Cryptography Stack Exchange
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Questions tagged [multi-prime-rsa]

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

RSA is typically used with a modulus n that's the product of exactly two primes. But it also works with a modulus that has more factors. Depending on the modulus size it's possible to use three to five prime factors without a loss of security. Using more factors speeds up the expensive private key operation using the Chinese remainder theorem

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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 boost in private-key operation, with little…
fgrieu
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Why is pqRSA in the NIST PQC submissions?

In the NIST post-quantum cryptography workshop, the round one submissions included pqRSA. If memory serves, this is an implementation of RSA using the product of a very large number of 4096-bit primes to protect against Shor's algorithm. It requires…
forest
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RSA with modulus product of many primes

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 $p$ and $q$ large prime numbers. I guess the…
CryptoBeginner
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Multiple-prime RSA; how many primes can I use, for a 2048-bit modulus?

In standard RSA, the modulus $n=p_1 p_2$ is a product of two primes $p_1,p_2$ of the same size. Suppose we construct the modulus as a product of multiple primes $p_1,\dots,p_k$, i.e., $n=p_1 p_2 \cdots p_k$, where all the primes are of about the…
D.W.
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RSA with 3 primes

I was trying to understand how does RSA with 3 primes work. I have checked Wikipedia but yet I didn’t fully understand their solution. I would like to know how do you encrypt for $n=p*q*r$ How do you decrypt for it, and why is it still proven to…
Jeremaiha
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RSA encryption and decryption with multiple prime modulus using CRT

Every information I found on internet about RSA-CRT encryption/decryption uses only two primes. I'm interested in my project in doing that using multiple (up to 8) primes. The general idea is to calculate $d_p = d\bmod(p-1)$, $d_q = d\bmod(q-1)$,…
tomQrsd
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Are there any standards of multi-prime RSA key generation?

FIPS 186-3 specifies a method to generate DSA parameters. Is there anything similar (official standard or widely-accepted recommendation) that shows how to generate the primes for multi-prime RSA?
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Subverting the key generation step in RSA public key cryptography

I am interested in the ways an RSA key generation implementation can or cannot be subverted so that the subverter has an advantage, but the owner of the key, and the people who interact with the owner, are left unaware that something is going on. I…
Pascal Cuoq
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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". Define “work correctly” as: allows encryption and…
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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 the optimal number. Example of my program (open…
alainalain
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What is multi-prime RSA (RSA-MP)?

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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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 can't find any way.
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Chinese Remainder Theorem and Elgamal

I am studying an encryption scheme which is Elgamal-like where I think CRT can help optimise the encryption and decryption but I am not sure if I am applying CRT the correct way. I have a cyclic group $G$ of order $n=p_1p_2q$, generator $g$ of $G$,…
Papa Delta
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Can multi-prime RSA be used to create an abuse-resistant lawful interception mechanism?

New to site so this may have been asked before: Can multi-prime RSA, i.e. where N is product of three or more distinct primes, be used for secure communication while allowing distinct authoritative entities to decrypt the messages when under a…
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what are multi-primes and how are they different from semiprimes?

I came to know of semiprimes recently. The simplest explanation of semiprimes is you take any two prime numbers and you multiply them, say 3*11 = 33 in which case 33 would be a semiprime. The numbers may grow bigger but the idea is…
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