NTRU
Definition
NTRU is one of the earliest lattice-based public-key cryptosystems, introduced in 1996. Using polynomial rings with efficient operations, NTRU provides encryption and signatures resistant to quantum attacks. NTRU's mathematical foundation influenced FALCON and other modern lattice schemes.
Technical Explanation
NTRU operates in the polynomial ring Z[x]/(xⁿ - 1). Key generation creates polynomials f and g with small coefficients; the public key is h = g/f mod q. Encryption multiplies the message by h and adds blinding. The trapdoor (knowing f) enables efficient decryption.
NTRU's security relies on the hardness of finding short vectors in NTRU lattices—a specific lattice structure. Unlike LWE-based schemes, NTRU doesn't add explicit noise but uses the polynomial structure for security. FALCON uses NTRU lattices for signature generation.
SynX Relevance
While SynX uses Kyber (Module-LWE based) rather than NTRU directly, the lattice cryptography heritage connects them. NTRU's decades of study contributed to confidence in lattice-based approaches. FALCON availability in SynX's architecture uses NTRU foundations for compact signatures.
Frequently Asked Questions
- Is NTRU NIST-standardized?
- NTRU influenced FALCON (selected for standardization) but wasn't directly standardized as a KEM.
- NTRU vs Kyber—which is better?
- Both are secure; Kyber's Module-LWE has stronger theoretical foundations while NTRU has longer history.
- How old is NTRU?
- Introduced in 1996—nearly 30 years of cryptanalysis with no practical breaks.
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