Ensuring Uniqueness of Public/Private Keys in RSA Algorithm
I’m new to security and crpyto, but I want to understand how algorithms ensure the uniqueness of public/private keys. Let’s take the RSA algorithm as an example.
The RSA algorithm generates public/private keys by generating a huge, random odd number of a specific size (e.g. 2048 bits) and checking for primality. If the number is not prime, it is incremented by two and checked again. This process repeats until a prime number is found. This ensures that the generated keys are unique.
There is no specific mechanism in place to prevent two private keys from being the same. However, the probability of such a collision is astronomically low and considered irrelevant. The RSA algorithm relies on the assumption that the system has a good source of random numbers. If the random number generation is flawed, it could potentially lead to key collisions and compromise the security of the algorithm.
It is important to note that using a bugged random number generator or a system with a poor source of randomness may generate RSA moduli that share a prime factor. This can be exploited for cryptanalysis purposes, as demonstrated by the Factorable.net attack.
To learn more about the odds of an RSA private key collision and further insights into key uniqueness, you can refer to the What are the odds of an RSA private key collision? discussion on Stack Exchange.