So using the inverse of 17 modulo 26
I have -3(y-4)(mod 26)
first am I correct? (I originally started with -3(y+22)(mod 26))
And im now trying to decipher a simple message. Which I will plug the numbers of the letters into the equation instead of y.
Again am I doing this correctly?
Thank you!
To verify if you're on the right track, let's break down your process step by step.
First, you mentioned starting with -3(y+22) (mod 26) but then changed it to -3(y-4) (mod 26). The original expression -3(y+22) (mod 26) would be equivalent to -3(y-4) (mod 26) since +22 and -4 have the same residue modulo 26. So both expressions are correct.
Next, you mentioned deciphering a simple message by plugging in the numbers of the letters into the equation instead of y. It seems like you're using a numerical representation of the alphabet, where each letter corresponds to a number. This approach is known as a substitution cipher.
To decrypt the message, you need to substitute the numbers corresponding to the letters in your encrypted message into the equation -3(y-4) (mod 26). Note that y in the equation represents the unknown number associated with the letter in the original message.
By solving the equation for each letter, you can determine the original message. To do this, you'll apply the modular inverse of 17 modulo 26 (the modulus used in the equation) to each letter number. The modular inverse of 17 modulo 26 is 23, as 17 * 23 ≡ 1 (mod 26).
So, for each encrypted letter, you'll compute the modular inverse, multiply it to the number associated with the letter, and take the result modulo 26. This will give you the decrypted letter number.
Finally, convert the decrypted letter numbers back to their corresponding letters to obtain the original message.
Overall, your approach appears to be correct. Remember to use the modular inverse, apply it to each letter number, and convert the resulting numbers back to letters to fully decrypt the message.