Security Assumptions

Cryptographic assumptions underlying QNSP's PQC primitives.

Lattice-based (Kyber, Dilithium)

Module Learning With Errors (MLWE)

• Finding short vectors in module lattices is hard
• Even with quantum computers
• Well-studied since 2005

Security reductions

• Kyber: IND-CCA2 security from MLWE
• Dilithium: EUF-CMA security from MLWE + SelfTargetMSIS

Hash-based (SPHINCS+)

Hash function security

• Collision resistance
• Second preimage resistance
• PRF security

Minimal assumptions

• Only relies on hash function properties
• Most conservative choice

NTRU-based (Falcon)

NTRU assumption

• Finding short vectors in NTRU lattices is hard
• Older than MLWE (1996)
• Different mathematical structure

Quantum security levels

NIST Level	Equivalent to	Quantum security
1	AES-128	64-bit quantum
3	AES-192	96-bit quantum
5	AES-256	128-bit quantum

Known attacks

Lattice attacks

• BKZ algorithm
• Primal/dual attacks
• Hybrid attacks

Mitigation

• Conservative parameter selection
• Regular security analysis review
• Algorithm agility for migration

QNSP's position

• Use NIST Level 3 by default
• Monitor cryptanalysis developments
• Maintain algorithm agility
• Hybrid mode for defense in depth