How is algebra used in cryptology?

In this specific method, each letter is first assigned a numerical value, commonly referred to as its encoding. This process converts the alphabet into a sequence of numbers, where each letter corresponds to a unique integer.

Cryptography, the art of encoding and decoding messages, involves intricate methods to ensure the confidentiality of information. One such technique involves transforming each letter of a message into a numerical counterpart and then applying a mathematical function to obscure its original form.

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Following the encoding step, the numbers are then subjected to a transformation governed by the formula ax + b. Here, 'a' and 'b' are predetermined constants that act as keys to the encryption process, making it difficult for unauthorized parties to decipher the message.

As an example, let's consider the scenario where a = 3 and b = 5. If we want to encrypt the letter 'H', which is encoded as 7, we apply the formula: 3 * 7 + 5. Performing the calculation, we get 21 + 5 = 26. Since the alphabet has only 26 letters, we wrap around to the beginning, and 26 corresponds to 'A'.