3.1 Public Key Cryptography in Onion Ecosystems

Public Key Cryptography (PKC) is the mathematical backbone of onion networks such as Tor, I2P, and modern mixnets.
Without public key systems, anonymity networks could not securely establish trust, negotiate session keys, authenticate services, or protect identities in hostile environments.

This chapter explains what role public key cryptography plays, where it is used, and why onion ecosystems depend on it, using accepted cryptographic and networking literature.

A. Why Public Key Cryptography Is Essential to Onion Networks

Onion networks operate in an environment where:

• participants do not trust each other

• nodes are run by volunteers

• adversaries may control parts of the network

• communication paths change frequently

Public key cryptography solves four fundamental problems:

1. Secure key exchange over untrusted networks

2. Authentication without revealing identity

3. Self-authenticating service addresses

4. Forward secrecy for past communications

Without PKC, onion routing would collapse into either:

• insecure plaintext routing, or

• centralized trust authorities (which anonymity networks avoid)

B. Core Concept: Public Key vs Private Key (Quick Refresher)

Public key cryptography uses a key pair:

• Public key

  • Shared openly

  • Used to encrypt data or verify signatures

• Private key

  • Kept secret

  • Used to decrypt data or create signatures

In onion ecosystems, public keys replace real-world identity.
A cryptographic key is the identity.

C. Where Public Key Cryptography Is Used in Onion Networks

Public key cryptography appears at multiple architectural layers.

1. Relay Identity Authentication

Each relay in Tor has:

• a long-term identity key

• a signing key

• short-term onion keys

These keys allow:

• verification that a relay is genuine

• protection against relay impersonation

• secure relay-to-relay communication

Relays publish signed descriptors so clients can verify authenticity without knowing who operates the relay.

2. Circuit Key Negotiation (Client ↔ Relay)

When a Tor client builds a circuit:

1. It retrieves relay public keys

2. It performs a Diffie–Hellman key exchange with each relay

3. A unique symmetric session key is created per hop

Public key cryptography is used only to bootstrap trust.
After that, faster symmetric cryptography takes over.

This design balances:

• strong security

• acceptable performance

3. Onion Encryption Layers

Each encryption layer corresponds to a different relay’s public key.

Conceptually:

• Outer layer → guard relay public key

• Middle layer → middle relay public key

• Inner layer → exit relay public key

Each relay can decrypt only its own layer, because only it holds the corresponding private key.

This layered PKC structure is what makes onion routing possible.

4. Onion Services (.onion) Identity

In Tor v3 onion services:

• the .onion address is derived from a public key

• the address itself is a cryptographic commitment

This is known as self-authenticating naming.

Implications:

• no DNS authority

• no certificate authority

• no third-party trust

• phishing resistance (you cannot fake a key-derived address)

Public key cryptography replaces the entire web PKI model.

D. Cryptographic Algorithms Used in Onion Ecosystems

Different onion networks use different algorithms, but all follow modern cryptographic standards.

1. RSA (Legacy, Mostly Deprecated)

• Used in early Tor (v2 hidden services)

• 1024-bit RSA is now considered weak

• Replaced due to performance and security concerns

2. Elliptic Curve Cryptography (ECC)

Modern onion systems prefer ECC because it offers:

• shorter keys

• faster computation

• equivalent or stronger security

Examples:

• Curve25519 (key exchange)

• Ed25519 (signatures)

Tor v3 onion services rely heavily on Ed25519.

3. Diffie–Hellman Key Exchange

Used to:

• establish shared secrets

• ensure Perfect Forward Secrecy (PFS)

Even if a private key is compromised later, past sessions remain secure.

4. Digital Signatures

Used to:

• authenticate relays

• sign directory information

• validate onion service descriptors

Signatures prove authenticity, not identity.

E. Trust Model: Cryptography Instead of Identity

Onion networks deliberately avoid:

• usernames

• passwords

• government identity

• real-world attribution

Instead, trust is established through:

• cryptographic proofs

• signed data structures

• consensus documents

This model is called trust by verification, not trust by authority.

F. Public Key Cryptography vs Traditional Web Security

Onion ecosystems intentionally remove centralized trust points.

G. Security Properties Achieved Through PKC

Public key cryptography enables onion networks to achieve:

1. Confidentiality — encrypted communication

2. Authentication — verifying relays and services

3. Integrity — data cannot be altered unnoticed

4. Forward Secrecy — past traffic remains protected

5. Unlinkability — identity separated from routing

These properties are repeatedly validated in academic security analysis.

H. Limitations and Challenges

Despite its strengths, PKC introduces challenges:

1. Computational cost
   Public key operations are slower than symmetric crypto.

2. Key management complexity
   Rotation, expiration, and revocation must be handled carefully.

3. Post-Quantum Threats
   Future quantum computers could break some public key schemes.

This is why modern onion ecosystems are exploring post-quantum cryptography, discussed in later chapters.

I. Why Public Key Cryptography Is Non-Negotiable

Onion ecosystems cannot rely on:

• shared secrets

• pre-established trust

• centralized authorities

Public key cryptography is the only scalable solution that allows:

• anonymous participation

• decentralized trust

• cryptographic identity

• resistance to surveillance

It is the foundation upon which every higher-layer anonymity mechanism is built.