision Process (MDP) encoding a given proof in the UC Framework, (2) define and proof notions of soundness and completeness for the constructed MDP, (3) implement a proof of concept and (4) demonstrate practical feasibility through experimental evaluation. In summary, in this work we lay out the formal foundations for model checking UC proofs and create a tool that can not only be used for proof verification but also as an assistant for developing proofs in the UC Framework.
attested.network — Proof of Payment for ATProtocol
An open specification for decentralized, cryptographically verifiable proof of payments.
Tutorial: Introduction to Formal Verification with Lean (Part 1) - HashCloak
A tutorial Formal Verification using Lean for cryptographic engineers. Implement and prove correctness of the One-Time pad following a cryptography book.
ATProtocol Attestations: Cryptographic Signatures for the Decentralized Web - Nick's Blog
This post introduces the formal ATProtocol attestation specification, a framework for adding cryptographic signatures to ATProto records through two complementary patterns: inline attestations that embed signatures directly in records, and remote attestations that store proof in separate repository records. The specification prevents replay attacks through repository binding, uses CID-based content addressing for integrity, and provides the cryptographic foundation for verified credentials, trusted content, and authenticated interactions in the decentralized ATProtocol ecosystem.
ZKPROV: A Zero-Knowledge Approach to Dataset Provenance for Large Language Models
As large language models (LLMs) are used in sensitive fields, accurately verifying their computational provenance without disclosing their training datasets poses a significant challenge, particularly in regulated sectors such as healthcare, which have strict requirements for dataset use. Traditional approaches either incur substantial computational cost to fully verify the entire training process or leak unauthorized information to the verifier. Therefore, we introduce ZKPROV, a novel cryptographic framework allowing users to verify that the LLM's responses to their prompts are trained on datasets certified by the authorities that own them. Additionally, it ensures that the dataset's content is relevant to the users' queries without revealing sensitive information about the datasets or the model parameters. ZKPROV offers a unique balance between privacy and efficiency by binding training datasets, model parameters, and responses, while also attaching zero-knowledge proofs to the responses generated by the LLM to validate these claims. Our experimental results demonstrate sublinear scaling for generating and verifying these proofs, with end-to-end overhead under 3.3 seconds for models up to 8B parameters, presenting a practical solution for real-world applications. We also provide formal security guarantees, proving that our approach preserves dataset confidentiality while ensuring trustworthy dataset provenance.
SyRA: Sybil-Resilient Anonymous Signatures with Applications to Decentralized Identity
We study Sybil-Resilient Anonymous (SyRA) signatures, a cryptographic primitive that enables credentialed users to generate, on demand, unlinkable pseudonyms tied to any given context, and issue signatures on behalf of these pseudonyms. Concretely, SyRA allows a distributed issuer to turn any legacy identity or personhood identifier, possibly of low entropy, into a unique associated cryptographic key of high pseudoentropy, for use in generating signatures for any given context. Sybil-resilient anonymous signatures achieve three main objectives: 1) Sybil resilience: every user is entitled to at most one digital identity, 2) anonymity: no information about the user’s real identity is leaked, and 3) non-interactive context switching: users can create on their own at most one credential for any given context in a manner that is unlinkable across contexts. We conceptualize the SyRA primitive as an ideal functionality in the Universal Composition (UC) setting and put forth SASSI, an efficient, pairing-based construction that realizes it by utilizing two levels of verifiable random functions (VRFs), a design which may be of independent interest. The first level consists of threshold VRF issuance of a user’s unique secret key tied to their real-world identifier. The second level allows a user to create signatures for each context, under a unique pseudonym per context. Compared to prior cryptographic tools capable of realizing SyRA, SASSI has the unique feature that issuers are stateless and hence do not need to retain any information about past user interactions, a relevant property for a decentralized implementation. We overview various applications of SASSI in multiparty systems, such as cryptocurrency account management and airdrops, e-voting (e.g., for decentralized governance), and privacy-preserving regulatory compliance (e.g., AML/CFT checks). In the context of creating addresses for digital assets, SyRA signatures enable users to embed their legacy identity into their address in a manner that protects their privacy for each application with which they interact. We demonstrate the practicality of SASSI by providing an implementation and performance evaluation of our construction.
Building Unforgeable Professional Endorsements with ATProtocol - Nick's Blog
Traditional professional endorsements on platforms like LinkedIn lack cryptographic proof—anyone could forge them, and the platform controls the truth. This article introduces a two-record architecture using ATProtocol's Content Identifiers (CIDs) and Decentralized Identifiers (DIDs) to create mathematically unforgeable mutual attestations. By separating proof creation from endorsement acceptance and leveraging the firehose for distributed validation, we build a system where both parties cryptographically consent and no central authority can manipulate the record.
Introducing attested.network: Proof of Payment for ATProtocol - Nick's Blog
attested.network is an open spec for decentralized proof of payments on ATProtocol, built on what we learned making atprotofans.com. It formalizes the three-party attestation model and opens it up for any app to implement.
Mathematics with large language models as provers and verifiers
During 2024 and 2025 the discussion about the theorem-proving capabilities of large language models started reporting interesting success stories, mostly to do with difficult exercises (such as problems from the International Mathematical Olympiad), but also with conjectures [Feldman & Karbasi, arXiv:2509.18383v1] formulated for the purpose of verifying whether the artificial intelligence could prove it. In this paper we report a theorem proving feat achieved by ChatGPT by using a protocol involving different prover and verifier instances of the gpt-5 model working collaboratively. To make sure that the produced proofs do not suffer from hallucinations, the final proof is formally verified by the lean proof assistant, and the conformance of premises and conclusion of the lean code is verified by a human. Our methodology is by no means complete or exact. It was nonetheless able to solve five out of six 2025 IMO problems, and close about a third of the sixty-six number theory conjectures in [Cohen, Journal of Integer Sequences, 2025].
Mathematics with large language models as provers and verifiers
During 2024 and 2025 the discussion about the theorem-proving capabilities of large language models started reporting interesting success stories, mostly to do with difficult exercises (such as problems from the International Mathematical Olympiad), but also with conjectures [Feldman & Karbasi, arXiv:2509.18383v1] formulated for the purpose of verifying whether the artificial intelligence could prove it. In this paper we report a theorem proving feat achieved by ChatGPT by using a protocol involving different prover and verifier instances of the gpt-5 model working collaboratively. To make sure that the produced proofs do not suffer from hallucinations, the final proof is formally verified by the lean proof assistant, and the conformance of premises and conclusion of the lean code is verified by a human. Our methodology is by no means complete or exact. It was nonetheless able to solve five out of six 2025 IMO problems, and close about a third of the sixty-six number theory conjectures in [Cohen, Journal of Integer Sequences, 2025].
Defeating Prompt Injections by Design
Large Language Models (LLMs) are increasingly deployed in agentic systems that interact with an untrusted environment. However, LLM agents are vulnerable to prompt injection attacks when handling untrusted data. In this paper we propose CaMeL, a robust defense that creates a protective system layer around the LLM, securing it even when underlying models are susceptible to attacks. To operate, CaMeL explicitly extracts the control and data flows from the (trusted) query; therefore, the untrusted data retrieved by the LLM can never impact the program flow. To further improve security, CaMeL uses a notion of a capability to prevent the exfiltration of private data over unauthorized data flows by enforcing security policies when tools are called. We demonstrate effectiveness of CaMeL by solving $77\%$ of tasks with provable security (compared to $84\%$ with an undefended system) in AgentDojo. We release CaMeL at https://github.com/google-research/camel-prompt-injection.
Formal Verification Reference - Aura
This document describes the formal verification infrastructure that provides mathematical guarantees for Aura protocols through Quint model checking, Lean theorem proving, and Telltale session type verification.
Decentralized Identity Verification using Zero-Knowledge Proofs: A Privacy-Preserving Authentication Framework
In the contemporary online interaction, digital iden- tity is central, but most systems follow a centralized provider like Google or Facebook. Although convenient, these models pose ma- jor risks to data breach, surveillance, and single point of failure. The proposed paper proposes a privacy-sensitive decentralized identity verification system that uses Zero-Knowledge Proofs (ZKPs) to allow users to make it through claims (e.g., age, citizen- ship, or enrollment) without any personal data being provided, thereby solving the challenges outlined in the paper. Our architecture integrates verifiable credentials, zero-knowledge-SNARKs and an issuer trust registry that is maintained on blockchain smart contracts to guarantee trustless verification and eliminate dependence on centralized authorities. Its system gives its users full control over credentials, allows reuse across applications, and does not expose data.A proof-of-concept implementation has shown the approach to be feasible with Circom and SnarkJS to generate proof, Solidity smart contracts to verify them, and a user interface implemented in React. Results of the evaluations showed that determination of the verification latency is low, the overhead to generate proofs is moderate, and no privacy leakage occurs. It can be used in potential applications such as education, e-governance, healthcare, finance, and online voting.
Cognitive Integrity Framework: Formal Foundations for Multiagent Security
Multiagent AI systems introduce cognitive attack surfaces absent in single-model inference. When agents delegate to agents, forming beliefs about beliefs through recursive trust hierarchies, manipulation of reason- ing processes—rather than mere data corruption—becomes a primary security concern. This paper presents the Cognitive Integrity Framework (CIF), providing formal foundations for cognitive security in multiagent operators. We develop four interconnected theoretical contributions: a Trust Calculus with bounded delegation (exponential 𝛿𝑑 decay) that prevents trust amplification through delegation chains; a Defense Com- position Algebra with series and parallel composition theorems establishing multiplicative detection bounds; Information-Theoretic Limits relating stealth constraints to maximum attack impact through a fundamental stealth-impact tradeoff; and a formal Adversary Hierarchy (Ω1–Ω5) characterizing external, peripheral, agent-level, coordination, and systemic threats with increasing capability and decreasing detectability. The framework provides complete coverage of the OWASP Top 10 for Agentic Applications through formal threat models grounded in cognitive state manipulation rather than traditional input/output filtering. CIF bridges classical security concepts with the cognitive requirements of agentic systems. We extend Byzantine fault tolerance to cognitive manipulation—agents that appear functional but hold corrupted beliefs—and adapt trust management systems to continuous trust evolution with provable decay bounds. The framework formalizes five architectural defense mechanisms (cognitive firewalls, belief sandboxing, behavioral tripwires, provenance tracking, Byzantine consensus) with composition rules enabling formal reasoning about layered security. Technical foundations include: operational semantics for message passing and trust updates; invariants for belief integrity, goal preservation, and trust boundedness; model checking configurations for safety property verification; and a complete notation system for attack parameterization, defense specification, and cognitive state representation. This is Part 1 of a three-part series: Part 1 (this paper, DOI: 10.5281/zenodo.18364119) presents formal foundations and theoretical analysis; Part 2 (DOI: 10.5281/zenodo.18364128) provides computational validation and implementation; Part 3 (DOI: 10.5281/zenodo.18364130) offers practical deployment guidance. The framework will continue to be developed and versioned at https://github.com/docxology/cognitive_integrity/ .
AIP: Agent Identity Protocol for Verifiable Delegation Across MCP and A2A
AI agents increasingly call tools via the Model Context Protocol (MCP) and delegate to other agents via Agent-to-Agent (A2A), yet neither protocol verifies agent identity. A scan of approximately 2,000 MCP servers found all lacked authentication. In our survey, we did not identify a prior implemented protocol that jointly combines public-key verifiable delegation, holder-side attenuation, expressive chained policy, transport bindings across MCP/A2A/HTTP, and provenance-oriented completion records. We introduce Invocation-Bound Capability Tokens (IBCTs), a primitive that fuses identity, attenuated authorization, and provenance binding into a single append-only token chain. IBCTs operate in two wire formats: compact mode (a signed JWT for single-hop cases) and chained mode (a Biscuit token with Datalog policies for multi-hop delegation). We provide reference implementations in Python and Rust with full cross-language interoperability. Compact mode verification takes 0.049ms (Rust) and 0.189ms (Python), with 0.22ms overhead over no-auth in real MCP-over-HTTP deployment. In a real multi-agent deployment with Gemini 2.5 Flash, AIP adds 2.35ms of overhead (0.086% of total end-to-end latency). Adversarial evaluation across 600 attack attempts shows 100% rejection rate, with two attack categories (delegation depth violation and audit evasion through empty context) uniquely caught by AIP's chained delegation model that neither unsigned nor plain JWT deployments detect.
Unforgeable Endorsements Technical Deep-Dive - Nick's Blog
Deep technical implementation of the unforgeable endorsement system. Covers step-by-step CID computation, complete code for the endorsement workflow, validation algorithms, firehose event processing, and detailed security analysis of attack vectors. Includes working code examples, lexicon definitions, and the cryptographic mechanisms that make forgery mathematically impossible.
Beyond DNS: Unlocking the Internet of AI Agents via the NANDA Index and Verified AgentFacts
The Internet is poised to host billions to trillions of autonomous AI agents that negotiate, delegate, and migrate in milliseconds and workloads that will strain DNS-centred identity and discovery. In this paper, we describe the NANDA index architecture, which we envision as a means for discoverability, identifiability and authentication in the internet of AI agents. We present an architecture where a minimal lean index resolves to dynamic, cryptographically verifiable AgentFacts that supports multi-endpoint routing, load balancing, privacy-preserving access, and credentialed capability assertions. Our architecture design delivers five concrete guarantees: (1) A quilt-like index proposal that supports both NANDA-native agents as well as third party agents being discoverable via the index, (2) rapid global resolution for newly spawned AI agents, (3) sub-second revocation and key rotation, (4) schema-validated capability assertions, and (5) privacy-preserving discovery across organisational boundaries via verifiable, least-disclosure queries. We formalize the AgentFacts schema, specify a CRDT-based update protocol, and prototype adaptive resolvers. The result is a lightweight, horizontally scalable foundation that unlocks secure, trust-aware collaboration for the next generation of the Internet of AI agents, without abandoning existing web infrastructure.