CRC32 collision probability with fixed length input

Question

My use case:

• I have a target device configuration with a fixed length of 1200 bits.
• I have the actual device configuration with a fixed length of 1200 bits.
• I like to detect an change in the system bei comparing the target device configuration with the acutal configuration
• Due to "large" length of the configuration I can not compare them, because then I have to send target configuration. This is not possible in my system
• Due to that, I like to calculate a first CRC32 checksum over the target configuration and second CRC32 checksum over the actual configuration
• If the to checksum don't match, I have to reconfigure the actual device by sending a lot of paylod
• Therefore I want to avoid to many collision of the checksum and still need to detect a change in the configuration ("normally" only some bits changes)

My question is:

• Is there a way how I can determine the probability of getting the identical checksum with another device configuraiton ( https://arstechnica.com/civis/viewtopic.php?f=20&t=149670 ) ?
• I can not use the calcualtion of https://crypto.stackexchange.com/questions/39641/what-are-the-odds-of-collisions-for-a-hash-function-with-256-bit-output , because CRC32 is not a hash function, right?
• Are there any links to website, were I can get some informations which fits to my use case ( CRC32 Collision Probability , CRC32 Collision ) ?

Answer 1

See this answer here. Yes, a CRC is a hash function. The probability of a collision depends on the length of the hash function in bits and the number of configurations that you compute the CRC on. It does not depend on the length of the configuration (so long as the configurations are longer than the CRC).