# Questions tagged [multi-prime-rsa]

A variant of RSA where the modulus is the product of more than two primes.

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### Why are the primes all the same size in pqRSA?

pqRSA is MP-RSA with 4096-bit primes to build up a modulus of up to 1TB. If the objective is to make processing the modulus as expensive as possible for the quantum computer why not use just two 4096-...
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### Does any proof exist for the optimal number of primes in a RSA key?

My guess is: Known attack algorithms only work on 2 primes factorization, they don't work on 3+ RSA primes. More than 3 primes is cpu waste time, better is to increase key length. So 3 primes will be ...
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### RSA: exploiting consecutive primes

It's given 2 plaintexts $m_1$ and $m_2$, and 5 different values of $n\quad\{n_1, n_2, n_3, n_4, n_5\}$ which are generated as follows: $n_1$ is a a product of two relatively small 128-bit $p$ and $q$ ...
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### Can we do Multi-Prime Diffie-Hellman?

What is the correct way, if any, to do Multi-Prime DH? From security point of view, is there any benefit to do it? Multi-Prime is not about multi participants. Multi prime is when we use two or more ...
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### Decrypting Multi-Prime RSA with e, N, and factors of N given

I was wondering if there was any way to compute the private key $d$ when knowing only $e$ and $N$, and being able to factor $N$ as 4 prime numbers $p, q, r$ and $s$. I've been searching for days and I ...
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### Who first published the interest of more than two prime factors in RSA?

Multi-prime RSA is now a well known technique (described here): it uses $k>2$ distinct secret prime factors in the public RSA modulus, with the advantage that, using the CRT, we can gain a speed ...
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### RSA with composite numbers

It has been said that RSA uses a modulus product of two prime numbers for security reasons. But does RSA even work correctly if we allow composite integers instead? I think that the answer is "NO". ...
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I would like to ask what happens if we build an RSA system with modulus a product of more than 2 primes, for example let $n=p_{1}p_{2}...p_{L}$. I know only the classical RSA system with $n=pq$ with \$...