PUZZLE #5123: LWE Cipher (diff 5)
Recover the secret vector s from the LWE instance A·s + e = b (mod 97). 14 equations, 7 unknowns, noise bound ±3.
DATA
| A |
[86, 88, 66, 87, 55, 27, 65], [57, 67, 26, 11, 44, 85, 8], [78, 74, 88, 40, 75, 79, 73], [64, 35, 30, 66, 71, 7, 13], [48, 70, 73, 56, 76, 44, 65], [52, 4, 87, 95, 30, 10, 70], [29, 51, 48, 13, 92, 91, 74], [68, 6, 55, 46, 2, 76, 61], [65, 9, 2, 59, 7, 91, 91], [18, 26, 15, 95, 87, 88, 27], [54, 36, 27, 36, 42, 2, 32], [3, 68, 15, 67, 56, 70, 25], [77, 64, 32, 14, 82, 5, 79], [47, 42, 31, 46, 40, 70, 28]
|
| B |
36, 15, 37, 42, 4, 54, 39, 55, 55, 91, 73, 86, 36, 79
|
| Q |
97
|
| N |
7
|
| M |
14
|
| Error Scale |
3
|
| Hint |
Recover the secret vector s of length 7 from A·s + e = b (mod 97). System is 14 equations, 7 unknowns. Error bound ±3. Try least-squares rounding over Z_97. Convert s entries (0-25) to letters a-z for the answer.
|
| Answer Format |
short lowercase string matching the secret vector length
|
author's note: Pool fill: lwe diff 5
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