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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RSA: If I sign the same digest with same key twice, will the signatures be identical? [duplicate]

If I don't have public keys to verify the signature, can I use this to discover that two signing services are using the same key? Can you send a reference?
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65 views

How often does RSA-OAEP have a leading zero?

We are working with a third party vendor who is very tight lipped about their security protocols, and one of our customers who used this vendor's products is claiming that approximately one in every ...
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3answers
636 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 ...
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1answer
57 views

RSA function over $Z_t^{*}$ where $t$ is prime

RSA function is defined over $Z_N^{*}$ where $N=pq$ with $p,q$ primes. A public key is a pair $(N,e)$ and a private key is $(N,d)$ where $d=e^{-1} \mod \phi(N)$. Assume that RSA function is defined ...
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2answers
8k views

How much computing resource is required to brute-force RSA?

It's been over 30 years since Rivest, Shamir and Adleman first publicly described their algorithm for public-key cryptography; and the intelligence community is thought to have known about it for ...
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1answer
157 views

Unblind a RSA blinded signature

I have blinded $m = 16$ with $r= 13$, $e = 7$ and $n = 209$. This resulted in $m' = 464$, which led to a $s' = 8$. Now, I want to unblind this $s'$ by using $s = s' \times r^{-1}$ but im stuck at ...
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1answer
58 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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1answer
2k 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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9answers
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Now that quantum computers have been out for a while, has RSA been cracked?

D-wave systems has released a commercially viable quantum computer. This means in theory, that all asymmetric encryption algorithms — such as RSA — are now useless due to the speed at which quantum ...
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1answer
242 views

Factoring large numbers

I am trying to factor few integers that are each between 115 and 135 digits long. I was wondering if anyone knew of any efficient methods or any programs that I could use to find the two primes $p$ ...
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21 views

RSA Signature Forgery

We all know that x509 certificates carry a signature that represents the certificate digest encrypted by the private key of the issuer. I believe that the digest is encrypted only providing one ...
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1answer
140 views

Factorize RSA knowing several N and E

I did a CRT challenge yesterday and there`s one problem I was unable to solve, probably due to my lack of understanding advanced crypto math. It`s about RSA. There are ten given pairs of N and E ...
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66 views

PGP public RSA key format

I have been trying to use Go (I could post the code, but I think I posted enough already...) to generate a PGP RSA key. However every time I try to encrypt something with it, something fails. However, ...
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2answers
100 views

Using ECB as RSA encryption mode, but encrypted messages are unique

As I understand, ECB should not be used as encryption mode unless you are encrypting single blocks of data which are always unique and only are encrypted once. I have a collection of ids represented ...
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1answer
105 views

Assemble RSA keys from components

I'm studying openpgp cryptography and struggling to understand some things. I can't use pgp tool for generating keys and ecryption, but have to write a simple app to generate keys, encrypt and decrypt ...
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0answers
19 views

Transform RSA private key to ssh-rsa public key [closed]

I am generating a RSA key pair and write it to disk. I would like to transform the public key to look like this: ...
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1answer
56 views

Why is the public/private key length used in libsodium so much shorter than needed for RSA [duplicate]

Reading the libsodium source I see that is uses a key length of 32 bytes (256 bit) for private/public key encryption. For RSA private/public key encryption a key length of 2048 (or 4095) bit is ...
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1answer
88 views

Montgomery and Galois fields

I'm a little bit confused about the design of a RSA module in VHDL. My question isn't directly related to hardware design. I've read a lot of publications and I bought also a book. In one publications ...
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2answers
197 views

What prime lengths are used for RSA?

Let's assume we have an RSA 2048 that was produced by two primes multiplication. What is the digit's difference in those 2 factors? For example one prime is 1024 digits and second one 1024 or, one is ...
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1answer
190 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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1answer
198 views

How does knowing the factorization of N can help to obtain the secret?

Assuming $x=a^2 \pmod n$ and knowing $x$, $p$, $q$ how is it possible to obtain $a$?
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1answer
258 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 ...
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83 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 ...
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1answer
169 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 ...
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1answer
41 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 ...
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1answer
81 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 ...
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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 ...
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86 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. ...
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103 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 ...
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1answer
314 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 ...
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1answer
43 views

Session key Exchange, some doubt

I have to find a solution to this problem: I have a network composed by 1 server and some client. The server has a couple of keys (public and private) and it shares a secret key with each client. My ...
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1answer
965 views

Bleichenbacher 1998 “Million message attack” on RSA

I have been reading Bleichenbacher's 1998 paper on a forged message attack on RSA. The paper assumes access to an Oracle that takes a ciphertext $c$ and will check the decrypted text for valid PKCS #1 ...
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1answer
62 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 ...
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1answer
34 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 ...
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29 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 ...
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1answer
68 views

Where I can find a list of certified software / hardware RNGs compliant to NIST SP 800-22?

I need to use NIST SP 800-22 approved software / hardware to generate RSA key pair. Where I can find a list of certified software / hardware RNGs compliant to NIST SP 800-22? And how is the SP ...
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2answers
117 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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1answer
61 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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3answers
4k views

How are primes generated for RSA?

As I understand it, the RSA algorithm is based on finding two large primes (p and q) and multiplying them. The security aspect is based on the fact that it's difficult to factor it back into p and q. ...
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1answer
67 views

Why isn't Rabin-Williams cryptosystem widely used?

I think we all know RSA. And of course we also know DJB (a.k.a. Daniel J. Bernstein). Now some already have noticed that he has an opinion towards cryptographic questions. In his 2008 paper on ...
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2answers
617 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 ...
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1answer
105 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 ...
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1answer
55 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: ...
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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 $m$ ...
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2answers
75 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: ...
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3answers
4k 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 ...
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1answer
96 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 ...
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1answer
109 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 $3$) ...
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45 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?
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2answers
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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 ...