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I have c1 and c2 as random numbers. I have 1000 keys. I use the random number generated from the sender, c1, to hash the a non-repeating and secured key and i can send it back to the sender for verification. But why do i need to use another random number c2, generated by myself, on top of c1+key to send it to the sender?
I depends on what you’re doing, which you don’t really say. Hashing is a general technique that involves neither keys nor random numbers. Salting involves random numbers, and keys are used for encryption or authentication.
Reading between the lines of your question, it appears that you’re using keys for authentication, but then why would you be sending them back to the sender at all? You might use two salts in a protocol like you describe if the two sides involved don’t fully trust each other to use a proper salt — by having both sides provide a salt, both can be assured that the salt is truly random and doesn’t involve a back door or a replay attack.