Linked Questions
22 questions linked to/from What security authorities and standards reject $e=3$ in RSA, when, and with what rationale?
40
votes
5answers
103k views
How to find modulus from a RSA public key?
I am studying the RSA cryptosystem. The public key consists of $(n, e)$, the modulus (product of two large primes), and the encryption exponent. I want to separate the modulus $n$ and exponent $e$. A ...
26
votes
9answers
23k views
RSA with small exponents?
Just to establish notation with respect to the RSA protocol, let $n = pq$ be the product of two large primes and let $e$ and $d$ be the public and private exponents, respectively ($e$ is the inverse ...
25
votes
2answers
3k views
Why is PuTTYgen-created RSA public exponent(e) not in {3,17,65537}?
As far as I know, RSA public exponent(e) should be one of {3,17,65537}.
However, I found PuTTYgen-created RSA public exponent(e) is 0x25(37) by default,as follows, (PuTTYgen version: 0.66)
I am ...
18
votes
5answers
5k views
Is there a situation where RSA cannot be replaced with ECC + symmetric algorithms? If no, why do we still use it?
RSA is both an asymmetric encryption algorithm and a digital signature algorithm. However, in recent years, many cryptographic protocols (TLS, for example) have moved away from the use of RSA to ...
9
votes
1answer
2k views
In textbook RSA with low public exponent, how big does a random message needs to be?
Assume RSA with a public modulus $N$ of $n$ bits, a small odd public exponent $e$, plaintext $M$ a random non-negative integer less than $2^m$ for some integer parameter $m$, with $M\mapsto C=M^e\bmod ...
5
votes
1answer
515 views
Proof of RSA security dependent on public key exponent
I am writing a (high-school) paper on the public key exponent's (in textbook RSA - no padding is discussed!) significance in terms of time and security. The time part is done; as for the security part,...
5
votes
1answer
622 views
Are RSA or ECC vulnerable to an attack where the same (unknown) plaintext is encrypted with multiple public keys?
I'm not sure what this attack model is called - it's not known-plaintext and also not quite cipher-text-only. It is similar to this question except the general case (not just two keys) and using keys ...
4
votes
2answers
3k views
Is there a way to systematically calculate the public exponent $e$ in RSA?
I'm learning RSA in one of my classes and we were given a problem:
$p = 5$, $q = 11$
I have done the following steps:
$n = 5 \cdot 11 = 55$
$\phi = (5-1)\cdot(11-1) = 40$
I know that to find ...
4
votes
2answers
531 views
how to iteratively calculate a^emod n with modulus n sized 4096 bits
In most sites the exponent of the RSA public key is 24 bits. But the modulus can get to 4096 bits size. I have an accelerator that can get max. 2112 bit size modulus. It calculates ...
4
votes
1answer
899 views
Relationship between exponent and modulus in RSA (as RSA properties as listed in X.509)
In one of my assignments, I had the following question (Please read on. Not a homework assignment :) ):
X.509 (1998 version) lists properties that RSA keys must satisfy to be
secure. One such ...
4
votes
1answer
2k views
Bleichenbacher's Attack on high public exponent RSA keys?
Why can't Bleichenbacher's Attack work for RSA public exponents with values equal to 65537 and above? Does the fact that 65337 is a prime number have any relevance to it?
3
votes
2answers
1k views
Key space vs Cardinality of 1024-bit RSA
I have been trying to figure out the encryption key space, and cardinality of 1024-bit RSA. From my understanding, the key generated from 1024-bit will be primes greater than $2^{1023}$ but less than $...
3
votes
3answers
5k views
RSA: Is it secure to use the private key to encrypt and the public key to decrypt?
This may sound weird:
What if I don't let others know my public key, then use my private key to encrypt, and the public key to decrypt? Is this secure?
Let me explain a little bit:
Common usuage: use ...
2
votes
1answer
1k views
Attack for RSA 1024 bit with Low Public Exponent
I am facing a challenge at university.
Our teacher give us the challenge to try to break an RSA 1024 bit.
We have public modulus N and public exponent e (0x03), we don't know the padding.
We have a ...
2
votes
2answers
4k views
RSA Key Generation Parameters - public exponent, certainty, string-to-key count
I want to know what values are appropriate for the public exponent and certainty when generating an RSA Key (for example using Bouncy Castle RSAKeyGenerationParameters function).
What is the ...