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Falcon is a cryptographic signature algorithm submitted to NIST Post-Quantum Cryptography Project on November 30th, 2017. It has been designed by: Pierre-Alain Fouque, Jeffrey Hoffstein, Paul Kirchner, Vadim Lyubashevsky, Thomas Pornin, Thomas Prest, Thomas Ricosset, Gregor Seiler, William Whyte, Zhenfei Zhang. The point of a post-quantum cryptographic algorithm is to keep on ensuring its security characteristics even faced with quantum computers. Quantum computers are deemed feasible, according to our current understanding of the laws of physics, but some significant technological issues remain to be solved in order to build a fully operational unit. Such a quantum computer would very efficiently break the usual asymmetric encryption and digital signature algorithms based on number theory (RSA, DSA, Diffie-Hellman, ElGamal, and their elliptic curve variants). Falcon offers the following features: Security: a true Gaussian sampler is used internally, which guarantees negligible leakage of information on the secret key up to a practically infinite number of signatures (more than 264). Compactness: thanks to the use of NTRU lattices, signatures are substantially shorter than in any lattice-based signature scheme with the same security guarantees, while the public keys are around the same size. Speed: use of fast Fourier sampling allows for very fast implementations, in the thousands of signatures per second on a common computer; verification is five to ten times faster. Scalability: operations have cost O(n log n) for degree n, allowing the use of very long-term security parameters at moderate cost. RAM Economy: the enhanced key generation algorithm of Falcon uses less than 30 kilobytes of RAM, a hundredfold improvement over previous designs such as NTRUSign. Falcon is compatible with small, memory-constrained embedded devices.