SPHINCS+ (Digital Signatures)

SPHINCS+ is a hash-based post-quantum digital signature scheme offering conservative security assumptions and no reliance on algebraic problems.

Overview

SPHINCS+ provides:

• Conservative Security: Based only on hash function security
• No Algebraic Assumptions: Unlike lattice-based schemes
• Stateless Operation: No state management required
• Multiple Variants: Different security/performance tradeoffs

Security Model

SPHINCS+ security relies solely on:

• Hash Function Security: SHA-256 or SHAKE-256 collision resistance
• No Quantum Vulnerability: Hash functions remain secure against quantum attacks
• Proven Reduction: Security reduces to underlying hash function

Parameter Sets

Cypheron Core implements multiple SPHINCS+ variants:

SPHINCS+-SHA256 Variants

SPHINCS+-SHAKE256 Variants

Basic Usage

Key Generation

#![allow(unused)]
fn main() {
use cypheron_core::sig::{SphincsPlusSha256128s, DigitalSignature};

// Generate a new keypair
let (public_key, secret_key) = SphincsPlusSha256128s::keypair()?;
}

Message Signing

#![allow(unused)]
fn main() {
let message = b"SPHINCS+ hash-based signature";

// Sign the message
let signature = SphincsPlusSha256128s::sign(&secret_key, message)?;
}

Signature Verification

#![allow(unused)]
fn main() {
// Verify the signature
let is_valid = SphincsPlusSha256128s::verify(&public_key, message, &signature)?;
assert!(is_valid);
}

Variant Selection

Small vs Fast Variants

#![allow(unused)]
fn main() {
use cypheron_core::sig::{SphincsPlusSha256128s, SphincsPlusSha256128f};

// Small signature variant (slower, smaller signatures)
let (pk_s, sk_s) = SphincsPlusSha256128s::keypair()?;
let sig_s = SphincsPlusSha256128s::sign(&sk_s, message)?;
println!("Small signature: {} bytes", sig_s.len());

// Fast variant (faster, larger signatures)  
let (pk_f, sk_f) = SphincsPlusSha256128f::keypair()?;
let sig_f = SphincsPlusSha256128f::sign(&sk_f, message)?;
println!("Fast signature: {} bytes", sig_f.len());
}

SHA-256 vs SHAKE-256

#![allow(unused)]
fn main() {
use cypheron_core::sig::{SphincsPlusSha256128s, SphincsPlusShake256128s};

// SHA-256 based variant
let (pk_sha, sk_sha) = SphincsPlusSha256128s::keypair()?;

// SHAKE-256 based variant
let (pk_shake, sk_shake) = SphincsPlusShake256128s::keypair()?;

// Both provide equivalent security, choose based on:
// - SHA-256: Wider acceptance, NIST standard
// - SHAKE-256: More flexible, part of SHA-3 family
}

Advanced Usage

Deterministic Key Generation

#![allow(unused)]
fn main() {
use cypheron_core::sig::SphincsPlusSha256128s;

// Generate keypair from seed
let seed = [0u8; 48];  // SPHINCS+ uses variable seed lengths
let (pk, sk) = SphincsPlusSha256128s::keypair_deterministic(&seed)?;
}

Context Separation

#![allow(unused)]
fn main() {
// Sign with context for domain separation
let context = b"document-signing-v2";
let signature = SphincsPlusSha256128s::sign_with_context(&secret_key, message, context)?;
let is_valid = SphincsPlusSha256128s::verify_with_context(&public_key, message, &signature, context)?;
}

Security Considerations

Conservative Security Model

• No Algebraic Assumptions: Security doesn’t depend on lattice problems
• Post-Quantum Safe: Hash functions remain secure against quantum computers
• Proven Security: Well-understood cryptographic foundations

Recommended Usage

• Use 128s variants for applications requiring smaller signatures
• Use 128f variants for applications requiring faster signing
• Use 192s/256s for higher security requirements
• Choose SHA-256 for maximum compatibility

Key Management

#![allow(unused)]
fn main() {
use secrecy::{ExposeSecret, Zeroize};

// Secret keys automatically zeroized on drop
impl Drop for SphincsSecretKey {
    fn drop(&mut self) {
        self.0.zeroize();
    }
}

// Safe secret key access
secret_key.expose_secret(|key_bytes| {
    SphincsPlusSha256128s::sign_with_raw_key(key_bytes, message)
})
}

Performance Characteristics

Typical Performance (x86_64, 3.0 GHz)

Memory Usage

• Small key sizes (32-128 bytes)
• Large signature sizes (7KB-50KB)
• Stack-based operations, no heap allocation

Error Handling

Common Errors

#![allow(unused)]
fn main() {
use cypheron_core::error::Error;

match SphincsPlusSha256128s::verify(&public_key, message, &signature) {
    Ok(true) => println!("Valid signature"),
    Ok(false) => println!("Invalid signature"),
    Err(Error::InvalidPublicKey) => println!("Malformed public key"),
    Err(Error::InvalidSignature) => println!("Malformed signature"),
    Err(Error::HashingFailed) => println!("Internal hash computation failed"),
    Err(e) => println!("Other error: {}", e),
}
}

Interoperability

NIST Compliance

• Implements NIST Round 3 SPHINCS+ specification
• Compatible with reference implementations
• Passes all official test vectors

Serialization

#![allow(unused)]
fn main() {
// Serialize keys and signatures
let pk_bytes = public_key.as_bytes();
let sk_bytes = secret_key.expose_secret(|bytes| bytes.to_vec());
let sig_bytes = signature.as_bytes();

// Deserialize from bytes
let public_key = SphincsPublicKey::from_bytes(&pk_bytes)?;
let signature = SphincsSignature::from_bytes(&sig_bytes)?;
}

Comparison with Other Schemes

SPHINCS+ vs Lattice-Based Schemes

Use Case Recommendations

• Choose SPHINCS+ for maximum conservative security
• Choose ML-DSA for practical performance and NIST standardization
• Choose Falcon for compact signatures
• Consider hybrid for transition periods

Hybrid Usage

SPHINCS+ can be combined with other schemes:

#![allow(unused)]
fn main() {
use cypheron_core::hybrid::EccSphincs;

// Hybrid ECDSA + SPHINCS+ signature
let (hybrid_pk, hybrid_sk) = EccSphincs::keypair()?;
let hybrid_sig = EccSphincs::sign(&hybrid_sk, message)?;
let is_valid = EccSphincs::verify(&hybrid_pk, message, &hybrid_sig)?;
}

Implementation Details

Hash-Based Construction

• Built on one-way hash functions and Merkle trees
• Uses WOTS+ (Winternitz One-Time Signature Plus)
• XMSS-style tree authentication
• No state management required (stateless)

Parameter Selection

• “s” variants: Optimize for smaller signatures
• “f” variants: Optimize for faster operations
• Security levels: 128, 192, 256-bit equivalent security
• Hash functions: SHA-256 or SHAKE-256

See Also

• ML-DSA Digital Signatures - Lattice-based alternative
• Falcon Digital Signatures - Compact lattice-based signatures
• Hybrid Cryptography - Combining schemes
• Security Model - Security considerations