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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Deterministically generate a RSA public/private key pair from a passphrase (with sufficient entropy)?

Is it possible to deterministically generate public/private RSA key pairs from passphrases? Would giving the (key generating) algorithm data made from key-stretching the passphrase (instead of a ...
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Encrypting small values with RSA private key

I'm looking for best practices when it comes to encrypting small (< 128 bytes) amounts of data with the RSA private key. Signing it would make the resulting payload too large.
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2answers
710 views

RSA Signature Weak Padding Attack

Assume that we have a message $m$ of size $n$, and it is padded with two 01 bytes in front. Then the signature $s$ is computed using a private key $ks$. Can we ...
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5answers
598 views

RSA leak bits to factor N

Suppose you randomly generate large primes p and q as in RSA, and then tell me N=pq but not p or q. Then, you would like to actually let me factor N, except you should tell me as few bits of ...
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6k views

Low Public Exponent Attack for RSA

I'm having trouble understanding the algorithm for finding the original message $m$, when there is a small public exponent. Here is the example I'm trying to follow (you can also read it in the 'Low ...
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Is RSASSA-PKCS1-v1_5 a good signature scheme for new systems?

Is RSASSA-PKCS1-v1_5 a good signature scheme to recommend that people use in new systems? Is it believed to be secure and represent the state-of-the-art in RSA-based signatures? I understand that ...
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1answer
236 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 $...
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What is a trapdoor permutation?

Can anyone explain to me what a trapdoor one-way permutation is? Is RSA a trapdoor one-way permutation? Context: I was reading about ring signatures. On page 560, it describes steps to ...
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1k views

Decrypted RSA 64 bit encryption using modulus and private exponent. Got gobbledygook [Verify] [closed]

As part of an experiment, I was given a .enc RSA (encrypted) file that was most likely generated using openssl. I had the public key, I factored it, obtained the private exponent, and decrypted the ....
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4k views

Assuming a 1024qb quantum computer, how long to brute force 1024bit RSA, 256bit AES and 512bit SHA512

Assuming in the future there was a functioning 1024 qubit quantum supercomputer and it could run Shor's algorithm or Grover's algorithm to crack encryption very quickly. I'm interested in how the ...
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Why does the PKCS1 RSA private key structure contain more than just exponent and modulus?

The ASN.1 spec for the PKCS1 RSA private key format is as follows: ...
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612 views

Given a message and signature, find a public key that makes the signature valid

Given a message $M$ and a signature $S$, is it feasible to find a RSA public key $(n,e)$ such that $S$ verifies as a valid signature on $M$ (using this public key)? What if we're given one public key ...
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227 views

How many qubits are required to break RSA 2048 or 4096 with a universal quantum computer?

So in the news this week, IBM have created a universal quantum computer with 5 fully functional qubits. Logic and Moore's law dictates they will be able to scale this up to a lot more qubits within a ...
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1answer
8k views

How much stronger is RSA-2048 compared to RSA-1024?

How much stronger is RSA-2048 compared to RSA-1024? It is hard to imagine very big numbers. So what would be your way to explain the difference to someone who doesn't know much about cryptography?
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678 views

Proof that padded RSA is CPA-secure

I'm referring to page 383 of J. Katz and Y. Lindell's Introduction to Modern Cryptography. The book presents a padded RSA: ${\bf Key Generation:}$ same as Textbook RSA (given security parameter $1^...
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2answers
883 views

uniqueness of the RSA public modulus

What is the probability that two separate RSA public moduli are the same? For example, consider a 2048-bit modulus. The number seems to be huge, but the choice for prime factors p and q is much more ...
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293 views

Using same modulus for RSA

I know that there exist some attack when using same modulus. Can two different pairs of RSA key have the same modulus? RSA cracking: The same message is sent to two different people problem But ...
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2k views

ECDSA vs RSA: Performance on Android platform and surprising results

For our privacy-preserving protocol, an encrypted channel is established. In order to protect our system from man-in-the-middle attacks, signature-based approach is used. After we've implemented it ...
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8k views

Cracking plain RSA without private key

I was wondering whether plain RSA encryption can be cracked given: The public key A plaintext of a known cipher text(s). In other words the decrypted message from an encrypted one (but without ...
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2answers
3k views

What data is saved in RSA private key?

What data is saved in RSA private key in openssl? How to view it? Wikpedia says these variables are saved.
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1answer
596 views

RSA Encryption and Signature - Weak Padding

Assume that I have an plaintext $m$ and it is padded with $randompad||00||m$ and then it is encrypted with RSA and a public encryption key so we get the encrypted $Sm$. Then to assure its integrity ...
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1answer
1k views

Montgomery Ladder vs Double-and-Add

I would like to know what (if any) are the advantages of using Montgomery Power ladder over the Double-and-Add-Always algorithm. I think that firstly, Monty would be slightly faster than DoubleAndAdd. ...
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624 views

Would RSA make sense if we used no computers?

I was recently wondering - would RSA be useful if we brought it to, say, medieval times? Could you choose the keys so that you could encrypt/decrypt messages quite easily, but factoring the private ...
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1answer
643 views

What is the harm if I publish an encrypted RSA private key publicly?

What is the harm if I publish an encrypted RSA private key publicly? Or in this case, what is the harm if I publish many thousands or millions of them? Assuming that the private key is encrypted ...
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Calculating private keys in the RSA cryptosystem

The number $43733$ was chosen as base for an implementation of the RSA system. $M=19985$ is the message, that was encrypted with help of a public key $K=53$. What is the plaintext text? What is the ...
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535 views

What is the key strength reduction encrypting only 160 bits of data using RSA1024 for signatures?

I am attempting to determine the strength of an incorrectly implemented 1024 bit RSA signature scheme. The weakness in the implementation is that the padding data lacks random numbers. As a result, ...
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3answers
662 views

Security equivalence proofs for breaking RSA

It is my understanding that while a practical solution to the factoring problem will definitely break RSA, it has never been proven that the security of RSA is equivalent to factoring. In otherwords, ...
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564 views

Threshold Signatures for RSA and DSA

I have a few questions relating to threshold signatures: a scheme where $n$ participants hold a key share and any $t$ of them can conduct a protocol using their shares that results in a valid RSA or ...
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How to calculate the time it'll take to crack RSA or DH?

Sometimes the easiest way to describe security of a type of cryptography is to say that "the time it takes to solve for an x-bit key would be y years". How would one go about doing such a calculation ...
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Pseudocode for constant time modular exponentiation

I'm looking to implement modular exponentiation (for RSA) in constant time, but most of the examples I've found are more mathematical descriptions of the operations. Are there any references with ...
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1answer
170 views

How to generate a bilinear group of prime order p for key generation

I am trying to implement an IEEE Paper In Cryptography. I read many reference regarding an RSA key generation. But i am confused with above statement. Please someone explain me What it says with ...
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1answer
268 views

Modular exponentiation on calculator for textbook RSA

How do you encrypt $51$ with public key $(n,e) = (91,23)$ I understand that $c = 51^{23} \bmod 91$. How can I calculate the result on a calculator?
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Why $n=pq$ with $p=2p'+1$ and $q=2q'+1$ instead of just $n=p'q'$ for RSA crypto?

For RSA cryptography, we know that the modulo $n$ is a product of two big prime numbers(say $p$ and $q$). However, in some documents I see an extension of $p=2p'+1$ and $q=2q'+1$ with $q'$ and $p'$ ...
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When is an asymmetric scheme considered broken?

Does the following quote imply that valid encrypted data can be created and decrypted by someone other than the owner of a private key: An asymmetric encryption scheme is considered to be broken ...
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1answer
90 views

For which RSA moduli, precisely, is $e=d$ for all $e$?

This question shows that there are at least two valid RSA moduli $n$, namely $35$ and $91$, such that for any $e$ coprime to $\lambda(n)$, $$e^2\equiv1\mod\lambda(n)\text.$$ Reading the linked ...
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1answer
436 views

Is it possible to determine the group order by knowing the “public” and “private” key exponents in an RSA group?

I have an RSA group with modulus $n = p \cdot q$, two safe primes $p=2p'+1$ and $q=2q'+1$ and the "public" and "private" key exponents $d$ and $e$. $\phi(n) = 4p'q'$ is the order of the RSA group. If ...
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1answer
750 views

Cracking an RSA with no padding and very small e

I have a project wherein I have to crack a given cipher text encrypted using RSA and have been given N and e. Can someone suggest an RSA attack using a very small exponent e(here e=3) and no padding?
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2answers
592 views

Is it possible to figure out the public key from encrypted text?

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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3answers
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If RSA is limited to 117-200 bytes or so, is that a very limited use case?

Am I missing something, or is RSA very very limiting when it comes to ecrypting data when it comes to the actual message size? I have read that you can only encrypt a message of around 117 to 200 ...
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2answers
635 views

Encryption with private key?

we normally always encrypt by public key and decrypt with private key. If i encrypt with private key, then its still secure as normal PKI ? i mean known-plain-text will not take private key on the ...
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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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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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3answers
802 views

RSA finding the inverse of the public exponent

I have a very basic doubt in RSA key generation and its usage. In RSA key generation you choose two large prime numbers of a very large order. Then you multiply them.(eq $p \cdot q = N$) Now, $\phi(N)...
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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 ...
2
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1answer
277 views

Short length asymmetric encryption?

I want to send out short messages to the world which listeners could verify to be send from me. The way this is usually done is to encrypt the message with a private key where the readers decrypt it ...
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2answers
242 views

RSA keys finding when messages are known

I have this situation, where, in a game, people send messages to each other (game moves etc...) These messages need to be encrypted, and should only be readable by the destination person. I am using ...
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638 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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File format of an $2048$ bits RSA public key

From here, there are $14$ bytes specifying the file format of the key. I am still quite confused about the format bytes. For example, the following public key 30 82 01 0a 02 82 01 01 00 8e a3 d1 c7 ...
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1answer
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1024 RSA Hash Signature attack. Forge a valid signature

I have an RSA signature of 1024 bit where i know the following: Public modulus N Public exponent (0x03) Cypher message Summary: An MD5 hash is calculated from a collection of byte and is used as ...
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How can I find the prime numbers used in RSA?

I got this question in a local hacking event, but I couldn't solve it. Problem Statement ---- Continuing their snooping habit, NSA kept bugging Alice's communication. Resorting to the age old ...