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The NTRUEncrypt public key cryptosystem, also known as the NTRU encryption algorithm, is a lattice-based alternative to RSA and ECC and is based on the shortest vector problem in a lattice (which is not known to be breakable using quantum computers). It relies on the presumed difficulty of factoring certain polynomials in a truncated polynomial ring into a quotient of two polynomials having very small coefficients. Breaking the cryptosystem is strongly related, though not equivalent, to the algorithmic problem of lattice reduction in certain lattices. Careful choice of parameters is necessary to thwart some published attacks. Since both encryption and decryption use only simple polynomial multiplication, these operations are very fast compared to other asymmetric encryption schemes, such as RSA, ElGamal and elliptic curve cryptography. However, NTRUEncrypt has not yet undergone a comparable amount of cryptographic analysis. A related algorithm is the NTRUSign digital signature algorithm. Specifically, NTRU operations are based on objects in a truncated polynomial ring with convolution multiplication and all polynomials in the ring have integer coefficients and degree at most ''N''-1: : NTRU is actually a parameterised family of cryptosystems; each system is specified by three integer parameters (''N'', ''p'', ''q'') which represent the maximal degree for all polynomials in the truncated ring ''R'', a small modulus and a large modulus, respectively, where it is assumed that ''N'' is prime, ''q'' is always larger than ''p'', and ''p'' and ''q'' are coprime; and four sets of polynomials and (a polynomial part of the private key, a polynomial for generation of the public key, the message and a blinding value, respectively), all of degree at most . ==History== The NTRUEncrypt Public Key Cryptosystem is a relatively new cryptosystem. The first version of the system, which was simply called NTRU, was developed around 1996 by three mathematicians (, Jill Pipher, and Joseph H. Silverman). In 1996 these mathematicians together with Daniel Lieman founded the NTRU Cryptosystems, Inc. and were given a patent〔 US Patent 6081597 - Public key cryptosystem method and apparatus〕 on the cryptosystem. During the last ten years people have been working on improving the cryptosystem. Since the first presentation of the cryptosystem, some changes were made to improve both the performance of the system and its security. Most performance improvements were focussed on speeding up the process. Up till 2005 literature can be found that describes the decryption failures of the NTRUEncrypt. As for security, since the first version of the NTRUEncrypt, new parameters have been introduced that seem secure for all currently known attacks and reasonable increase in computation power. Now the system is fully accepted to IEEE P1363 standards under the specifications for lattice-based public-key cryptography (IEEE P1363.1). Because of the speed of the NTRUEncrypt Public Key Cryptosystem (see http://bench.cr.yp.to for benchmarking results) and its low memory use (see below), it can be used in applications such as mobile devices and Smart-cards. In April 2011, NTRUEncrypt was accepted as a X9.98 Standard, for use in the financial services industry.〔http://www.businesswire.com/news/home/20110411005309/en/Security-Innovation%E2%80%99s-NTRUEncrypt-Adopted-X9-Standard-Data〕 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「NTRUEncrypt」の詳細全文を読む スポンサード リンク
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