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

4
votes
4answers
447 views

Where does the $\varphi(n)$ part of RSA come from?

$e d \equiv 1 \pmod{\varphi(n)}$ Where does the $\varphi(n)$ part come from? How did the inventors of RSA arrive at $\varphi(n)$?
4
votes
4answers
570 views

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 $p'$ ...
4
votes
3answers
643 views

P = NP and current cryptographic systems

I've recently heard some people claiming that if the fact that P = NP is proven, most (all?) the current cryptographic algorithm considered secure like RSA will be unusable in secure systems. My ...
4
votes
3answers
1k views

What is the likely cause the RSA algorithm gives back plain text in this case?

Text book question of Chapter 9 of "Crypto and Network Security" by William Stallings: When using the RSA Algorithm — if a small number of repeated encodings give back the plain text, what is the ...
4
votes
2answers
2k views

Is RSA in a ECB-like-mode safe for bulk encryption?

Let's say I would like to communicate with my friend using asymmetric/public-key encryption, e.g. RSA. (Note: I do realize that in practice this is done through an intermediate symmetric key, but ...
4
votes
3answers
389 views

Can an ephemeral RSA key give forward secrecy?

Suppose party A generates an ephemeral RSA key and sends the public key to B. Party B then generates a symmetric key, encrypts it with Party A's public key and sends the Ciphertext to Party A. Party ...
4
votes
3answers
774 views

How can mega store my login details and still be secure?

I understand how Mega's encryption works. For a quick summary of all those in the future looking for an answer on this... here is how it works: Upon first signing up for an account you make a ...
4
votes
2answers
216 views

Does a high exponent compensate for a low degree of certainty?

If a RSA certificate is created with a low degree of certainty, does the value of the exponent compensate for this? I'm asking because certain implementations of key generation software hide the ...
4
votes
1answer
236 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?
4
votes
1answer
201 views

RSA time function

I am doing a paper on textbook RSA (highschool-level). I am explaining and proving the significance of the public key exponent in time and security. So far, I have encrypted a constant message with a ...
4
votes
4answers
1k views

Tamper-proofing log files

Problem Overview I want to securely store log files so the contents are secret, and they can't be modified without detection. The files will be encrypted using authenticated encryption (AES in GCM ...
4
votes
1answer
1k views

What happens if an RSA key pair has identical public and private exponents?

Rather, is it possible for big prime numbers? Classroom examples usually involve smaller primes, so for example if you are given a prime number pair $p = 3$, $q = 13$ you would get $n = 39$ and $e = ...
4
votes
3answers
7k views

RSA Proof of Correctness

Can anyone provide an extended (and well explained) proof of correctness of the RSA Algorithm? And why is it needed? I can't say that this or this helped me much, I'd like a more detailed and newbie ...
4
votes
2answers
508 views

X.509 CSR: Why does CA remove signature?

I just read this article on Wikipedia: Certificate Signing Request I'm not a PKI or Crypto expert. As I understand, a CSR (certification request) is always signed by the PKCS#10-Request creator. ...
4
votes
1answer
2k views

RSA: If n=35, show that e will equal d

Show that if $n = 35$ is used as an RSA modulus then the encryption exponent $e$ always equals the decryption exponent $d$? What I have so far: $n = 35$ Therefore $p = 5$ and $q = 7$ or vice versa, ...
4
votes
1answer
329 views

For RSA keys, is the safety of a given key-length different for signing vs encryption?

I'm wondering if considerations of key-length are different when thinking about signing vs encryption. If for some reason, it was safter to use smaller keys for signing that would be interesting.
4
votes
3answers
224 views

Why are we not using multiple ciphers per message?

I am aware of at least rsa, elgamal-encryption, and variations of elliptic-curves relying on different problems and that those problems are considered hard. However, if someone figures out a way to ...
4
votes
1answer
7k views

HMAC SHA256 vs RSA SHA256 - which one to use

Salesforce recently announced they are moving away from HMAC SHA256 to RSA SHA256. Why did they make that move?. Any technical factors? Is HMAC really easy to break? ...
4
votes
2answers
281 views

how to iteratively calculate a^emod n with modulus n sized 4096 bits

In most sites the exponent of the RSA public key is 24 bits. But the modulus can get to 4096 bits size. I have an accelerator that can get max. 2112 bit size modulus. It calculates ...
4
votes
3answers
5k views

Is javascript RSA signing safe?

I'm currently working on a secure open source messaging system (https://github.com/DSMNET/DSMNET). I'm currently using the cryptico.js (https://github.com/wwwtyro/cryptico) library to encrypt all the ...
4
votes
1answer
1k views

Why is ElGamal considered non-deterministic?

One difference between RSA and ElGamal is that ElGamal isn't necessarily deterministic (while RSA is). What makes it non-deterministic? Is this advantageous to security? How else does this property ...
4
votes
1answer
187 views

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 ...
4
votes
2answers
94 views

RSA 3072 is 65,536 more difficult to factor than 2048?

If RSA 3072 is equal to 128 bit symmetric and 2048 is equal to 112 bit symmetric then 128-112= 16 and 2^16= 65,536. In that case wouldn't this make 3072 more future proof against quantum computers or ...
4
votes
1answer
102 views

Distribution based integer factorization

The past week I've been looking into - and playing with - algorithms for factoring RSA moduli. From what I understand, it's important that the primes p and q are of the same magnitude as the square ...
4
votes
1answer
401 views

Is knowing the private key of RSA equivalent to the factorization of $N$?

Given the RSA modulus $N$ the fastest method to factor it is of sub-exponent order. But, now if I know the private key $d$ of RSA, does that mean I can factor $N$ efficiently?. It intuitively seems ...
4
votes
1answer
261 views

Solve a Modular Exponentiation

It might be common, but if we had to solve an equation like this $m=s^{e}$ mod $n$ where $m,e,n$ are known. How can we find $s$. What optimisations could be applied? And what would the complexity of ...
4
votes
3answers
197 views

Why can an RSA signature be authenticated ONLY with the signer's public key?

I'm an undergraduate Math student currently taking a cryptology course. I have a question about the RSA signature authentication mechanism. An RSA signature can be authenticated with the public key ...
4
votes
1answer
3k views

Constructing RSA private key, given public key

As part of a puzzle I was given an RSA 256-bit public key and an encrypted message. The key itself is very weak, having exponent e = 65537 and modulus N = ...
4
votes
1answer
272 views

Signing a GCM MAC

If I encrypt a message with AES-GCM, is it safe to use the MAC as the hash in a DSA/RSA signature? That is, if someone knows the AES key and nonce, will they be able to generate a different message ...
4
votes
1answer
421 views

How to sign a large file for random-access reading?

I need to write an "Authoring" application which produces large files. These files must be signed so that the "Consuming" application knows that it was authored with a matching key. The consuming ...
4
votes
2answers
241 views

Why is 2048-bit RSA always paired with 320-bit ECC?

You may already have noticed that most smart cards ship with 2048-bit RSA support and 320-bit ECC over GF(p) support. You may have already asked yourself "why exactly 320-bit?". Now I remember having ...
4
votes
1answer
2k views

RSA example-calculation: Public Key = Private Key (e = d)

I am a bit confused. I just calculated manually the single steps of RSA for an implementation with small numbers and suddenly $d$ was equal $e$. Please help me understand what I am doing wrong. ...
4
votes
1answer
223 views

Is the strength of RSA over quadratic or other cyclotomic fields as strong as over the integers?

If we assume the strength of RSA is based on the difficulty of factoring (which I know we can't guarantee) and we compose the modulus of some other quadratic ring that is a unique factorization domain ...
4
votes
1answer
712 views

Recent attacks on RSA

At Blackhat 2013 this week, there was a talk saying RSA is (essentially) doomed in the near future. networkworld.com ~ “Black Hat: Elliptic curve cryptography coming as smarter algorithms threaten ...
4
votes
2answers
370 views

It is reasonably safe to leave a SSH private key with a 30+ character passphrase public?

I'm curious about exploring uses for a distributing a single RSA private key with a passphrase instead of trying to secure the private key and distribute the public key. With the private key (and ...
4
votes
1answer
725 views

Are RSA signatures deterministic?

If I sign the word HELLO with the mechanism "NONEwithRSA" with the same private key, do I always will have the same signature? A Java example always return ...
4
votes
1answer
221 views

Why work in a subgroup QR(n) of an RSA group $Z^*_n$?

I sometimes read in papers that a (sub-)group generator $g$ is taken from $\mathrm{QR}(n)$ instead of $\mathbb{Z}^*_n$, where $n = p \cdot q$ and $p$ and $q$ are prime. Is there a reason for this? ...
4
votes
2answers
817 views

Attacks on the RSA Cryptosystem

I was reading some articles about attacks on RSA system and I wonder about some generalization of the following theorem. Theorem (Coppersmith). Let $N=pq$ be an $n$-bit RSA modulus, where ...
4
votes
3answers
3k views

Is it safer to encrypt twice with RSA?

I wonder if it's safer to encrypt a plain text with RSA twice than it is to encrypt it just once. It should make a big difference if you assume that the two private keys are different, and that the ...
4
votes
2answers
2k views

Homomorphic cryptosystems in RSA

Hopefully Crypto can help me understand homomorphic cryptosystems. I'm designing a high score server for a game I made, and because of facets in the language i'm using, the player would be able to ...
4
votes
2answers
4k views

Secure private key storage

I'm developing application in Java that has to store RSA keys in software for foreseeable future (that is, at least 10 years). The two most common standards of storing private keys are PKCS12 and JKS ...
4
votes
2answers
637 views

Calculate the RSA private exponent from the CRT parameters

I am trying to make the RSA structure of Openssl manually, knowing the public key ($n$, $e$) and the CRT parameters $p$, $q$, $d_P$, $d_Q$, and $u = q^{-1} \mod p$. That is, I want to get the $d$ ...
4
votes
3answers
1k views

Creating a license system based on asymmetric encryption (RSA or ECDSA)

I’ve spent a couple of days researching the topic of creating a license system for my desktop software. While I fully understand that there’s no perfect copy protection, this approach seems to have ...
4
votes
2answers
2k 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.
4
votes
1answer
239 views

What is the property of RSA where N=e?

In RSA, suppose we know that $e=N$ and we are given the value of $e$. ($N = p\cdot q$ for some large primes $p$ and $q$; $\gcd(e, \varphi(N) = 1)$ Can we calculate $d$ ($d = e^{-1} \mod ...
4
votes
3answers
90 views

Choosing which is public vs private key

When I calculate two RSA keys, what if anything, would make any difference which I call the public vs which I call the private key?
4
votes
1answer
92 views

Does rsa-oaep provide or not plaintext integrity in addition to confidentiality?

My own understanding (possibly wrong of course) of RSA-OAEP encryption scheme is that it provides plaintext integrity (in addition to confidentiality) due to MGF function which for encryption ...
4
votes
1answer
759 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 ...
4
votes
3answers
565 views

Does RSA operate over a Finite Field (Galois Field)?

Is it correct to say that RSA operates over a Finite Field (Galois Field)? In this case GF(p)? I do understant that the modulo in RSA is not itself a prime number, but all the operations ...
4
votes
2answers
217 views

How can one encrypt with RSA (or ElGamal) without revealing whom the ciphertext is intended for?

Imagine Alice wants to encrypt for Bob and post this encryption publicly, so that only Bob can decrypt but no one can other than Alice or Bob tell that the message was encrypted for Bob. The naive ...