Design choices

The designers of NewHope made several choices in developing the algorithm:^[6]

Binomial Sampling: Although sampling to high-quality discrete Gaussian distribution is important in post-quantum lattice-based compact signature scheme such as Falcon (GPV-style Hash-and-Sign paradigm) and BLISS (GLP-style Fiat–Shamir paradigm) to prevent signature from leaking information about the private key, it's otherwise not so essential to key exchange schemes. The author chose to sample error vectors from binomial distribution.
Error Reconciliation: What distinguishes NewHope from its predecessors is its method for error reconciliation. Previous ring learning with error key exchange schemes correct errors one coefficient at a time, whereas NewHope corrects errors 2 or 4 coefficients at a time based on high-dimension geometry. This allows for lower decryption failure rate and higher security.
Base Vector Generation: The authors of NewHope proposed deriving the base "generator" vector (commonly denoted as A or $a$ ) from the output of the XOF function SHAKE-128 in order to prevent "back-doored" values from being used, as may happen with traditional Diffie–Hellman through Logjam attack.
Security Levels: In the early versions of the papers describing NewHope, authors proposed using 1024-degree polynomial for 128-bit "post-quantum" security level, and a 512-degree polynomial as "toy" instance for cryptanalysis challenge.^[7] In the version submitted to NIST, the 512-degree version is codified to provide 128-bit "classical" security level.

References

Public-key cryptography

Algorithms

Integer factorization	Benaloh Blum–Goldwasser Cayley–Purser Damgård–Jurik GMR Goldwasser–Micali Naccache–Stern Paillier Rabin RSA Okamoto–Uchiyama Schmidt–Samoa
Discrete logarithm	BLS Cramer–Shoup DH DSA ECDH X25519 X448 ECDSA EdDSA Ed25519 Ed448 ECMQV EKE ElGamal signature scheme MQV Schnorr SPEKE SRP STS
Lattice/SVP/CVP/LWE/SIS	BLISS Kyber NewHope NTRUEncrypt NTRUSign RLWE-KEX RLWE-SIG
Others	AE CEILIDH EPOC HFE IES Lamport McEliece Merkle–Hellman Naccache–Stern knapsack cryptosystem Three-pass protocol XTR

Theory

Standardization

Topics

v t e Cryptography
General	History of cryptography Outline of cryptography Cryptographic protocol Authentication protocol Cryptographic primitive Cryptanalysis Cryptocurrency Cryptosystem Cryptographic nonce Cryptovirology Hash function Cryptographic hash function Key derivation function Digital signature Kleptography Key (cryptography) Key exchange Key generator Key schedule Key stretching Keygen Cryptojacking malware Ransomware Random number generation Cryptographically secure pseudorandom number generator (CSPRNG) Pseudorandom noise (PRN) Secure channel Insecure channel Subliminal channel Encryption Decryption End-to-end encryption Harvest now, decrypt later Information-theoretic security Plaintext Codetext Ciphertext Shared secret Trapdoor function Trusted timestamping Key-based routing Onion routing Garlic routing Kademlia Mix network
Mathematics	Cryptographic hash function Block cipher Stream cipher Symmetric-key algorithm Authenticated encryption Public-key cryptography Quantum key distribution Quantum cryptography Post-quantum cryptography Message authentication code Random numbers Steganography
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