# Questions tagged [rsa]

An asymmetric (e.g. public-key) cryptosystem, based on modular exponentiation with big exponents and modulus. RSA can be used both for signature and encryption with proper paddings.

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### RSA attack when size of $M^e$ and $N$ is close

Let say we have the following information: $$e = 3$$ $C$ is the Cipher text and $M$ is the Plain text with $C=M^3\pmod N,$ and $N$ is a product of two primes. and we have the size of the original ...
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### In the DGK Cryptosystem, how hard is it to recover g, if we have knowledge of the private key?

Given the knowledge of the values for $v_p$, $v_q$, $n$ and $u$, and knowing that $g^{u*v_p*v_q} \mod n = 1$, how hard is it to compute the value of $g$? My assumption is that it is as hard as the RSA ...
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### Coppersmith's Method when you know half of one of the RSA Semprimes [closed]

I have the following 300 digit semiprime ...
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### 300 digits semiprime factorization with the first half of the factor known

Imagine this: there is a 300-digit semiprime, and you are given the first half of one of its prime factors (i.e., you are given the first 75 of 150 digits of that prime factor). Would you be able to ...
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### Encrypting AES-GCM Key with AES or RSA?

I am building an application with a hierarchy of key-sets (think encrypted messaging). Each key-set contains: Symmetric (AES-GCM-256) Asymmetric (RSA-OASEP-256) Each key-set defines an encrypted &...
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### Security analysis of using RSA-OAEP and RSA-PSS with the same key

We all know that it is a bad idea to use the same key for multiple purposes. However it sometimes happens that non-cryptography-savvy people will make this mistake - specifically, that they'll use an ...
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### What is the difference between public and private RSA keys? [duplicate]

I have been learning about generating RSA keys and am wondering if there is a particular reason why the private key is the private key and the public the public. As far as I know the encryption is bi-...
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### Can an RSA 2048 public key be recovered from encrypted- and decrypted data?

I have a binary file and an encrypted file (.sgo). Can I get the public key from this data? The encryption used is RSA-2048.
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### What exactly is a VRF?

Random numbers are useful in many use cases such as blockchain. I know many blockchains or smart contracts employ VRF to generate "provably fair random numbers". But what exactly is a VRF? I'...
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### Generating Carmichael numbers in polynomial time

I'm generating RSA 2048-bit keys with $p$ and $q$ of 1024-bit primes. For primality, I'm using the Miller-Rabin test. As Carmichael numbers pass the MR test, I tried to compute how many such numbers ...
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### How can I demonstrate the existence of such an isomorphism(look at the image below)?

While I was reading a paper from "Daniel Shumow" about recovering all possible plaintexts when bad RSA keys ($e$ and $\phi(N)$ aren't co-prime) generation occurs, I found this isomorphism (...
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### How to find N and e knowing that e = p and N = p*q?

I've been stuck in this problem for a while, this is a challenge about Symmetric RSA: We know that $N = p*q$ $e = p$ $ct = pt^p \bmod N$ (1) We are given $ct$ (which is the flag encrypted) and 4 ...
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### Peculiar case of RSA

I am dealing with a case as follows: P = 73, Q = 97. N = 7081, phi(N) = 6912. e = 7. Now, to find decryption exponent 'd' we have to satisfy: (e * d) mod phi(N) = 1 - (i). Aliter: d = e^(-1) mod phi(N)...
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### Is it really safe to exchange data without a handshake?

I want to be able to exchange data between personal devices within a local network via HTTP. The point is that I want to use the same pair of personal asymmetric keys on both sides. It turns out that ...
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### Probability of Enhanced MR test outcome for NOT A POWER OF PRIME

I come up with an approach to find the probability of the outcome "PROVABLY COMPOSITE AND NOT A POWER OF A PRIME" of enhanced MR test. In context of this question, the probability/error ...
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### Source code of generating private exponent for RSA?

I'm learning math of RSA. I'm interesting about realisation of computing private expoinent in source code. Where can I read a well made implemenation? (I prefer Python or Go implementation) I tried to ...
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### What Digital Signature Methods are Suitable for Microcontrollers?

Given the constraints in terms of processing power, memory, and energy, what digital signature schemes are commonly used and efficient for Microcontrollers? I have come across RSA with low public ...
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### Can the RSA public key be used for both encryption and decryption?

My understanding of RSA Cryptography is that the Public Key is used for data encryption and Private Key is used for data decryption. But on this website(https://www.devglan.com/online-tools/rsa-...
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### Weakness when encrypting using RSA private key?

I know that usually with RSA, you encrypt data using the public key, and decrypt using the private key. Or alternatively, you sign using the private key, and verify the signature using the public key. ...
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### Reduction from factoring to RSA and the Oracle RSA problem

Recently I read some papers related to RSA Brown16,AM09,BNPS01 and I learned that there is a variant problem of RSA is The oracle RSA problem (or one more RSA Problem) is $m+1$ copies of the classic ...
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### Does unlimited signing oracle leak the private key?

I am writing a PC software that uses a type of USB dongle as licensing key. The dongle functions as a signing oracle and does nothing more: Given any message $M$, it first pads $M$ to $PadM$, then ...
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### RSA problem with unconventional calculation of phi

I have $\phi$,$N$ and ciphertext. But the $\phi$ is calculated with $\phi=(p+1)(q+1)$. I normally calculate $d$ but cannot recover the message.
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### P, Q, and G values in a public key

I came across a certificate that contains values $P,Q$, and $G$ besides the public key. Obviously, $P$ and $Q$ here are primes, but not the two secret primes. I am curious are those values ...
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### rsa special private key attack

This is a level 3 challenge in Mystery Twister. https://mysterytwister.org/media/challenges/add/mtc3-kitrub-04-speciald-paramter.txt https://mysterytwister.org/media/challenges/pdf/mtc3-kitrub-04-...
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### RSA small private key attack: the private key is slightly larger than the bound given by Boneh and Durfee

$N$ = ...
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### Shannon's Perfect Security for Asymmetric Encryption

I have the following definition of Shannon's Perfect Security. Assuming messages and keys are drawn randomly from some distribution then: The probability of guessing plaintext m is not enhanced by ...
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### Why does it take longer to generate suitably large primes for Diffie-Hellman key exchange as opposed to for RSA encryption / decryption?

For RSA, we need two primes p and q to define N = pq. We will only look how long it takes to generate a prime for p because the process is similar for q. From my lecture slides, my professor states ...
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### What is the best possible security for authentication of entity?

The classical security for authentication is computational provided by RSA or EC based signatures. With the advent of new PQ schemes the security claims are upgraded though nothing is proved. So the ...
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### Why doesn't the existence of the Quadratic Sieve algorithm imply that integer factorization is in the class SUBEXP?

SUBEXP is defined as the intersection of DTIME(2^n^c) over all c>0. The order of the Quadratic Sieve algorithm is O(exp((k+o(1))(logN)^1/2(loglogN)^1/2)). Doesn't this imply that the decision ...
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### Reaching the bound of Boneh and Durfee Attack

According to the paper, theoretically,we can get $\delta=0.292 \lt 1-\frac{1}{\sqrt{2}}$,but how to set the lattice and implement it in sagemath? I generated some data by ...
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### sign a JWT with RS256 using a RSA-PSS SHA256 key pair?

Given a private key using algorithm RSA-PSS with SHA256 is it possible to use this key to sign a JWT using algorith RS256 (RSA with SHA256) instead of PS256 (RSA-PSS with SHA256)? The German ...
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