SPHINCS+ Signatures Explained: Post-Quantum Digital Signatures

🔏 Quick Facts About SPHINCS+

• Official Name: SLH-DSA (FIPS 205)
• Type: Stateless Hash-Based Signature
• Security Basis: Hash functions only (SHAKE, SHA-256)
• Standardized: August 2024 by NIST
• SynX Variant: SPHINCS+-SHAKE-128f

How SPHINCS+ Works

SPHINCS+ creates signatures using a hierarchy of one-time signature (OTS) schemes organized in Merkle trees. Here's the conceptual structure:

1. Hypertree – Multiple layers of Merkle trees for authentication
2. XMSS Trees – Extended Merkle Signature Scheme trees at each layer
3. FORS – Few-time Signature scheme at the bottom for message signing
4. WOTS+ – Winternitz One-Time Signatures for tree nodes

Why Hash-Based = Quantum-Safe

The security of SPHINCS+ depends only on hash function properties:

• Pre-image resistance – Can't find input from hash output
• Second pre-image resistance – Can't find colliding input
• Collision resistance – Can't find any two colliding inputs

Quantum computers can use Grover's algorithm to speed up hash attacks, but this only halves the security level (e.g., 256-bit → 128-bit). SPHINCS+ parameters account for this, maintaining full security against quantum adversaries.

SPHINCS+ vs ECDSA vs Dilithium

Feature	SPHINCS+	ECDSA	Dilithium
Quantum Resistant	✅ Yes	❌ No	✅ Yes
Security Basis	Hash functions	ECDLP	Lattices
NIST Approved	✅ FIPS 205	✅ (legacy)	✅ FIPS 204
Signature Size	~17-50 KB	64 bytes	~2.4 KB
Signing Speed	Slower	Fast	Fast
Security Assumptions	Minimal (hashes)	ECDLP hard	MLWE hard

Why SynX Chose SPHINCS+

SynX uses SPHINCS+ despite larger signature sizes because:

• Conservative security – Relies only on well-studied hash functions
• No structured lattice assumptions – Lattice cryptography is newer
• Battle-tested primitives – Hash functions have decades of analysis
• Future-proof – Even if lattice attacks improve, SPHINCS+ remains safe

SPHINCS+ Technical Specifications

Parameter (SPHINCS+-SHAKE-128f)	Value
Security Level	NIST Level 1 (128-bit)
Public Key Size	32 bytes
Secret Key Size	64 bytes
Signature Size	17,088 bytes
Hash Function	SHAKE-128
Tree Height	66 (total)

Frequently Asked Questions