Use Pohlig-Hellman to encrypt large files

Question

I have an application that needs to combine two cascaded (symmetric) encryption keys using the Pohlig-Hellman cipher.

For example:

The system needs two keys for encryption $c = E_a(E_b(x))$ while it only needs one key for decryption $D_{a\otimes b}(c)=x$. The system may NOT need to consider Known Plaintext Attack or Chosen-plaintext Attack because the key is only used once.

Is it possible that the PH-based method can support encrypting large blocks? For example, can it support 1GB file encryption?

I am quite new to this area. Very much appreciated it if you could provide any tutorials on this.

It's usually recommended to avoid the Pohlig-Hellman cipher. Is there a reason why you specifically need this? — Anonymous20DB28, Apr 29 '20 at 11:36
I need to merge two cascaded keys (for encryption) into a single one (for decryption) thus to prevent the leakage of the two cascaded keys. — Yuhang Ye, Apr 29 '20 at 13:40
@YuhangYe cascading is not secure Is the encryption more secure if we apply Pohlig-Hellman cipher twice with different keys but with the same modulus?. — kelalaka, Apr 29 '20 at 15:00
@kelalaka In my application senario, I do not need to worry about KPA or CPA. The key is only used once then it will be disposed. — Yuhang Ye, Apr 29 '20 at 15:26
@YuhangYe For Pohlig-Hellman Cipher double encryption is equal to single encryption so that it doesn't increase the key size. Why not AES, ChaCha20, etc? — kelalaka, Apr 29 '20 at 15:51
@kelalaka Thank you very much for your reply. I may not need to stick to Pohlig-Hellman. I will switch to AES if it is more secure. May I have another question: how can I find a newbie tutorial about how to merge (aggregate) two AES keys (or ChaCha20)? It seems not easy to found one online. — Yuhang Ye, Apr 29 '20 at 16:17
In modern Cryptography, we prefer Auyheticated Encryption mode with Associated Data (AEAD). AES-GCM or ChaCha-Poly1305 are nice choices. What do you mean merge two AES keys? — kelalaka, Apr 29 '20 at 16:20
@kelalaka "merge" means that I encrypt a text using two keys (a and b) and decrypte the text using a single key (merged from a and b). — Yuhang Ye, Apr 29 '20 at 16:37
You can encrypt large files by applying some mode of operation like ECB,CBC, by using a secure enough modulus. As Fgrieu noted in his answer mplementing the Pohlig-Hellman cipher use OAEP to make it secure. — kelalaka, Apr 29 '20 at 19:29

Use Pohlig-Hellman to encrypt large files

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