PROXY Network

Part I: Introduction

Executive Summary

Blockchain systems derive their security model from cryptographic ownership: control of a private key provides exclusive control over associated assets. This fundamental property has enabled the creation of permissionless financial systems but simultaneously created unprecedented operational challenges in key management. The loss, theft, or compromise of private keys has resulted in billions of dollars of irrecoverable losses.

PROXY Network addresses this challenge through a novel combination of threshold cryptography and economic incentives. The protocol enables the creation and operation of distributed signing infrastructure where:

• Private keys are generated across a network of independent agents using Distributed Key Generation (DKG), with the complete key never existing at any point
• Transaction signing requires threshold consensus (t-of-n), preventing any minority coalition from producing signatures
• Key shares are proactively refreshed, rendering compromised shares obsolete
• Economic incentives through staking and slashing ensure honest agent behavior
• On-chain verification enables trustless integration with any blockchain application

This paper provides the complete technical specification of the PROXY Network protocol, including formal definitions, mathematical proofs, and implementation guidelines.

The Private Key Problem

In asymmetric cryptography, a keypair consists of a private key x and corresponding public key P. The security of this construction relies on the computational infeasibility of deriving x from P.

This creates a fundamental security tension: the private key must be accessible for signing operations but must remain secret from all adversaries. Any system storing private keys faces inherent tradeoffs between availability and security.

Historical Security Failures

The cryptocurrency industry has experienced numerous catastrophic key management failures:

These incidents share a common pattern: centralization of key material created exploitable single points of failure.

Existing Solutions and Limitations

Multi-Signature Wallets

Multi-signature (multisig) wallets require m of n parties to authorize transactions through separate signatures combined on-chain.

Limitations:

• Each signer possesses a complete private key (single point of failure at each location)
• On-chain coordination reveals signer set and threshold publicly
• Gas costs scale with number of signatures
• Protocol-specific implementation required for each blockchain

Hardware Security Modules (HSM)

HSMs provide tamper-resistant hardware for key storage and cryptographic operations.

Limitations:

• Physical device represents single point of failure
• Cannot scale horizontally
• Expensive procurement and operational costs
• Limited programmability

Centralized MPC Providers

Several companies offer MPC-based custody services where key shares are distributed across their infrastructure.

Limitations:

• Single company controls all infrastructure
• Counterparty risk remains
• Regulatory vulnerability to jurisdiction actions
• Not censorship resistant

PROXY Network Design Goals

PROXY Network is designed to achieve the following properties:

Part II: Mathematical Foundations

Notation and Preliminaries

We establish the following notation used throughout this paper:

Elliptic Curve Cryptography

Group Structure

An elliptic curve over a finite field 𝔽_p is defined by the Weierstrass equation:

where a, b ∈ 𝔽_p and 4a³ + 27b² ≠ 0 (non-singularity condition).

For points P = (x₁, y₁) and Q = (x₂, y₂) on E, the group operation P + Q = R = (x₃, y₃) is computed as:

The Discrete Logarithm Problem

The security of elliptic curve cryptography relies on the computational hardness of ECDLP. For a curve with 256-bit group order, approximately 2¹²⁸ operations are required for the best known attack.

Supported Curves

PROXY Network supports the following standardized curves:

Digital Signature Schemes

ECDSA

The Elliptic Curve Digital Signature Algorithm (ECDSA) is defined as follows:

EdDSA/Schnorr

EdDSA is a variant of Schnorr signatures optimized for the Edwards curve ed25519:

Secret Sharing

Shamir's Secret Sharing

Shamir's Secret Sharing (SSS) enables distribution of a secret among n parties such that any t parties can reconstruct the secret, but t-1 parties learn nothing.

Verifiable Secret Sharing

Feldman's Verifiable Secret Sharing (VSS) extends SSS by allowing recipients to verify their shares without learning the secret.

Commitment Schemes

We use Pedersen commitments defined as follows:

Zero-Knowledge Proofs

We use Schnorr's protocol for proving knowledge of discrete logarithm:

Part III: Threshold Cryptography

Threshold Signature Schemes

A threshold signature scheme consists of the following algorithms:

• KeyGen(t, n) → (pk, {sk₁, ..., skₙ}): Generates public key and secret shares
• Sign(m, S, {skᵢ}ᵢ∈S) → σ: Parties in S (|S| ≥ t) produce signature on m
• Verify(pk, m, σ) → {0, 1}: Standard signature verification

Threshold ECDSA Protocols

Threshold ECDSA is significantly more complex than threshold Schnorr due to the non-linear relationship s = k⁻¹(e + rx) in the signature equation.

The GG18 Protocol

Gennaro and Goldfeder (2018) introduced a two-round threshold ECDSA protocol based on Paillier encryption.

The GG20 Protocol

Gennaro and Goldfeder (2020) improved their protocol to achieve identifiable abort: if signing fails, dishonest parties can be identified and removed.

Security Analysis

Threshold EdDSA

Threshold EdDSA is simpler than threshold ECDSA due to the linear signature equation s = r + ex.

Part IV: Distributed Key Generation

DKG Protocol Specification

Distributed Key Generation (DKG) enables parties to jointly generate a keypair such that no party learns the complete private key.

Key Resharing

Key resharing enables changing the set of shareholders while maintaining the same keypair.

Proactive Secret Sharing

Proactive Secret Sharing (PSS) refreshes shares periodically to maintain security against mobile adversaries who may eventually compromise t parties.

Part V: Protocol Architecture

Network Topology

The PROXY Network operates as a permissionless peer-to-peer network where agents communicate through a gossip protocol overlay. The network maintains both the security properties of threshold cryptography and the liveness requirements of a production signing infrastructure.

Agent Nodes

Each agent node in the network maintains the following state:

Communication Protocols

Agent Selection

For each signing operation, a subset of t agents must be selected from the pool of n registered agents. The selection algorithm must ensure randomness, unpredictability, and stake-weighted fairness.

Signing Protocol

The complete signing flow integrates agent selection, threshold signing, and on-chain verification.

Protocol Timing

Communication Layer

Part VI: Smart Contracts

Contract Architecture

The PROXY Network on-chain components are implemented as a set of upgradeable smart contracts following the proxy pattern for future protocol improvements.

┌─────────────────────────────────────────────────────────────┐
│                    PROXY Network Contracts                   │
├─────────────────────────────────────────────────────────────┤
│                                                             │
│  ┌─────────────┐  ┌─────────────┐  ┌─────────────────────┐ │
│  │   Agent     │  │   Staking   │  │    Key              │ │
│  │  Registry   │  │   Manager   │  │   Registry          │ │
│  └──────┬──────┘  └──────┬──────┘  └──────────┬──────────┘ │
│         │                │                     │            │
│         └────────────────┼─────────────────────┘            │
│                          │                                  │
│                   ┌──────▼──────┐                          │
│                   │   Slashing  │                          │
│                   │   Manager   │                          │
│                   └──────┬──────┘                          │
│                          │                                  │
│                   ┌──────▼──────┐                          │
│                   │   Treasury  │                          │
│                   └─────────────┘                          │
│                                                             │
└─────────────────────────────────────────────────────────────┘
        

Agent Registry

Staking and Slashing

Part VII: Economic Model

Token Economics

The PROXY token serves multiple functions within the network ecosystem:

Fee Structure

Fee Distribution

Game-Theoretic Analysis

Part VIII: Security Analysis

Threat Model

We consider the following adversary capabilities:

Security Proofs

Attack Analysis

Side-Channel Resistance

Part IX: Implementation

Reference Implementation

The PROXY Network reference implementation is written in Rust for performance and memory safety, with bindings available for JavaScript, Python, and Go.

Core Libraries

Performance Benchmarks

Scalability Analysis

Appendices

Appendix A: Full Protocol Pseudocode

Appendix B: Mathematical Notation

Part X: Extended Mathematical Foundations

Finite Field Arithmetic

All cryptographic operations in PROXY Network are performed over finite fields. This section provides the complete mathematical foundation necessary for implementation.

Modular Exponentiation

Modular exponentiation is a fundamental operation in public-key cryptography, required for computing powers in finite fields efficiently. The naive approach of computing a^e and then reducing modulo p is impractical for cryptographic-sized exponents (typically 256 bits or larger), as intermediate results would be astronomically large. Instead, we employ the square-and-multiply algorithm, which reduces the complexity from O(e) to O(log e) multiplications by exploiting the binary representation of the exponent.

This optimization is critical for PROXY's threshold signature operations, where each participant must perform multiple exponentiations during key generation and signing. The algorithm's efficiency directly impacts the overall protocol latency and computational cost.

Modular Inversion

Computing multiplicative inverses modulo p is essential for division operations in finite fields. The Extended Euclidean Algorithm provides an efficient method to find a^-1 mod p by simultaneously computing the GCD and the Bézout coefficients. This operation appears frequently in elliptic curve point addition (computing slopes) and in signature generation (computing k^-1 in ECDSA).

Alternatively, Fermat's Little Theorem offers a simpler but slightly less efficient approach: since a^p-1 ≡ 1 (mod p) for prime p, we have a^-1 ≡ a^p-2 (mod p). This can be computed using the square-and-multiply algorithm, trading algorithmic simplicity for a small performance penalty.

Elliptic Curve Mathematics

Elliptic curves provide the mathematical foundation for modern threshold cryptography. Unlike traditional discrete logarithm systems based on multiplicative groups of finite fields, elliptic curves offer equivalent security with much smaller key sizes—a 256-bit elliptic curve provides security comparable to a 3072-bit RSA key. This efficiency is crucial for PROXY's distributed architecture, where key shares and signatures must be transmitted across the network.

The security of elliptic curve cryptography rests on the Elliptic Curve Discrete Logarithm Problem (ECDLP): given points P and Q = kP on an elliptic curve, finding the scalar k is computationally infeasible for properly chosen curves. This hardness assumption underpins the security of ECDSA signatures and threshold signature schemes used throughout PROXY.

Weierstrass Form

secp256k1 Parameters

Point Addition Formulas

The elliptic curve group law defines how to "add" two points on the curve to produce a third point, also on the curve. Geometrically, point addition corresponds to drawing a line through two points P and Q, finding where it intersects the curve at a third point, and reflecting that point across the x-axis. This geometric intuition translates into algebraic formulas involving the curve equation.

Point addition is the fundamental operation underlying all elliptic curve cryptography. In PROXY's threshold signatures, participants must perform point additions when combining partial signatures and when verifying commitments during distributed key generation. The efficiency and correctness of these formulas directly impact the protocol's performance and security.

Scalar Multiplication

Scalar multiplication—computing kP for a scalar k and point P—is the most computationally intensive operation in elliptic curve cryptography. A naive implementation would add P to itself k times, requiring O(k) point additions. For cryptographic scalars (256 bits), this is completely impractical. Instead, we use the double-and-add algorithm, analogous to square-and-multiply for exponentiation, reducing complexity to O(log k) point operations.

However, the basic double-and-add algorithm has a critical security flaw: it performs different operations depending on whether each bit of k is 0 or 1, creating a timing side channel that can leak the secret scalar. For PROXY's threshold signing, where key shares must remain confidential, we employ constant-time algorithms like the Montgomery ladder, which perform the same operations regardless of bit values, eliminating timing leaks.

Hash Function Specifications

Cryptographic hash functions are essential building blocks in PROXY's security architecture, serving multiple critical roles: deriving message digests for signatures, generating deterministic nonces (RFC 6979), creating commitments in zero-knowledge proofs, and implementing the Fiat-Shamir transform to make interactive protocols non-interactive. The security of these applications depends on the hash function's collision resistance, preimage resistance, and pseudorandomness properties.

PROXY supports both SHA-256 (used by Bitcoin and most ECDSA implementations) and Keccak-256 (used by Ethereum), ensuring compatibility across different blockchain ecosystems. Understanding the internal structure of these hash functions is important for implementation correctness and for analyzing their security properties in the context of threshold cryptography.

SHA-256 Internals

Keccak-256 (Ethereum)

Keccak-256, the hash function used in Ethereum, is based on the sponge construction—a fundamentally different design paradigm from the Merkle-Damgård construction used in SHA-256. The sponge construction provides inherent resistance to length-extension attacks and offers greater flexibility in output length. For PROXY's Ethereum integration, using Keccak-256 ensures that message hashes match exactly what Ethereum smart contracts expect, preventing subtle incompatibilities.

ECDSA Mathematics

The Elliptic Curve Digital Signature Algorithm (ECDSA) is the signature scheme used by Bitcoin, Ethereum (for EOAs), and most blockchain systems. Understanding its complete mathematical specification is essential for implementing threshold ECDSA correctly. The security of ECDSA relies on the hardness of the ECDLP and on the proper generation of the per-signature nonce k—any bias or reuse of k can lead to complete private key recovery.

In PROXY's threshold setting, generating k becomes significantly more complex because no single party can know the full nonce. Instead, parties must collaboratively generate k using distributed key generation or verifiable secret sharing, while ensuring that k remains unpredictable and is never reused. The threshold ECDSA protocols in Part III build upon this single-party specification.

Complete Signature Generation

Signature Verification

Polynomials over Finite Fields

Polynomials over finite fields are the mathematical foundation of Shamir's Secret Sharing and all threshold cryptography schemes used in PROXY. The key insight is that a polynomial of degree t-1 is uniquely determined by t points: given t evaluations f(x₁), f(x₂), ..., f(xₜ), we can reconstruct the entire polynomial f(x) using Lagrange interpolation. This property enables threshold schemes where any t participants can reconstruct a secret (the polynomial's constant term f(0)), but t-1 or fewer participants learn nothing.

Efficient polynomial evaluation and interpolation are critical for PROXY's performance. During distributed key generation, each participant evaluates their polynomial at n points to create shares. During signing, participants use Lagrange interpolation to combine partial signatures. These operations occur in every signing request, so their efficiency directly impacts PROXY's throughput and latency.

Part XI: Formal Security Definitions

Formal security definitions provide the mathematical foundation for proving that cryptographic protocols are secure. Unlike informal arguments or heuristic analysis, formal security uses rigorous mathematical frameworks to define what it means for a protocol to be "secure" and to prove that breaking the protocol is as hard as solving a well-studied computational problem (like the discrete logarithm problem). This approach, pioneered by Goldwasser and Micali in the 1980s, has become the gold standard for cryptographic research and is essential for high-assurance systems like PROXY.

The core methodology of provable security is the security game (also called a security experiment). In a security game, we define an adversary A who interacts with a challenger C according to specific rules. The adversary's goal is to "win" the game by accomplishing some task that violates the security property we care about (e.g., forging a signature, recovering a secret key). We say a protocol is secure if no probabilistic polynomial-time (PPT) adversary can win the game with non-negligible probability.

For PROXY's threshold signature protocol, we must prove security against multiple threat models: an adversary who can corrupt up to t-1 participants, an adversary who can observe network traffic, an adversary who can adaptively choose which messages to sign, and even an adversary who can cause some participants to behave maliciously. Each threat model corresponds to a different security game, and our protocol must be proven secure in all relevant games.

Cryptographic Security Models

Before defining specific security games, we must establish the mathematical foundations: what does it mean for a function to be "negligible"? What does it mean for two probability distributions to be "indistinguishable"? These concepts, formalized below, allow us to make precise statements about security that hold asymptotically as the security parameter λ grows.

ECDLP Assumption

Security Games

Security games formalize the interaction between an adversary and a cryptographic system. The most important security notion for digital signatures is Existential Unforgeability under Chosen Message Attack (EUF-CMA), which captures the requirement that an adversary cannot forge a valid signature on any new message, even after seeing signatures on many messages of their choice. This is the strongest standard security notion for signature schemes and is essential for PROXY's use in blockchain transactions.

In the EUF-CMA game defined below, the adversary A can adaptively query a signing oracle on any messages they choose, building up a set Q of signed messages. The adversary wins if they can produce a valid signature on any message m* that was not in Q. The scheme is secure if no PPT adversary can win with non-negligible probability. This definition ensures that PROXY signatures cannot be forged, even by an attacker who has observed millions of legitimate signatures.

Threshold Security Definitions

Threshold cryptography introduces additional complexity to security definitions because we must account for adversaries who can corrupt some participants. The security model must specify: (1) how many participants the adversary can corrupt (typically up to t-1 in a (t,n)-threshold scheme), (2) whether corruption is static (chosen before the protocol starts) or adaptive (chosen during execution), and (3) whether corrupted participants are passively monitored or actively controlled by the adversary.

For PROXY, we require security against a static adversary who can corrupt up to t-1 participants and fully control their behavior. This means that as long as t honest participants follow the protocol correctly, the threshold signature scheme remains unforgeable and the secret key remains secure. This is formalized in the threshold unforgeability definition below, which extends the standard EUF-CMA game to the threshold setting.

MPC Security

Part XII: Detailed Attack Analysis

Attack Taxonomy

This section provides comprehensive analysis of potential attacks against the PROXY Network and corresponding mitigations.

Attack Category 1: Cryptographic Attacks

Attack Category 2: Protocol Attacks

Attack Category 3: Economic Attacks

Side-Channel Attacks

Part XIII: Case Studies and Applications

Case Study 1: Cross-Chain Bridge

This case study demonstrates integration of PROXY Network as the signing backend for a cross-chain asset bridge between Ethereum and Solana.

Integration Code

Case Study 2: DeFi Protocol Treasury

Case Study 3: Institutional Custody

Part XIV: Governance and Roadmap

Governance Framework

Governance Parameters

Development Roadmap

Part XV: Extended Appendices

Appendix D: Wire Protocol Specification

Appendix E: Test Vectors

Appendix F: Glossary

Appendix G: PROXY Network - The First Decentralized Signing Layer

PROXY Network represents a new category of blockchain infrastructure: the decentralized signing layer. Just as Chainlink created the oracle network category for off-chain data, PROXY Network creates the signing network category for cryptographic operations. This is not an evolution of existing solutions—it is a fundamentally new primitive.

The Infrastructure Stack

Why PROXY Network is Unique

No existing protocol operates at the signing layer. Other solutions either operate at a different layer or serve a different purpose:

• Multi-signature wallets (Gnosis Safe): Application-layer smart contracts, not infrastructure. Require on-chain transactions for every signature.
• Centralized MPC providers: Not decentralized, not permissionless, not infrastructure—they are services.
• Bridge-specific solutions: Purpose-built for single use cases, not general-purpose signing infrastructure.

PROXY Network is the first and only on-chain, decentralized, permissionless signing network—a new infrastructure layer that any application can integrate to gain threshold signing capabilities without building their own MPC infrastructure.

Part XVI: Performance Analysis and Benchmarks

Computational Complexity Analysis

Latency Breakdown

Throughput Analysis

Benchmark Results

Test Environment

DKG Performance

Signing Performance

Part XVII: SDK and API Reference

JavaScript/TypeScript SDK

REST API Reference

Smart Contract Interfaces

Part XIX: Super-Linear Staking Economics

Quadratic Security Model

Traditional staking systems provide linear security guarantees: doubling the stake doubles the cost of attack. PROXY Network implements super-linear (quadratic) staking, where the security guarantee grows as the square of total stake, making attacks economically infeasible at scale.

Concentrated Alerter System

Game-Theoretic Equilibrium Analysis

Part XX: Fair Sequencing Services (FSS)

MEV Mitigation Framework

Maximal Extractable Value (MEV) attacks exploit transaction ordering to extract value from users. PROXY Network's Fair Sequencing Services (FSS) implements cryptographic ordering guarantees that prevent front-running, sandwich attacks, and other MEV exploitation.

FIFO Ordering with Cryptographic Timestamps

MEV Extraction Prevention

Part XXI: Decentralized Services Protocol

Verifiable Random Function (VRF) Service

Many applications require provably fair randomness that cannot be manipulated by any party. PROXY Network provides threshold VRF, where randomness generation is distributed across agents.

Proof of Reserve Service

Keeper Automation Service

Part XXII: Network Deployment and Operations

Node Hardware Requirements

Geographic Distribution

Disaster Recovery

Part XXIII: Formal Security Reductions

Reduction to Standard Assumptions

Universally Composable (UC) Security

Concrete Security Bounds

Part XXIV: Cross-Chain Interoperability Protocol

Atomic Cross-Chain Messaging

PROXY Network enables trustless cross-chain communication through threshold-signed messages that are verifiable on any destination blockchain. This section provides the complete mathematical specification for cross-chain message passing.

Hash Time-Locked Contracts (HTLC)

Merkle Proof Verification

Part XXV: Privacy-Preserving Computation Layer

Secure Multi-Party Computation

PROXY Network implements general-purpose secure computation allowing parties to compute functions on private inputs without revealing those inputs.

Confidential Transaction Amounts

Zero-Knowledge Proof Integration

Part XXVI: Regulatory Compliance Framework

KYC/AML Integration

PROXY Network supports optional compliance layers for institutional users requiring regulatory compliance while preserving privacy through threshold cryptography.

Travel Rule Compliance

Sanctions Screening

Part XXVII: Dynamic Committee Architecture

Decentralized Agent Network

PROXY Network is a fully on-chain decentralized infrastructure where independent operators run agent nodes. Unlike centralized custody solutions, no single entity controls the network. Security derives from cryptographic thresholds and economic incentives, not trust in any operator.

Agent Registration Protocol

Committee Formation

Part XXVIII: Value-Based Security Scaling

Dynamic Committee Sizing

PROXY Network implements adaptive security where committee size scales with the value at risk. Higher-value wallets receive larger committees with stronger security guarantees, while lower-value wallets use smaller committees for efficiency.

Automatic Committee Resizing

Volume-Based Scaling for DeFi Applications

Part XXIX: Proactive Key Resharing Protocol

Key Share Redistribution

When committee membership changes (agents added, removed, or rotated), key shares must be redistributed without changing the public key or wallet address. PROXY implements proactive secret sharing to achieve this securely.

Committee Contraction

Periodic Key Rotation

On-Chain Resharing Verification

Part XXX: Performance and Scalability Architecture

106. Throughput Analysis

PROXY Network is designed to achieve 100,000+ signatures per second (SPS) while maintaining sub-200ms latency. This section provides rigorous mathematical analysis of the performance characteristics and the architectural decisions enabling this throughput.

107. FROST Protocol Implementation

FROST (Flexible Round-Optimized Schnorr Threshold signatures) reduces the communication complexity from O(n²) rounds to O(n) with a single online round, enabling sub-50ms signing latency.

108. BLS Signature Aggregation

For extreme throughput scenarios, PROXY supports BLS (Boneh-Lynn-Shacham) signatures enabling aggregation of multiple signatures into a single constant-size signature.

109. Parallel Committee Architecture

110. Latency Optimization

111. Hardware Acceleration

Part XXXI: Cost Economics and Fee Model

112. Cost Structure Analysis

113. Fee Model Design

114. Subscription and Stake-Based Access

115. Operator Economics

116. Batch Aggregation Economics

Part XXXII: Multi-Chain Signature Architecture

117. Universal Chain Support

PROXY Network provides native signature generation for all blockchain platforms through implementation of chain-specific threshold cryptographic protocols. This section formalizes the multi-chain signature architecture enabling a single wallet to transact across any blockchain.

118. Threshold ECDSA Protocol (GG20)

For Ethereum, BSC, Polygon, and all EVM-compatible chains, PROXY implements the GG20 (Gennaro-Goldfeder 2020) threshold ECDSA protocol with 4-round signing.

119. Threshold Ed25519 Protocol

120. Chain Address Derivation

Part XXXIII: On-Chain Decentralized Infrastructure

121. On-Chain Architecture Overview

PROXY Network is a fully on-chain decentralized protocol where all critical state, governance, and economics are enforced by smart contracts. This section details the on-chain components that guarantee decentralization and trustlessness.

122. Agent Registry Contract

123. Committee Manager Contract

124. Decentralization Guarantees

Part XVIII: Research Directions and Future Work

Post-Quantum Cryptography

Current threshold signature schemes rely on the hardness of ECDLP, which is vulnerable to quantum computers running Shor's algorithm. This section outlines our research roadmap for post-quantum security.

Lattice-Based Threshold Signatures

Zero-Knowledge Proofs Integration

Scalability Research

Asynchronous Threshold Signatures

Decentralized Agent Market

Cross-Chain Atomic Operations

Formal Verification Roadmap

Appendix C: References