NTRU: A ring-based public key cryptosystem. We describe NTRU, a new public key cryptosystem. NTRU features reasonably short, easily created keys, high speed, and low memory requirements. NTRU encryption and decryption use a mixing system suggested by polynomial algebra combined with a clustering principle based on elementary probability theory. The security of the NTRU cryptosystem comes from the interaction of the polynomial mixing system with the independence of reduction modulo two relatively prime integers p and q.

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  1. Shao, Changpeng; Li, Yang; Li, Hongbo: Quantum algorithm design: techniques and applications (2019)
  2. Bagheri, Khadijeh; Sadeghi, Mohammad-Reza; Panario, Daniel: A non-commutative cryptosystem based on quaternion algebras (2018)
  3. Bauch, Jens; Bernstein, Daniel J.; de Valence, Henry; Lange, Tanja; van Vredendaal, Christine: Short generators without quantum computers: the case of multiquadratics (2017)
  4. Biasse, Jean-François; Espitau, Thomas; Fouque, Pierre-Alain; Gélin, Alexandre; Kirchner, Paul: Computing generator in cyclotomic integer rings. A subfield algorithm for the principal ideal problem in (L_|\varDelta_\mathbbK|\left(\frac12\right)) and application to the cryptanalysis of a FHE scheme (2017)
  5. Cramer, Ronald; Ducas, Léo; Wesolowski, Benjamin: Short Stickelberger class relations and application to Ideal-SVP (2017)
  6. Hoffstein, Jeff; Pipher, Jill; Schanck, John M.; Silverman, Joseph H.; Whyte, William; Zhang, Zhenfei: Choosing parameters for NTRUEncrypt (2017)
  7. Kim, Jeongsu; Park, Suyong; Kim, Seonggeun; Jang, Busik; Hahn, Sang Geun; Jung, Sangim; Roh, Dongyoung: Analysis of error terms of signatures based on learning with errors (2017)
  8. Kirchner, Paul; Fouque, Pierre-Alain: Revisiting lattice attacks on overstretched NTRU parameters (2017)
  9. López-Alt, Adriana; Tromer, Eran; Vaikuntanathan, Vinod: Multikey fully homomorphic encryption and applications (2017)
  10. Lyubashevsky, Vadim; Neven, Gregory: One-shot verifiable encryption from lattices (2017)
  11. Yasuda, Masaya; Yokoyama, Kazuhiro; Shimoyama, Takeshi; Kogure, Jun; Koshiba, Takeshi: Analysis of decreasing squared-sum of Gram-Schmidt lengths for short lattice vectors (2017)
  12. Yu, Yang; Xu, Guangwu; Wang, Xiaoyun: Provably secure NTRU instances over prime cyclotomic rings (2017)
  13. Albrecht, Martin; Bai, Shi; Ducas, Léo: A subfield lattice attack on overstretched NTRU assumptions. Cryptanalysis of some FHE and graded encoding schemes (2016)
  14. Buchmann, Johannes A.; Butin, Denis; Göpfert, Florian; Petzoldt, Albrecht: Post-quantum cryptography: state of the art (2016)
  15. Castryck, Wouter; Iliashenko, Ilia; Vercauteren, Frederik: On error distributions in ring-based LWE (2016)
  16. Cheon, Jung Hee; Jeong, Jinhyuck; Lee, Changmin: An algorithm for NTRU problems and cryptanalysis of the GGH multilinear map without a low-level encoding of zero (2016)
  17. Chung, Kyungmi; Lee, Hyang-Sook; Lim, Seongan: An efficient lattice reduction using reuse technique blockwisely on NTRU (2016)
  18. Costello, Craig; Longa, Patrick; Naehrig, Michael: Efficient algorithms for supersingular isogeny Diffie-Hellman (2016)
  19. del Pino, Rafael; Lyubashevsky, Vadim; Pointcheval, David: The whole is less than the sum of its parts: constructing more efficient lattice-based AKEs (2016)
  20. Doröz, Yarkın; Hu, Yin; Sunar, Berk: Homomorphic AES evaluation using the modified LTV scheme (2016)

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