NTRUstyle

NTRUstyle is an informal label used in cryptography discussions to describe a family of public-key cryptosystems and design patterns that trace their roots to NTRUEncrypt, a lattice-based scheme introduced in the 1990s. The term is not an official standard, and its precise meaning varies by author. In general, NTRUstyle refers to schemes that operate on polynomials over a finite ring, typically Zq[x]/(x^N − 1) or Zq[x]/(x^N + 1), with small coefficient polynomials. Key generation, encryption, and decryption in these schemes resemble fast, convolution-like operations rather than large-integer modular arithmetic.

Core characteristics of NTRUstyle designs include the use of a polynomial ring structure, small-norm private polynomials, and public keys derived from convolutions of polynomials with small coefficients. Multiplication is implemented efficiently via fast polynomial arithmetic, enabling rapid key agreement or encryption. Parameters are chosen to balance security against known lattice-based attacks with practicality for software and hardware implementations. The security basis typically involves hard lattice problems in the underlying NTRU lattice, with reductions or heuristics guiding parameter selection.

NTRUstyle has produced several real-world variants and descendants, most notably NTRUEncrypt and the newer NTRU Prime, which aim to address specific structural weaknesses and quantum-era considerations. The term remains primarily descriptive and heuristic, used to categorize schemes sharing the same polynomial-ring and lattice-based design ethos rather than to denote a formal cryptographic standard.

See also: NTRUEncrypt, NTRU Prime, lattice-based cryptography, ring-learning-with-errors.