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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How does this happen in RSA malleability?

I don't understand how the $E(m)$ turns into $E(mt)$. I mean, I don't know how does that transformation happen and how does the equation occur. $$E(m) \cdot t^e \bmod n = (mt)^e \bmod n = E(mt)$$ ...
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2answers
2k views

How does one deal with a negative “d” in RSA?

I'm trying to write my own RSA implementation using the textbook approach — which I know is not optimal — of picking primes $p$ and $q$, then computing Euler's totient $phi$, then randomly picking an '...
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4answers
899 views

Why is public key cryptography (RSA) used in sites like Google or Facebook?

The RSA algorithm is used for encryption (plain text to cipher text) and decryption (cipher text to plain text) of data. What is the need for using public keys in these sites; why is data is encrypted ...
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901 views

Why RSA uses {d,n} as private key instead of {e,n}?

While studying the RSA algorithm I referred to some books and some sites such as RSA (wikipedia) and all of them chose {d,n} as the secret (private) key and release {e,n} as the public key but as d ...
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1answer
738 views

ABC Conjecture's Impact on RSA Encryption

A recent proof of the ABC Conjecture has been released by one Shinichi Mochizuki. Now, I'm not well versed in mathematics but it would appear that this proof implies that finding prime factors could ...
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3k 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 ...
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153 views

how to let other people respond to emails only decrypt-able with my private key

First of all I have to say it's a homework question but since I have no one to consult with, I ended up here :) Suppose a case in which you are the manager of a company and all employees encrypt ...
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2answers
632 views

How do RSA and ElGamal key sizes compare?

I have a rather silly question regarding the comparison of RSA with ElGamal over integers. If you want to compare their performance in the same level of security, does the modulus of both of them need ...
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3k 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 ...
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1answer
133 views

How does DH work when combined with ECC or RSA?

I know that Diffie-Hellman is used to create keys in a secure way over an insecure channel. But there is one thing which I cannot understand: I see that a lot of sites use ECC or RSA alongside DH. ...
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244 views

Can e = 2 be used in unpadded RSA?

I am wondering whether $e = 2$ can be used in unpadded RSA... It seems like it is not possible to use it: the value of e needs to be coprime with $tot(n)$. $tot(n) = (p - 1)(q - 1)$ where $p$ and $q$ ...
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416 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: ...
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2answers
343 views

Can RSA signing be implemented on top of RSA encryption/decryption?

I need to use RSA-SHA256 signing. Unfortunately not all Microsoft CryptoAPI providers support that. It's possible that I might get a handle to a CryptoAPI provider that can just encrypt/decrypt with ...
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1answer
325 views

Why is verification using DSA slower than verification with RSA?

We read in literature that verification of a digital signature is slower using DSA than if we used RSA. Why is this? DSA parameter generation: choose prime number $p$ choose prime number $q$ such ...
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1answer
274 views

RSA Signature Verification Implementation on Cortex M0

I have to implement RSA Signature Verification procedure (RSA-2048) on a Cortex M0 based MCU. My budget is 15kB Flash and 2-4kB Flash RAM. Is it even possible to do RSA on a low end MCU based on ...
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1answer
300 views

ECDH or RSA more secure for symmetric key wrapping?

Suppose a message is encrypted with a symmetric block cipher with a random key. RSA is often used to wrap the symmetric key using the recipient's public key. In this case, the size of the message is ...
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131 views

Present an attack for the combination of OTP and textbook RSA

Let $N=p \times q$ where $p$ and $q$ are two primes. Compute $\Phi (N) = (p-1)(q-1)$. Choose $e$ s.t. $1 < e < \Phi(N)$ and $gcd(e,\Phi(N))=1$. Compute $d = e^{-1}(mod \ \Phi(N))$. Set ...
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2answers
142 views

Do all attacks against PKCS1 v1.5 encryption require an oracle

As far as I know, all attacks against RSA PKCS1 v1.5 require an oracle; is that true? Or are there any other attacks against it which are able to break it without an oracle? Background: I need to ...
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2answers
95 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 \phi(...
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2answers
576 views

Toy public/private key example open to frequency analysis?

I've been looking at an online Public Key Encryption Example (summarized below). It seems to me that choosing cyphertext = plaintext^(key) mod n would produce the ...
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1answer
2k views

Certificate signature with SHA-1 and RSA: where do 1888 bits come from?

Plenty of X.509 Certificates use "PKCS#1 SHA1 with RSA encryption" as the Certificate Signature Algorithm for generating a 2048-bit signature. The SHA-1 hash function generates a hash value of 160 ...
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1answer
429 views

What kind of machine can generate 100-400 digits prime number? RSA

The 64 bit machine's biggest number can be 2^63 (9,223,372,036,854,775,807). So what kind of a monstrous machine can generate 100-400 digits prime number? I probably don't understand something, so ...
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2answers
416 views

Please punch holes in this authentication scheme

Folks, I am undertaking a crypto course in Uni. Our professor asked us to try and design some authentication schemes which are resistant to active attacks. This was just a in class exercise to get us ...
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384 views

Is semantic security important in a hybrid cryptosystem?

RSA doesn't provide semantic security when used unmodified, and neither does the commonly used PKCS#1 v.1.5 padding scheme for encryption. Is this a problem for hybrid cryptosystems at all? My ...
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580 views

What is the strength of unpadded RSA?

I would like to use unpadded RSA for homomorphic encryption in a toy P2P game, for things like fair coin flips and shuffling. How many bits of security does unpadded RSA have, in relation to its key ...
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1answer
2k views

How to sign a message using RSA?

Assuming I already have a D, P, Q, etc of an RSA key: How do I now sign a message? If it matters – the message is around 100 bits. I don't know much about cryptography, but I can get these numbers ...
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1answer
117 views

Forgery attack against Textbook RSA with simple redundancy

I know how to forge vanilla Textbook RSA message signatures (easy). I've learnt that by adding a good redundancy to the message, it cannot be forged anymore. How can one add redundancy so that the ...
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1answer
131 views

textbook RSA signature scheme security

Are textbook RSA signatures secure if an Adversary does not have access to ask signing oracle queries?
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2answers
111 views

Is it possible to recover an RSA modulus from its signatures?

Let's say that you have some small number of RSA signatures of known data: you know some pairs $(m_k, c_k)$ such that ${c_k}^e \equiv m_k \pmod n$. If you know $e$, because probably it's one of $\{3, ...
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1answer
121 views

Why isn't a table used to solve the large number factoring problem?

Lots of modern encryption (RSA comes to mind) are based on the fact that factoring large numbers is hard. However, multiplying large numbers is much easier, and table lookups are very easy. Since ...
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73 views

How badly does disclosing an M-bit prefix of an N-bit private key compromise security?

I apologize profusely for knowing nothing about cryptography, please go easy on me! I'm working on a project where I have a 2048-bit RSA private key and a public certificate generated from the ...
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1answer
627 views

Why should the primes used in RSA be distinct?

The two primes $p$ and $q$ part of the public key need to be distinct. What's the reason for them to be distinct? Is it because factorization of $p^2$ where $p$ is a prime is relatively easier, or is ...
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1answer
113 views

RSA private exponent primality

I know that the public exponent is always a prime, but what about the private exponent? Is it always a prime too?
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163 views

Publicly exposed hash of private key

Would exposing a cryptographic hash function's digest (e.g. SHA-3) of RSA private key data compromise the key? If so, what are the possible (cryptanalysis-) vectors for attacking the key if an ...
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1answer
2k views

Why does plain RSA not work with big messages ($m>n$)? [duplicate]

From what I can remember, RSA is something like this: Generate 2 distinct prime numbers $p$ and $q$ that have similar bit length. Compute $n=pq$ and $\phi(n)=(p-1)(q-1)$ Compute $e$ such that $1<...
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2answers
855 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 ...
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1answer
696 views

RSA Decryption with Private Key but no public exponent

I manually set the RSA private key, given the private exponent and modulus. When I use this key to decrypt a message encrypted using a public key (also set with public exponent and modulus) seems to ...
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1answer
780 views

RSA smaller number work-out-by-hand not working - I think I made a mistake

I tried out the paper/pencil explanation @ http://sergematovic.tripod.com/rsa1.html, and it seemed to make sense just fine until I came to decryption. Here is what I worked out: Key Creation: Choose ...
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1answer
847 views

How does OAEP improve the security of RSA?

The heart of OAEP algorithm used for RSA encryption are the cryptographic hash functions $H$ and $G$. Does everybody (so also an adversary) know these functions? If YES: How does it help the ...
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2answers
541 views

Why is the following RSA PRNG cryptographically secure?

One requirement states that the generator has to withstand the next-bit test. Consider the following PRNG, where we calculate next output $x_i$ via the formula $x_i = x_{i-1}^ e\mod n$. I can see ...
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1answer
532 views

What algorithm does PGP use to encrypt email?

I know it uses RSA/DSA to create keys, but does it use that same algorithm for the actual cipher?
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1answer
22 views

Can MGF1 within OAEP and PSS be replaced by a XOF?

Do we still need MGF1 as used in the PKCS#1 v2.x specifications for SHA-3 hash functions? MGF1 is currently used for OAEP and PSS as Mask Generation Function. Now that the SHA-3 specification contains ...
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1answer
62 views

How to prove a lemma that is based on phi-hiding assumption?

Assume that the $\phi$-hiding assumption is true, i.e. that for a composite number $m$, a PPT adversary A cannot distinguish between a prime $p_0$ that divides $\phi(m)$ and another prime $p_1$ that ...
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1answer
95 views

Why can you reverse a modulo function when knowing its primes

We are dealing with cryptography in school right now and superficially went over the Rabin cryptosystem with the (apparently usual) example of p=7 and q=11 etc (we didn't do RSA). I understand that ...
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95 views

Securely generating auth tokens

(Disclaimer: I'm an experienced server-side Java programmer, but with little crypto experience.) Objective: I've got a login server which, given a login+password pair, should issue a unique auth ...
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1answer
297 views

RSA vs ECDSA/ECDH

So we've been using RSA for a while now. I wonder, is it still secure? I'm wondering whether surveillance agencies can at this point read traffic encrypted with say, TLS_ECDH_RSA_WITH_AES_128_GCM? ...
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115 views

Inverting RSA function

I am in high school and I am writing a paper on RSA. I want to show that low values of the public key exponent can make it easy to 'invert' the function so that the encrypted message can be recovered. ...
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1answer
349 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 ...
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2answers
222 views

RSA private key d knowing e,n

I need to find RSA private key $(d, N)$ knowing $(e, N)$. It's "own" RSA implementation. As i know $p$ is random 70 bit number, then $q$ is $p-2^{10} < q < p+2^{10}$ $d$ is max 16 bit long with ...
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1answer
166 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 ...