| 1 | import math |
| 2 | import re |
| 3 | |
| 1 | 4 | def encode(plain_text: str, a: int, b: int) -> str: |
| 2 | | pass |
| 5 | m = 26 # size of the alphabet |
| 6 | |
| 7 | # Edge Case: Check if a and m are coprime |
| 8 | if math.gcd(a, m) != 1: |
| 9 | raise ValueError("a and m must be coprime.") |
| 10 | |
| 11 | # Edge Case: Handle negative values for a or b by taking them modulo m |
| 12 | a = a % m |
| 13 | b = b % m |
| 14 | |
| 15 | # Convert to lowercase and remove non-alphanumeric characters |
| 16 | cleaned_text = re.sub(r'[^a-z0-9]', '', plain_text.lower()) |
| 17 | |
| 18 | # Edge Case: Handle empty input string |
| 19 | if not cleaned_text: |
| 20 | return "" |
| 21 | |
| 22 | result = [] |
| 23 | for char in cleaned_text: |
| 24 | if char.isdigit(): |
| 25 | result.append(char) |
| 26 | else: |
| 27 | # Encrypt letter |
| 28 | i = ord(char) - ord('a') |
| 29 | encrypted_index = (a * i + b) % m |
| 30 | result.append(chr(encrypted_index + ord('a'))) |
| 31 | |
| 32 | # Group into chunks of 5 |
| 33 | grouped_result = [] |
| 34 | for i in range(0, len(result), 5): |
| 35 | grouped_result.append(''.join(result[i:i+5])) |
| 36 | |
| 37 | return ' '.join(grouped_result) |
| 38 | # Handled Edge Cases: a and m not coprime, negative a or b, empty input string, non-alphanumeric characters |
| 3 | 39 | |
| 4 | 40 | |
| 5 | 41 | def decode(ciphered_text: str, a: int, b: int) -> str: |
| 6 | | pass |
| 42 | m = 26 # size of the alphabet |
| 43 | |
| 44 | # Edge Case: Check if a and m are coprime |
| 45 | if math.gcd(a, m) != 1: |
| 46 | raise ValueError("a and m must be coprime.") |
| 47 | |
| 48 | # Edge Case: Handle negative values for a or b by taking them modulo m |
| 49 | a = a % m |
| 50 | b = b % m |
| 51 | |
| 52 | # Find modular multiplicative inverse of a |
| 53 | # Edge Case: This will always exist since we checked gcd(a, m) == 1 |
| 54 | a_inv = None |
| 55 | for x in range(1, m): |
| 56 | if (a * x) % m == 1: |
| 57 | a_inv = x |
| 58 | break |
| 59 | |
| 60 | # Edge Case: Remove spaces and non-alphanumeric characters |
| 61 | cleaned_text = re.sub(r'[^a-z0-9]', '', ciphered_text.lower()) |
| 62 | |
| 63 | # Edge Case: Handle empty input string |
| 64 | if not cleaned_text: |
| 65 | return "" |
| 66 | |
| 67 | result = [] |
| 68 | for char in cleaned_text: |
| 69 | if char.isdigit(): |
| 70 | result.append(char) |
| 71 | else: |
| 72 | # Decrypt letter |
| 73 | y = ord(char) - ord('a') |
| 74 | decrypted_index = (a_inv * (y - b)) % m |
| 75 | result.append(chr(decrypted_index + ord('a'))) |
| 76 | |
| 77 | return ''.join(result) |
| 78 | # Handled Edge Cases: a and m not coprime, negative a or b, a_inv not found (impossible when coprime), non-alphanumeric characters, empty input string |