ECB vs. CBC, I've seen the pictures, but what's the actual strength difference? I hope that this is not a duplicate because I'm looking for nuance.  I understand the difference between ECB and CBC for a block cipher, and I understand that ECB is susceptible to replay attacks, but my question is just from the standpoint of strength.  If I have cipher that has 256-bit key and 128-bit data that is used to encrypt a file on a disk, the mathematical complexity does not increase between CBC and ECB for cracking the cipher?  I read a lot of answers saying "ECB is insecure", but there's a difference in theory and practice.  I expect to only have 1k 128-bit blocks.

I have an extremely power constrained system, and I'm trying to determine if the 10% overhead required for CBC over a ECB architecture matters from the standpoint of security.  The reason is that if I do have a significant gain using CBC over ECB, perhaps I should just use a smaller cipher size because I'd basically be trading up circuits.  

Any suggestions from the engineering perspective would be appreciated.
There is no good way to calculate a strength difference between ECB and CBC. ECB is broken as a generic cipher - it is not indistinguishable under chosen plaintext attack - as repeating blocks will confer information to an attacker. That particular piece of information doesn't let itself be quantified compared to the amount of bits within the key. It's even completely separate from the key size by definition (AES-256-ECB will be as broken as AES-128-ECB).

CBC with a static IV is vulnerable for the first blocks that could be identical. CBC with a predictable IV is vulnerable as well. However CBC - when used correctly - is secure for confidentiality of data at rest.

The key stays protected by the block cipher itself. If that's "cracking the cipher" then any mode is OK. However, the key only exists to protect the confidentiality of the plaintext. And if that is compromised the security of the system is compromised. So the security of the cipher is inconsequential.



Side note: replay attacks can happen in transport security. They can happen even if the ciphertext is authenticated. Replay attacks have little to do with ECB or CBC mode as neither is a good fit - on its own - for transport mode security. ECB mode is simply susceptible to repetition of plaintext blocks; that's different from replay attacks.