Alice and Bob decide to communicate using NTRUEncrypt with parameters (N, p, q) = (7, 3, 29). Alice’s public key is h(x) = 3 + 14X − 4X2 + 13X3 − 6X4 + 2X5 + 7X6 . Bob sends Alice the plaintext message m(x)= 1+ X − X2 − X3 − X6 using the random element r(x) = −1 + X2 − X5 + X6.

(a) What ciphertext does Bob send to Alice?

(b) Alice’s private key is f(x) = −1 + X − X2 + X4 + X6 and F 3(x)=1+ X + X2 + X4 + X5 − X6. Check your answer in (a) by using f and F 3 to decrypt the message.

Security Innovation NTRU cryptographic software invention and reference source code for NTRUEncrypt are released to public domain under CCO 1.0 license.

InventionU.S. Patent No.U.S. Issue DateU.S. Application No. U.S. Filing DateCountries

Public key cryptosystem method and apparatus6,081,597Jun 27, 2000 08/914,449 Aug 19, 1997US, Japan, Canada, Australia, Israel, China, Europe

Ring-based public key cryptosystem method6,298,137Oct 2, 2001 09/543,708 Apr 5, 2000US, Europe, Canada

Speed enhanced cryptographic method and apparatus 7,031,468 Apr 18, 200609/939,531 Aug 24, 2001US, Europe, Canada

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