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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The modulus of RSA public key

I am studying the RSA cryptosystem. The public key consists of $(n, e)$, the modulus (product of two large primes), and the encryption exponent. I want to separate the modulus $n$ and exponent $e$. A ...
2
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1answer
287 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 ...
2
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1answer
107 views

Given only RSA public key parameters, what security issues might I be able to detect?

I'm attempting to automate some checks against a large list of .NET assemblies, and want to include a test to see if the RSA parameters used to sign the assemblies are sensible. However, since I don't ...
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1answer
63 views

RSA signatures without padding

Suppose I have a message $M$ for which I generate an RSA-2048 digital signature as follows: $H = H(M)$, $H(M)$ being the SHA-256 of the message $M$ $S = H^d \bmod N$ Assume $N = pq$ is properly ...
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4answers
5k 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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29 views

RSA-PSS salt size in certificate

In RFC 4055, the signature RSAPSS algorithm has the following ASN 1 parameters: ...
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0answers
47 views

RSA_DH vs ECDH implementation

In ECDH protocol is possible, naturally, to use the same algorithm for calculate a secret key for both communication parties (Alice and Bob for example). It is possible to design also a same algorithm ...
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2answers
221 views

ECDH anonymous key exchange to avoid PKI

I want to use TLS to encrypt the communication between peers in a P2P network. Each peer has a well known 256bit peer identifier (the public key of a 256bit elliptic curve keypair). Both peers need ...
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1answer
16 views

PK systems using groups in practice

The four Public-key cryptosystems: RSA, ElGamel, DH, and Rabin (all with others) all require some group operations in an integer field or multiplication group of some residue classes. When it comes ...
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64 views

RSA algorithm assignment [duplicate]

Alice wants to share a symmetric key with Bob. She encrypts the small (64-bit) secret key $K$ with Bob’s public RSA key $(n,e)$ by padding it with zeroes to 2048 bits (the length of n) and computing ...
3
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1answer
52 views

RSA: Range of public modulus

I know the public modulus is the product of two primes. For key with length L, the public modulus N should be such ...
6
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1answer
741 views

If RSA is only used to encrypt symmetric keys which are random, what's wrong with textbook RSA?

IND-CPA is used to protect against frequency analysis AFAICT. But if RSA is only used to encrypt symmetric keys (AFAICT) then what's wrong with using only textbook RSA because random keys are very ...
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0answers
20 views

Are there UFDs where the factorization problem is difficult but finding irreducibles is cheap?

Factorization of integers is hard, but finding irreducibles is expensive. Is there a ring where factorization is assumed hard but finding irreducibles is much cheaper than over $\Bbb Z$? It could ...
4
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1answer
177 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 ...
3
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1answer
101 views

RSA with $\lambda(n)$ or $\varphi(n)$

The PKCS #1 v2.0 specifications suggest using $\lambda(n) = \mathrm{lcm}(p-1,q-1)$. What is the benefit of choosing $\lambda(n)$ over $\varphi(n) = (p-1)(q-1)$ in RSA key generation?
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1answer
68 views

In what cases will RSA not work? [duplicate]

I know that there are cases when RSA will not work like when the number to feed into the system is greater than the modulus. I was wondering if there were any other cases when RSA won't work I looked ...
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2answers
98 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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0answers
20 views

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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1answer
100 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 ...
3
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3answers
750 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 ...
0
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1answer
59 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
3k 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
265 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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27 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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2answers
126 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
93 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
89 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
207 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 ...
2
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1answer
221 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 ...
12
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1answer
327 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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0answers
85 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 ...
3
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1answer
279 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
46 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 ...
0
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1answer
88 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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0answers
96 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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0answers
88 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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105 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
345 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 ...
2
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1answer
67 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 ...
2
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1answer
40 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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0answers
34 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 ...
2
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2answers
196 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 ...
3
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2answers
716 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 ...
3
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1answer
123 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 ...
0
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1answer
64 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
61 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
120 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
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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 ...