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NTRU is a patented and open source public-key cryptosystem that uses lattice-based cryptography to encrypt and decrypt data. It consists of two algorithms: NTRUEncrypt, which is used for encryption, and NTRUSign, which is used for digital signatures. Unlike other popular public-key cryptosystems, it is resistant to attacks using Shor's algorithm and its performance has been shown to be significantly better.


The first version of the system, which was called NTRU, was developed in 1996 by mathematicians Jeffrey Hoffstein (de), Jill Pipher, and Joseph H. Silverman. That same year, the developers of NTRU joined with Daniel Lieman and founded the NTRU Cryptosystems, Inc., and were given a patent on the cryptosystem.[1] In 2009, the company was acquired by Security Innovation, a software security company.[2] In 2013, Damien Stehle and Ron Steinfeld created a provably secure version of NTRU which is being studied by a post quantum crypto group chartered by the European Commission.[3]

In May 2016, Daniel Bernstein, Chitchanok Chuengsatiansup, Tanja Lange and Christine van Vredendaal released NTRU Prime,[4] which adds defenses against potential attack to NTRU by eliminating worrisome algebraic structure.


At equivalent cryptographic strength, NTRU performs costly private key operations much faster than RSA does.[5] The time of performing an RSA private operation increases as the cube of the key size, whereas that of an NTRU operation increases quadratically.

According to the Department of Electrical Engineering, University of Leuven, "[using] a modern GTX280 GPU, a throughput of up to 200 000 encryptions per second can be reached at a security level of 256 bits. Comparing this to a symmetric cipher (not a very common comparison), this is only around 20 times slower than a recent AES implementation."[6]

Resistance to quantum-computer-based attacks[edit]

Unlike RSA and Elliptic Curve Cryptography, NTRU is not known to be vulnerable to quantum computer based attacks. The National Institute of Standards and Technology wrote in a 2009 survey that "[there] are viable alternatives for both public key encryption and signatures that are not vulnerable to Shor’s Algorithm” and “[of] the various lattice based cryptographic schemes that have been developed, the NTRU family of cryptographic algorithms appears to be the most practical".[7] The European Union's PQCRYPTO project (Horizon 2020 ICT-645622) is evaluating the provably secure Stehle–Steinfeld version of NTRU (not original NTRU algorithm itself) as a potential European standard.[3] However the Stehle-Steinfeld version of NTRU is "significantly less efficient than the original scheme."[8]


  • The standard IEEE Std 1363.1, issued in 2008, standardizes lattice-based public key cryptography, especially NTRUEncrypt.[9]
  • The standard X9.98 standardizes lattice-based public key cryptography, especially NTRUEncrypt, as part of the X9 standards for the financial services industry.[10]
  • The PQCRYPTO project of the European Commission is considering standardization of the provably secure Stehle-Steinfeld version of NTRU[8]


Originally, NTRU was only available as a proprietary, for-pay library and open source authors were threatened with legal action.[11][12] It was not until 2011 that the first open-source implementation appeared,[13] and in 2013, Security Innovation exempted open source projects from having to get a patent license,[14] and released an NTRU reference implementation under the GPL v2.[15]

The proprietary, for-pay option is still offered by Security Innovation.[16]

Three open-source NTRU implementations now exist:

  • The GPL-licensed reference implementation[15]
  • A BSD-licensed library[13]
  • bouncycastle [17]

Each is available in Java and C.


  1. ^ Robertson, Elizabeth D. (August 1, 2002). "RE: NTRU Public Key Algorithms IP Assurance Statement for 802.15.3" (PDF). IEEE. Retrieved February 4, 2013. 
  2. ^ Robinson, Maureen (July 22, 2009). "Security Innovation acquires NTRU Cryptosystems, a leading security solutions provider to the embedded security market" (Press release). Wilmington, MA: Security Innovation. Retrieved February 4, 2013. 
  3. ^ a b Lange, Tanja (1 March 2015). "Initial recommendations of long-term secure post-quantum systems" (PDF). PQCRYPTO.EU. Horizon 2020 ICT-645622. Retrieved 18 January 2015. 
  4. ^ https://ntruprime.cr.yp.to/ntruprime-20160511.pdf
  5. ^ "NTRU: Quantum-Resistant High Performance Cryptography". 
  6. ^ Hermans, Jens; Vercauteren, Frederik; Preneel, Bart (2010). Pieprzyk, Josef, ed. "Speed Records for NTRU" (PDF). Topics in Cryptography – CT-RSA 2010. Lecture Notes in Computer Science. San Francisco, CA: Springer Berlin Heidelberg. 5985: 73–88. doi:10.1007/978-3-642-11925-5_6. ISBN 978-3-642-11924-8. ISSN 0302-9743. Retrieved February 4, 2013. 
  7. ^ Perlner, Ray A.; Cooper, David A. (2009). Seamons, Kent; McBurnett, Neal; Polk, Tim, eds. "Quantum resistant public key cryptography: a survey" (PDF). Proceedings of the 8th Symposium on Identity and Trust on the Internet. New York, NY: ACM: 85–93. doi:10.1145/1527017.1527028. ISBN 978-1-60558-474-4. Retrieved February 3, 2013. 
  8. ^ a b "Cryptology ePrint Archive: Report 2013/004". eprint.iacr.org. Retrieved 2016-01-18. 
  9. ^ "IEEE P1363: Standard Specifications For Public Key Cryptography". Grouper.ieee.org. Retrieved 7 December 2014. 
  10. ^ "Security Innovation's NTRUEncrypt Adopted as X9 Standard for Data Protection - Business Wire". Businesswire.com. Retrieved 7 December 2014. 
  11. ^ "Statement by the libtomcrypt (LTC) author". 
  12. ^ "Email exchange between Security Innovation and a software author". 
  13. ^ a b Buktu, Tim. "NTRU: Quantum-Resistant cryptography". Independent / not affiliated with NTRU Cryptosystems, Inc. Retrieved February 4, 2013. 
  14. ^ "FOSS Exception". 
  15. ^ a b "Open Source NTRU Public Key Cryptography and Reference Code". 
  16. ^ "Security Innovation - NTRU Cryptography". 
  17. ^ "-ext-". Independent / not affiliated with NTRU Cryptosystems, Inc. Retrieved February 13, 2016. 

External links[edit]