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?
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1$\begingroup$ possible duplicate of RSA with composite numbers $\endgroup$– BissiCommented Feb 4, 2019 at 8:44
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3$\begingroup$ Possible duplicate of Are there any standards of multi-prime RSA key generation? $\endgroup$– kelalakaCommented Feb 4, 2019 at 8:45
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1$\begingroup$ It's history and some benefits are also discussed here: crypto.stackexchange.com/questions/14552/… $\endgroup$– VincBreakerCommented Feb 4, 2019 at 8:47
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$\begingroup$ Thank you! I had only found one of those question so far! $\endgroup$– ErwinCommented Feb 4, 2019 at 9:09
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$\begingroup$ @Erwin Is your question answered by any of these Q/A's? If yes, which one. If no, what's missing? $\endgroup$– Maarten Bodewes ♦Commented Feb 5, 2019 at 1:11
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2 Answers
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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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1$\begingroup$ note that the primes must be distinct. $\endgroup$– kelalakaCommented Feb 4, 2019 at 8:51
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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...
answered Jun 7, 2022 at 11:28
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1$\begingroup$ With "safe number of primes" essentially defined as "no less secure than (biprime) RSA", that conclusion is certainly true! $\endgroup$– fgrieu ♦Commented Jun 7, 2022 at 11:38
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1$\begingroup$ @fgrieu By "safe", he's referring back to the rest of the paper, esp. Tables
5.1and7.2; it's not "only" trivially true. $\endgroup$ Commented Aug 31, 2022 at 21:16 -
$\begingroup$ @JamesTheAwesomeDude: yes, table 5.1 is relevant. It's a (too) much shortened version of table 1 from cited work, correctly summarized. Indeed, if referring to this, the sentence is more than a tautology. Table 7.2 is about dual RSA, thus irrelevant to that citation. $\endgroup$– fgrieu ♦Commented Sep 1, 2022 at 5:33