up:: [[Post-Quantum Cryptography (PQC)]] # FALCON FALCON (Fast-Fourier Lattice-based Compact Signatures over NTRU) is a [[digital signature]] scheme that's designed to be resistant to [[Quantum Computing|quantum computer]] attacks. Rooted in [[lattice-based cryptography]], it's specifically built upon the NTRUEncrypt and NTRUSign constructions. FALCON is among the finalists in the NIST [[Post-Quantum Cryptography (PQC)]] standardization project. ## Key Concepts - **[[Post-Quantum Cryptography (PQC)]]**: Cryptographic methods envisioned to be secure against potential threats posed by [[Quantum Computing|quantum computers]]. - **[[Lattice-Based Cryptography]]**: A form of [[cryptography]] relying on the complexity of lattice problems to ensure security. - **NTRU**: A set of cryptographic constructions that have been around since the 1990s, encompassing both encryption (NTRUEncrypt) and signature (NTRUSign) schemes. ## Features 1. **Compact Signatures**: FALCON is optimized to produce relatively small signature sizes, making it efficient for many practical applications. 2. **Performance**: FALCON boasts high-speed signing and verification processes. 3. **Quantum Security**: Crafted with quantum threats in mind, it's expected to offer a solid level of security even in a post-quantum scenario. ## Real-world Importance - **NIST [[Post-Quantum Cryptography (PQC)|PQC]] Standardization**: FALCON's shortlisting in the NIST post-quantum cryptographic standardization process indicates its potential as a trustworthy scheme in the forthcoming post-quantum age. ## Implementation - **Noise and Errors**: Like other lattice-based systems, FALCON integrates the concept of noise into its design, essential for its security. - **Fast Fourier Transforms (FFT)**: These are employed to speed up polynomial multiplications, lending FALCON its "Fast-Fourier" designation and boosting its efficiency. ## Challenges 1. **Implementation Security**: Practical deployment of lattice-based cryptosystems like FALCON necessitates careful consideration to sidestep potential side-channel attacks. 2. **Public Perception**: As with all newer cryptographic methods, convincing the broader public and industries of its reliability can be challenging. ## Related Concepts - **[[Lattice-Based Cryptography]]**: The broader domain where FALCON belongs, characterized by cryptographic solutions originating from lattice-related problems. - **[[Post-Quantum Cryptography (PQC)]]**: The wider field working on cryptographic techniques that remain secure in the face of quantum adversaries.