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.

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When homomorphic encryption goes wrong?

Consider I have two ciphertext $c_1$ and $c_2$ encrypted using RSA encryption. By definition if I multiply them I'd get $c_1.c_2 \ modN$. My question is what would happen if $c_1.c_2 >N$. Can we ...
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Implementing a web app where the server cannot decrypt its own data?

I'm a cryptography novice, but I think that the world needs to move towards an "encrypt everything" mentality as much as possible. As a result, I've been thinking a lot about ways to build a web app ...
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Question on RSA trapdoor permutation

You plan to use a public-key cryptosystem based on the RSA trapdoor permutation in three different real-life applications, in which the attacker has, respectively, only one of the following resources: ...
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How many bits to flip in an RSA public key to do signature forgery?

Scenario: Alice wants to verify a signature from Bob. Alice knows Bob's RSA public key (e, n). However, Alice is getting the data, the signature of the data and the public key from an attacker Eve. ...
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In what cases will RSA not work? [duplicate]

I know that there are cases when RSA will not work like when the number to feed into the system is greater than the modulus. I was wondering if there were any other cases when RSA won't work I looked ...
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How to determine the exponent when using RSA

Can someone please explain to me how, when using RSA, to determine the exponent to be used in encryption and decryption? I have attempted a worked example on using RSA (shown below) but I can't ever ...
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88 views

RSA: How effective is this keypair-trash attack [duplicate]

A question that could very well be part of xkcd's "what if?": Let's say Monica made a piece of software that sends all RSA keypairs to a central database after they're not used anymore. Something ...
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326 views

Practical Attack on RSA

Currently I am designing an RSA based application, and I am thinking of how long should the key be in order to be secure against attacks. I know that RSA 4096 bit key can be recovered using Sound ...
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261 views

Is RSA with SHA1 broken?

I am using CryptSignMessage to sign a string/file. Is using RSASha1 insecure? I know Sha1 is broken as a hashing algorithm, but does that also mean that using it for signing with RSA is broken?
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Physical Level Encryption

What types of algorithms that are capable of signing a message are out there that run on a physical level, e.g. lacking the infrastructure of a standard PC, no memory, processor or motherboard in the ...
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141 views

Certificate == signed public key

For primes p and q used to create a keypair, I understand that the following operation is used to create a signature: $M^d (\bmod\ N)$ where d and N have their usual meanings and M is the message. ...
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inverse of 985 mod(φ60131)

Alright Ive been working on this one for a while I found φ(60131) to be 97294 ½(60131+60131(5)^.5) = 97294 then I worked through the GCD ...
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How to calculate RSA CRT parameters from public key and private exponent

Given the public key (n, e) and private exponent (d), how to calculate CRT parameters (p, q, dP, dQ, and qInv) of this RSA key pair?
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Common Modulus Attack in RSA

Consider the following scenario: The Information Security Department (ISD) of an organization issues each of the organization's employees, domestic and abroad, with an individual RSA key. To simplify ...
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992 views

How to decrypt a '.enc' file that has been encrypted with RSA using a public key? [closed]

While solving a CTF challenge online, I came across a situation where I needed to decrypt a '.enc' file that has been encrypted using someone's public key. The ...
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Identification by RSA

Suppose we have identification scheme as such: Bob takes random $r$, and encrypts it with Alices public RSA key $(n,e)$, sends $r^e$ to Alice. Alice decrypts $r$ and sends it back to Bob, becomes ...
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RSA generation of private key using public key

In RSA private key generation e*d ≡ 1 mod φ e is public, also n is public. How to prove mathematically, generation of ...
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Proof that $gcd(e, \lambda(N)) = 1 \hspace{1mm} \Longleftrightarrow \hspace{1mm} gcd(e, \varphi(N)) = 1$

What is the proof for the fact that $gcd(e, \lambda(N)) = 1 \hspace{1mm} \Longleftrightarrow \hspace{1mm} gcd(e, \varphi(N)) = 1$ Where: $N = P * Q$ where $P$ and $Q$ are both primes. $\varphi(N)$ ...
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How does RSA padding work exactly?

I've read everywhere online and people say plain text RSA is very unsafe. To make it safe you pad it but no examples are shown anywhere on how to do it. It's explained that random data is added to the ...
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RSA signing security

I'm curious about the security of RSA signing with the same public private key pair when the same message is sent multiple times. It's my understanding that once you generate the hash of the message ...
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105 views

What are the potential (major) flaws in this security scheme?

It’s been a few years since I read anything involving crypto. I’ve come across this scheme and I wonder how secure it is: Alice generates an RSA keypair (we assume Alice is using proper random ...
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120 views

Determining message given cipher-text and public key [duplicate]

Consider the following scenario: Suppose A and B have set up their RSA public keys, namely $(e_a, n)$ and $(e_b, n)$, where the n-value is the same. Also, it happens that the $\gcd (e_a, e_b) ...
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104 views

RSA: Fermat-Euler Theorem - coprimality of message and modulus [duplicate]

I understand the implication of the Fermat-Euler theorem and how it applies to RSA and the detailed explanation by user Ninefingers at What is the relation between RSA & Fermat's little ...
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86 views

In RSA, why does Alice's $N$ need to be relatively prime to Bob's $N$?

I was asked this by my professor and I didn't understand the reasoning behind it. If Alice has a the key pair $(p_a, n_a)$ and Bob has the key pair $(p_b, n_b)$, why do $n_a$ and $n_b$ have to be ...
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103 views

RSA CRT modulo reduction

I am working on RSA CRT and there is a point that I don't understand : So we have $n=pq$ and $c = m^e \bmod n$ an encrypted message. To decrypt $c$ with RSA CRT, we have to compute : $d_p = d \bmod ...
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120 views

Is there any probabilistic version of RSA?

I have now studying the RSA, but I think that is it possible to have some probabilistic version like a random bit string "r" XORed with the key? Is there any probabilistic version of RSA? Thak you ...
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Why would an RSA library tell me that the public key must be at least 512 bits in size?

I'm trying to interoperate with a web service by reverse-engineering it. Currently, when sending a POST request, it encrypts the form data one-by-one with a 'RSA' function. But it's rather weird as ...
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196 views

RSA Proof - Is Z(n) closed under multiplication

In RSA proof it can be proved that $\mathbb{Z}^*_n$ is closed under multiplication. Can it be also proved that $\mathbb{Z}_n$ is closed under multiplication? If yes, then how?
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444 views

Decrypting a small Message using RSA with a Private Key [closed]

If I have a private key of (43, 341). What would be the steps I need to take to decrypt a small message using RSA? I have looked ...
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254 views

Digital signatures under plain RSA

Show that digital signatures under plain RSA are insecure (Plain RSA means that signing is done by calculating $m^d\bmod n$, with $0\le m<n$, and no padding or hashing of $m$). Write an algorithm ...
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129 views

Is it possible to decrypt an RSA ciphertext with only $N$ and $e$?

Is it possible to perform RSA decryption if one only knows $N$ and $e$? Failing that, what is the maximum key length where brute-force is still practically feasible?
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113 views

What is the difference between exhaustive search and factorization in relationship to determining a key?

It seems to me an exhaustive search would simply try to use all the possible bit combinations of a key, while factorization is some mathematical formula for determining the key? When discussing the ...
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334 views

Key space: Dense and sparse

I'm taking a cryptography class and I come across these terms dense and sparse key space allt he time. What do they mean? As far as I can I understand, dense key space means that there are more ...
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201 views

PKCS1 and blind RSA signatures

Wikipedia's article on RSA blind signatures says that you need to raise the message $m$ to the secret exponent $d$ modulo the public modulus $N$. Implicit within that, it seems to me, is that m needs ...
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How to choose the appropriate public (i, m) and private (j, m) keys?

I studied some encryption and decryption and I have found some very interesting problem to solve on the internet. I hope I am writing to right site - there are so many in StackExchange otherwise I ...
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272 views

Solving congruences using PARI

I'm having trouble finding info in the docs about how to solve a system of congruences. The closest I can find is 'matsolvemod' in here: ...
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276 views

How can we find Public key have only 8 or 16bits? How many messages does Eve need to know the Public key in RSA?

Suppose Alice sends messages to Bob by encrypting the messages with Bob's public key. Eve knows that the data is encrypted using RSA, but does not know the public key. Can Eve figure out the public ...
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RSA signature attack check on lowest 16 bytes - Implementation

I am referring to solution given in this question I need help to implement Poncho hint in this comment: As the first question i have an RSA signature of 1024 bit applied on an hash (MD5) of the ...
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35 views

Key exchange resilience to DoS attack

I am designing a user registration protocol for a system where I control both clients and servers. The aim is to establish a symmetric key for subsequent authentication, while minimizing the work ...
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59 views

RSA function over $Z_t^{*}$ where $t$ is prime

RSA function is defined over $Z_N^{*}$ where $N=pq$ with $p,q$ primes. A public key is a pair $(N,e)$ and a private key is $(N,d)$ where $d=e^{-1} \mod \phi(N)$. Assume that RSA function is defined ...
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93 views

Why is the public/private key length used in libsodium so much shorter than needed for RSA [duplicate]

Reading the libsodium source I see that is uses a key length of 32 bytes (256 bit) for private/public key encryption. For RSA private/public key encryption a key length of 2048 (or 4095) bit is ...
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187 views

PGP public RSA key format

I have been trying to use Go (I could post the code, but I think I posted enough already...) to generate a PGP RSA key. However every time I try to encrypt something with it, something fails. However, ...
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101 views

Finding public exponent e

I'm trying to create an algorithm to find the public exponent e given a plain (non-CRT) private key that doesn't include the public exponent, i.e. I've only got $n$ and $d$. A question has already ...
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75 views

Rsa Key Exchange Protocol

Moderators: Maybe this question will be move to other sub-forum. My question is Anybody know some link with a tutorial of how implement the RSA key exchange protocol using java for chat comunication?
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RSA: How to calculate the private exponent?

I have this problem: In RSA algorithm considering $n=33$ (modulus) and public exponent $e=3$, calculate the corresponding private exponent $d$. I know that $d = e^{-1} \pmod{\varphi(n)}$ and ...
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58 views

RSA: Why must e be relative prime to phi(n) [duplicate]

I've got a question concerning fields used in RSA: Let's use the following symbols for my example: {p,q} = primes {e,n} = public key {d,n] = private key I learnt that an inverse element exists if a ...
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Knowing N and a relationship between the 2 prime numbers(p and q) find p and q generated with RSA

Let there be $p$ and $q$, 2 prime numbers for which the following relationship is true: $|p-q| < 2 \cdot N^{1/4}$. The algorithm first generates the prime number $p$, then it generates $q$ close ...
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73 views

RSA weak padding

Suppose to have a function for numbers expressed in 8-bit $\in [0,2^8-1]$ defined as: $$f(x)=x||x||x||x$$ where $|f(x)|$ is exactly 32 bits. e.g., suppose x=2 (00000010) so ...
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105 views

Where I can find a list of certified software / hardware RNGs compliant to NIST SP 800-22?

I need to use NIST SP 800-22 approved software / hardware to generate RSA key pair. Where I can find a list of certified software / hardware RNGs compliant to NIST SP 800-22? And how is the SP ...
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RSA Decryption from samples

I am working on a project for a client which involves decryption of data which was encrypted using RSA. The system in question retains three independent copies of each data-set, but each copy is ...