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 much plainext could be known without reducting security of RSA?

It is known, for example, that exposing 50% of most significant bits of RSA private exponent does not provide security risk (when a small public exponent it used). So how to qualify security ...
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RSA reencryption scheme

Is there such an algorithm that would allow to upgrade the encryption of a RSA-encrypted message without revealing the plaintext to the untrusted user? Basically, such an algorithm would probably be ...
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123 views

RSA security assumptions - does breaking the DLP also break RSA? [duplicate]

Possible Duplicate: Would the ability to efficiently find Discrete Logs have any impact on the security of RSA? I'm wondering if breaking the DLP, that is the basis for ElGamal and DSA, ...
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615 views

Does it make sense to have a 4000 bit long key?

My question is about the key length of a asymetric algorithm. How is it possible to memorize or remember a key that is about 4000 bits long?
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Is 512-bit RSA still safe for signature generation?

The standard CSP on Windows XP only supports RSA up to 512-bit, which means that it's the maximum key size I can use for authenticity verification of updates. The public key is embedded in the ...
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When NIST disallows the use of 1024-bit keys, what effect will that have on SHA-3 (with max. 512 bits)?

Quoting the article Gone in 60 Months or Less: The National Institute of Standards and Technology (NIST) has disallowed the use of 1024-bit keys after 31 December 2013 because they are insecure. ...
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186 views

Is it safe to use RSA as a proof-of-work system?

Suppose I devised the following challenge-response proof-of-work system: A server generates a 2048-bit RSA modulus, and uses the "public" exponent (usually 65537) to sign a random nonce a fixed ...
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313 views

Is it possible to attack RSA with a WalkSat derivative?

We consider a large $n$-bit number $N$. We want to find a factor, if it admits any. For $m$ taking values from $1$ to $n$, perform the following three steps (actually, for each $m$, perform many ...
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5k views

What is the meaning of “trapdoor” in cryptography?

I do not really understand the meaning of a "trapdoor" in cryptography, so here are my questions: What is the meaning of trapdoor and how can I convert a word or string using a trapdoor in ...
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678 views

How exactly are GPG keys mathematically related, and prime numbers inside of GPG general

Before anyone suggest it, I've yet to pick up "Applied Cryptography" I'm planning on picking it up the next time I visit amazon. I know that the keys are somehow mathematically related, and I know ...
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460 views

In RSA, why does $p$ have to be bigger than $q$ where $n=p \times q$?

In openSSL – during RSA key generation – if $q$ is bigger than $p$, they exchange them. Why is that?
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RSA assumption and cryptography

The RSA assumption states that it is hard to find $m$, given $c = m^e \bmod{n}$, $e$, and $n$ (for appropriate choice of $n,e$). Suppose that there exists an algorithm, $D(c,e,n)$, that finds $m$ in ...
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RSA with composite numbers

It has been said that RSA uses a modulus product of two prime numbers for security reasons. But does RSA even work correctly if we allow composite integers instead? I think that the answer is "NO". ...
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81 views

How do I classify my RSA encryption strength?

So I generated 2 1024 bit prime numbers, I generated N and got a 2048 bit number, does that make my encryption 2048 bit or 1024 bit?
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385 views

What do numbers in a crypto algorithm stand for? Is there a convention?

What do the numbers stand for in the names of cryptographic functions, for example AES-256, RSA-1024 or ...
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2answers
480 views

Is it safe to reuse a symmetric key when using asymmetric encryption?

I've written a C# Library that I hope will be used for security purposes in a commercial application. The application will communicate through the internet and not on an internal network. I am using ...
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662 views

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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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
859 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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733 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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150 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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849 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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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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216 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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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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333 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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311 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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How to decrypt this RSA-like cipher

Suppose we have a RSA-type Modulus $n = pq$ with $p,q$ prime. We also pick a random public exponent $e$ with $\gcd(e,\varphi(n)) = 1$ and compute the private exponent $d$ with $de \equiv 1 ...
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158 views

Checking the integrity of RSA public key

Let's say I need to verify a digital signature and the public key is stored in untrusted storage which I need to fetch before I verify the digital signature. However, I can store the cryptographic ...
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242 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
239 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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375 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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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 $d = e^{-1}(mod \ \Phi(N))$. ...
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137 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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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 ...
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557 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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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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423 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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407 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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375 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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341 views

RSA Key generation Public exponent too big

I'm currently writing a paper about RSA (a self-chosen subject). I'm writing about the key-generation in RSA, and I have problem finding the public exponent e. I have chosen p = 61 and q = 53. Then ...
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569 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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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
115 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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106 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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120 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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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
612 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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659 views

what are DP and DQ in Encryption by RSA in c#

I want to know about these tags in RSA Encryption by private Key. when I use this code: ...
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110 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?