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.

learn more… | top users | synonyms

12
votes
1answer
314 views

RSA with probable primes

I am a bit of a newbie to RSA encryption, so please be patient. I understand that for a 4096 bit RSA, the numbers p and q should be prime. And to have the best security, the p and q should both be ...
0
votes
0answers
84 views

What is the danger if a non-prime is chosen for RSA? [duplicate]

I was reading this question about generating primes for RSA keys. The answers point out that most implementations of of the algorithm use probabilistic prime-ness checking algorithms. The answer by ...
2
votes
1answer
193 views

ECC vs RSA: how to compare key sizes?

I know and I have understood the details of RSA, elliptic curve cryptography, (EC)DH and (EC)DSA. I keep reading everywhere that (if we don't consider non-deterministic computers) "ECC can achieve ...
0
votes
1answer
44 views

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 ...
0
votes
1answer
85 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 ...
1
vote
0answers
93 views

RSA Key Blinding

I was looking the answer to the following question (Timing attack on modular exponentiation), discussing the Private Key Blinding as a countermeasure for timing attacks. Therefore I'm asking if ...
0
votes
0answers
87 views

Montgomery Multiplication in FPGA explanation

I'm trying to implement an RSA module in a FPGA. I choose to use Montgomery multiplication. I've found a document where the Montgomery Multiplication is pretty clear. I don't understand only a step. ...
1
vote
0answers
104 views

RSA timing attack

Given an RSA implementation that uses Montgomery multiplications and CIOS exp algo, but NOT CRT. Given a decryption1 oracle that takes chosen cipher text and responds the plain text and the time it ...
5
votes
1answer
333 views

Difference RSA keypair creation openSSL and openPGP?

Creating a 2048bits RSA keypair I figured that doing this using openssl takes as an input 32bytes of "randomness" from ...
2
votes
1answer
65 views

How to make PKCS conformation oracle for trying Bleichenbacher’s RSA attack?

I was trying to understand Bleichenbacher’s CCA attack and thought of work it out in python. Can some one throw some light on the the logic behind the oracle used to check PKCS conformation? Will a ...
2
votes
1answer
37 views

Establish Trust By Signing Random Seed

I'm trying to get my server to establish trust with a client. Neither is on the Internet, so there are no certificate authorities. The typical way to establish trust in my domain is for a client to ...
1
vote
0answers
32 views

Digital signature in a group chat scenario?

I understand that RSA is great for 1-to-1 digital signature. In the group chat of N people, other than storing and maintaining N public keys, is there a simpler way of authenticating each and everyone ...
0
votes
2answers
139 views

Why are RSA ciphertexts different for the same plaintext?

I am using SpongyCastle for a project in android. I have used RSA to encrypt the data and then decrypt it in another activity, the keys are stored in the shared preferences. I discovered a thing I ...
3
votes
2answers
660 views

What does an RSA signature look like?

I am using OpenSSL libs to generate signatures. Internally, I learn that a signature is a hash of the message with some padding added to it. I am trying to understand the structure of a signature. If ...
3
votes
1answer
112 views

RSA public key recovery from signatures

Is it possible (how) to recover public (512 bit long) RSA key from multiple signatures having corresponding plain texts. Padding is not randomized. I need it to verify any future message comming from ...
0
votes
1answer
60 views

Euler's Totient function for semiprime numbers

I have noticed, during the period I spent studying RSA, that Euler's Totient function can be calculated in another way than $ϕ(N) =(p-1).(q-1)$ Let me explain myself by pointing to a brief example: ...
1
vote
1answer
60 views

How to choose the integer m in the general number field sieve (GNFS)?

Given an integer you want to factor $N$, GNFS starts by selecting a monic irreducible polynomial $f \in \mathbb{Z}[X]$ and an integer $m$ such that $f(m) \equiv 0 \text{ mod } N$. In practice, if $m$ ...
0
votes
2answers
87 views

How to decrypt a PGP message with only the two primes and the public exponent?

I'm trying to decrypt a PGP Message that is encrypted with an RSA key, but I only have this information: Public exponent: 65537 Prime 1: ...
9
votes
3answers
5k views

Why hash the message before signing it with RSA?

The diagram below illustrates the process of digitally signing a message with RSA: As diagram shows, the message is first hashed, and the signature is then computed on the hash, rather than on the ...
0
votes
1answer
100 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 ...
2
votes
1answer
113 views

RSA public key exponent generation confusion

Quote from Wiki: $e$ having a short bit-length and small Hamming weight results in more efficient encryption — most commonly $2^{16} + 1 = 65537$. However, much smaller values of $e$ (such as $3$) ...
0
votes
1answer
62 views

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?
5
votes
2answers
2k views

In RSA, why is it important choosing e so that it is coprime to φ(n)?

When choosing the public exponent e, it is stressed that $e$ must be coprime to $\phi(n)$, i.e. $\gcd(\phi(n), e) = 1$. I know that a common choice is to have $e = 3$ (which requires a good padding ...
0
votes
1answer
163 views

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 ...
1
vote
1answer
61 views

one-way deterministic hash for low entropy input?

My problem is the following: we have a low entropy data called ID. (personal id number of 10 decimal digits plus a sum, and it contains a date) We want to create a data (H) which is the same for the ...
-4
votes
1answer
105 views

Can i get a list of over hard and long RSA keys? i think i have found a vulnerability in RSA Algorithm [closed]

al-right, I need some examples of hard and long RSA keys cause i think i have found vulnerability in RSA. i need you to give me few hard Values of n (which is pxq) and i will tell you what p and q ...
0
votes
1answer
58 views

RSA Signature : Process of Sign the message and Verify

I have read that the RSA numeric signature works as the following: Generation of keys : $p,q,N,e,d$ Process of signing the message $m$ (which is BigInteger) : it uses the secret key $sk=(p,q,d)$ so ...
0
votes
1answer
67 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?
2
votes
1answer
87 views

How do we guarantee plaintext is coprime in RSA?

The specifications for RSA state: $P^{\phi(N)} \equiv 1 ~mod~N$ if and only if $P$ and $N$ are coprime. Here $P$ is the plaintext and $N$ is the product of two suitable primes $x_1, x_2$. My question ...
1
vote
1answer
114 views

Why doesn't this defeat RSA?

Apologies for the obviously ridiculous question but I need to know where I'm going wrong here. For RSA, we compute $n=pq$ for primes $p$ and $q$. We then choose an $e$ such that $gcd(e, ...
0
votes
1answer
269 views

Timelock puzzle improvment

I came across this question with this answer about a cryptographic timelock-puzzle that needs approximately 30 years to be solved. There is also an explanation with source code for that puzzle ...
2
votes
2answers
548 views

Computing p and q from private key

We are given n (public modulus) where n=pq and e (encryption exponent). Then I was able to crack the private key d, using Wieners attack. So now, I have (n,e,d). My question is, is there a way to ...
-1
votes
3answers
57 views

with RSA encryption, how do I find the md5sum of the private key from the public key?

This is a purely mathematical question on RSA encryption. Having $e$ as the public key exponent and $n$ the modulus of a public key. Can I recover the md5sum of the private key $d$ (inverse of $d$ ...
4
votes
4answers
700 views

How do institutions like banks do RSA with big primes?

When encrypting with RSA it is often infeasible to decrypt by just doing c^d mod n, because for example when using the primes $(p,q)=(12553,1233)$, which are small ...
0
votes
1answer
52 views

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 ...
1
vote
1answer
76 views

How to create a PEM file for storing an RSA key?

I have an RSA private key $\{d,n\}$ and a public key $\{e,n\}$, where $n$ is the modulus, and I also have the prime factors $p$ and $q$ of $n$. I want to create a PEM file containing this ...
0
votes
1answer
65 views

If someone had a list of all primes, would it be possible for them to factor any integer in polynomial time? [duplicate]

For example, if they somehow got a function that would churn out any arbitrary amount of primes in a row. Could they break the RSA problem then?
2
votes
2answers
66 views

Is it hard to recover $p$ from $k \phi(p)$?

Given $k\phi(p)$, is it hard to recover $p$? Here, $p$ is a large prime, $\phi(\cdot)$ is Euler's totient function and $k$ is an unknown integer. Or what's the complexity to recover $p$ from $k ...
0
votes
0answers
71 views

How do I prove IND-CPA security of RSA-OAEP?

How do I prove that RSA-OAEP is IND-CPA secure? It would be very good to show how to prove it formally, but an informal proof would also be enough. Because of the random number in RSA-OAEP, RSA gets ...
1
vote
2answers
384 views

Is ECB mode safe to use with RSA encryption? [duplicate]

Firstly, bear with me, I'm relatively new to cryptography. In a recent static analysis scan of our application, one of the findings complained that we are using ECB: A mode of operation of a block ...
0
votes
0answers
41 views

trying to get calculator and RSA calculatin does not make sense [duplicate]

got two question, I am novice in the area of crypto and currently in big learning curve. From crypto book I am going over with, I see the RSA algorithm example as follows: it chose two rand #-s: ...
3
votes
2answers
196 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 ...
0
votes
1answer
55 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 ...
2
votes
2answers
2k views

phi(P*Q) = (P-1) * (Q-1)

I was trying to understand RSA when I encountered the Euler Function. I do understand this: $\phi(P)$, where $P$ is a prime is $P-1$. However it seems that for a number $N$ such at $N=P\cdot Q$ where ...
2
votes
1answer
70 views

Retrieve value of private key after encryption with the public key

Is there a way to find an RSA private key after it is encrypted with the corresponding public key? Does there exist an algorithm to recover the private key in this special case?
0
votes
1answer
71 views

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 ...
0
votes
1answer
83 views
4
votes
1answer
215 views

Factoring two RSA modulus with known $|p_1 - p_2| < \ell $

I have two 1024bit RSA modulus $N_1 = p_1q_1$ and $N_2 = p_2q_2$ such that $0 <|p_1 - p_2| < \ell$, and $\ell$ is at most 64bit integer. Can I factorise $N_1$ and $N_2$? What's the answer when ...
2
votes
1answer
125 views

How multiplicative property of RSA can be exploited

It is known that RSA has the multiplicative property $E(m_1) \cdot E(m_2) = E(m_1 \cdot m_2)$ because $m_1^e \cdot m_2^e = (m_1 \cdot m_2)^e \pmod n$ But how can this property be used to break ...
2
votes
1answer
124 views

What use is the signature without the message under RSA?

Using RSA for signing & verification, is there a way to take a valid signature for an unknown message, and for someone else to generate a valid signature using a different key against the valid ...