Question

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.

Answer 1

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

Invention U.S. Patent No. U.S. Issue Date U.S. Application No. U.S. Filing Date Countries

Public key cryptosystem method and apparatus 6,081,597 Jun 27, 2000 08/914,449 Aug 19, 1997 US, Japan, Canada, Australia, Israel, China, Europe

Ring-based public key cryptosystem method 6,298,137 Oct 2, 2001 09/543,708 Apr 5, 2000 US, Europe, Canada

Speed enhanced cryptographic method and apparatus 7,031,468 Apr 18, 2006 09/939,531 Aug 24, 2001 US, Europe, Canada

Step-by-step explanation: