Linked Questions
11 questions linked to/from RSA encryption and decryption with multiple prime modulus using CRT
77
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3
answers
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Impacts of not using RSA exponent of 65537
This RFC says the RSA Exponent should be 65537. Why is that number recommended and what are the theoretical and practical impacts & risks of making that number higher or lower?
What are the ...
- 2,601
32
votes
7
answers
33k
views
Why does RSA need p and q to be prime numbers?
Despite having read What makes RSA secure by using prime numbers?, I seek clarification because I am still struggling to really grasp the underlying concepts of RSA.
Specifically, why can't we choose ...
- 423
55
votes
2
answers
9k
views
What security authorities and standards reject $e=3$ in RSA, when, and with what rationale?
In RSA, some security authorities and/or standards allow the public exponent $e=3$, others require or recommend $e>2^{16}$ (or perhaps some other minimum). I gathered the following:
PKCS#1 allows $...
- 138k
16
votes
2
answers
4k
views
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 \...
- 36.2k
11
votes
1
answer
10k
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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 ...
- 117
39
votes
1
answer
2k
views
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 ...
- 138k
1
vote
2
answers
3k
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In RSA, why would we ever want to find the values of p and q if we already know phi(n)?
I'm studying RSA for the first time, and I know that $p$ and $q$ must be kept secret because with them we can calculate $\phi(n)$, which then lets us calculate the private key $d$. So $p$, $q$, and $\...
- 125
2
votes
2
answers
258
views
How to handle modular arithmetic with regard to two's-complement negative numbers?
The reason for asking, is that this occurs in real life with CRT calculation of RSA decryption/signing. In CRT RSA, there's the need to calculate subtraction, and it's known negative numbers could ...
- 9,001
-3
votes
1
answer
416
views
How to attack RSA with 13 primes
Could give me method to attack RSA when N decomposes into multiple primes
And this is the topic
N = ...
2
votes
1
answer
152
views
Paillier's scheme generalisation
Paillier's scheme assume has message and ciphertext space equal to $\mathbb{Z}_N$ with $N=pq$, that is $N$ is the product of two different primes.
Is there a way to generalise this for $N$ that is ...
- 21
0
votes
2
answers
98
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Will the value of the "version" fields always be 0 and the "NULL" fields always be "NULL" in PKCS#1, PKCS#8, and X.509/SPKI keys?
Consider the fields highlighted in red in the following keys.
Will the "version" fields (i.e. INTEGER 0) always be zero for the specified structure?
Will ...
- 217