Uniqueness public and private key

What mechanism exists for proof unique public and private key when creating a wallet with several offline sources such as www-liteaddress-org , www-alletgenerator-net ?

P.S. the mechanism in the central model a center engine checks uniqueness with the generated key in the past

Any good random number generator is what is needed…256bit random number generator to be exact…
Can use sha256 and scrypt with a 1024 size nonce as well as AES256 to create keys using hashing or encryption as well
Then use an ecdsa module to create a public key from a private key

Is a place you can check to see if it’s a secure public key…do NOT enter your private key here…