Alice uses the GGH cryptosystem with private basis (58, 53, -68), V1 = and public basis...

  

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Alice uses the GGH cryptosystem with private basis (58, 53, -68), V1 = and public basis v₂ = (-110, -112, 35), v3 = (-10, -119, 123) W₁ = (324850, -1625176, 2734951), w2 = (165782, -829409, 1395775), W3 = (485054,-2426708, 4083804). (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 = (8930810, -44681748, 75192665). 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 {w₁, W2, W3}. Is the output equal to the plaintext? Activate Go to Setting Alice uses the GGH cryptosystem with private basis (58, 53, -68), V1 = and public basis v₂ = (-110, -112, 35), v3 = (-10, -119, 123) W₁ = (324850, -1625176, 2734951), w2 = (165782, -829409, 1395775), W3 = (485054,-2426708, 4083804). (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 = (8930810, -44681748, 75192665). 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 {w₁, W2, W3}. Is the output equal to the plaintext? Activate Go to Setting

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The image shows a question about the GoldreichGoldwasserHalevi GGH cryptosystem which is a latticebased cryptosystem The GGH cryptosystem uses a private basis that consists of short nearly orthogonal ... View the full answer