I found some related question but no real explanation of what it is and when and why to use it. What are the benefits and downsides and is it recommended?
2 Answers
Multi-prime RSA is simply using more than 2 prime numbers in generating RSA public key - The public modulus would have more than 2 factors.
We use it because it has more efficient key-generation and decryption/signing operation, which is the benefit of it.
The downside being it might be easier to factor a multi-prime RSA public key than a dual-prime one.
It's neither recommended or recommended against, it's simply an possible option without any endorsement.
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The security of Multi-prime RSA is analyzed in Jason Hinek's PhD Thesis which can be accessed at
In this thesis, Hinek writes
...Considering all of the known attacks on multi-prime RSA (with or without CRT decryption), the evidence suggests that multi-prime RSA with a safe number of primes is no less secure than RSA...
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