Question

PLEASE ANSWER A) THROUGH C)

2. Alice uses the GGH cryptosystem with private basis Di = (4.13), 09 = (-57,-45), and public basis wu = (25453, 9091), W2 = (-16096, -5749). (a) Compute the determinant of Alice's lattice and the Hadamard ratio of the private and public bases. (b) Bob sends Alice the encrypted message e = (155340,55483). Use Alice's private basis to decrypt the message and recover the plaintext. Also determine Bob's random perturbation r. (c) Try to decrypt Bob's message using Babai's algorithm with the public ba- sis {1,09}. Is the output equal to the plaintext?

Answer 1

ANSWER

Given that

Goldreich–Goldwasser–Halevi (GGH) Cryptosystem : It is an asymmetric cryptosystem based on lattices that can be used for encryption. Lattices are pretty cool because lattice-based cryptography has some interesting properties (some lattice-based cryptosystems are believed to be quantum resistant!).GGH is pretty cool because it is straightforward to learn. GGH also has interesting properties that could allow an adversary to recover plaintext from a given ciphertext.

Soli given that Alice uses the GGh cryptosystem with primate basis is W, 2(4,13);V2 1057,-45) bablic baiss is . ro, a (25453, 90919 w2.2(-16096, 9749) ② det (L) =561 the Hadamard ratio of the private key is 0.75362 & the Hadamard ratio of the public key is a.colli € 8 .39 w. -22.92 w plantent This yields the innocement (-8; -23)