# Why can't we use the IDEA's decryption rule for decrypting a block on CTR mode?

Suppose that a block is ciphered with IDEA using CTR mode operation. To get the original message, why can't we use the cyphered rule?

• It is not at all clear what your question is about. Can you please elaborate on the title and specify what it is that you want to know? – Ella Rose May 11 '18 at 1:53
• Are you asking why $\operatorname{enc}_k(n) \neq \operatorname{dec}_k(n)$ for a key $k$ and counter $n$? – cypherfox May 11 '18 at 2:30
• I read the question title to mean "Why does CTR mode not use [a block cipher's] decryption [algorithm] for message decryption?" (Even though it does use the block cipher's (block) encryption algorithm for message encryption.) – Future Security May 11 '18 at 2:46

CTR uses only a block cipher's forward algorithm, not its inverse. Both sender and recipient compute $N_? = E_K(nonce || counter)$ for each block. Then the plaintext is XORed with $N$ to get ciphertext. The recipient XORs ciphertext with $N$ to get plaintext.
$C_i = E_K(nonce || i) \oplus P_i$
$P_i = E_K(nonce || i) \oplus C_i$
Note: XOR is it's own inverse. $A \oplus B \oplus B = A$