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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What followed findings of A. Lenstra et al. concerning shared factors of practical RSA moduli?

A. Lenstra et al. had a paper in 2012 "Ron was wrong, Whit is right", in which one reads: "What surprised us most is that many thousands of 1024-bit RSA moduli, including thousands that are contained ...
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1answer
89 views

Why can you reverse a modulo function when knowing its primes

We are dealing with cryptography in school right now and superficially went over the Rabin cryptosystem with the (apparently usual) example of p=7 and q=11 etc (we didn't do RSA). I understand that ...
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94 views

Exactly how slow is asymmetric encryption?

I'm currently doing a project on RSA, and have just come across this website. https://www.namecheap.com/support/knowledgebase/article.aspx/798/67/what-is-an-rsa-key-used-for On here, it says that ...
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1answer
202 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 ...
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3answers
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In RSA, do I calculate d from e or e from d?

In the original paper introducing RSA, it is implied that one should first choose $d$ and then calulate $e$ from $p$, $q$, and $d$. However, I have found in other places (such as the wikipedia article ...
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1answer
268 views

Signing/verification between Java and the OpenSSL

I'm trying to sign/verify data between a C application and a Java application. In java for now I was using the built-in JCE provider with SHA256withRSA as ...
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2answers
92 views

Securely generating auth tokens

(Disclaimer: I'm an experienced server-side Java programmer, but with little crypto experience.) Objective: I've got a login server which, given a login+password pair, should issue a unique auth ...
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1answer
236 views

Encrypt large data with RSA through blocks in java

I'm working on a communication protocol where a client sends encrypted data to a server. What happens is that in some point, the client creates a symmetric key used to create data digests through the ...
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1answer
44 views

What part of an RSA key is referred to by the number of bits? [duplicate]

When we speak about 4096- or 2048-bit RSA keys, what part of the key is this number of bits? The public key comprises both the modulus and the public exponent, and the strength of the key can also be ...
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2answers
111 views

Leading 00 in RSA public/private key file

I found these following values ALWAYS have the leading 00 in public/private key, public key: modulus private key: modulus, p,q, d mod (p-1), d mod (q-1), coefficient e.g., modulus ...
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17 views

Strength of a cryptography algorithm [duplicate]

I'm just read this article from Atmel corporation in comparing RSA with ECC cryptography algorithms. First of all please read these two paragraphs quoted from the article: P1: Strength of an ...
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1answer
177 views

Consequence of a change on the Guillou-Quisquater Protocol

In the Guillou-Quisquater Protocol, the prover convinces the verifier that he knows an $e$-th root of an element $y \in \mathbb{Z}^*_n$ ($p, q, e$ are primes, $n = pq$ and $e$ is coprime with ...
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62 views

Calculating Phi(M) and D for RSA decryption given p,q,e

I've been given a message in 4 digit numbers but it doesn't seem to work when I use my calculated values for phi(m) and d. If I'm correct phi(m) = (p-1)(q-1) correct? And d is given by ed = ...
2
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1answer
211 views

RSA vs ECDSA/ECDH

So we've been using RSA for a while now. I wonder, is it still secure? I'm wondering whether surveillance agencies can at this point read traffic encrypted with say, TLS_ECDH_RSA_WITH_AES_128_GCM? ...
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4answers
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Why is RSA encryption key based on modulo $\varphi(n)$ rather than modulo $n$?

While calculating RSA encryption key we take modulo $\varphi(n)$ rather than modulo $n$. I can’t understand why it’s done this way.
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1answer
106 views

Why is RSA encryption version 1.0 not specified in an RFC?

I saw that there are three RSA encryption versions, as follows: RSA encryption version 1.5 (RFC 2313) RSA cryptography specification version 2.0 (RFC 2347) RSA cryptography specification version 2.1 ...
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1answer
72 views

Find a constant $C$ in $O(Cn^2)$?

I am writing a paper on RSA, and I am calculating some encryption running times. I have been told that the encryption running time is $O(n^2)$ where $n$ is the modulus. I have also been told that ...
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2answers
218 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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1answer
90 views

How to write the encrypted message after using RSA

I have created a RSA encryption/decryption program but how do i write out the results after doing a encryption? Right now I have it so that it will just print out the decimal value of one character ...
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1answer
78 views

Diffie-Hellman using a different modulus on both sides

For Diffie-Hellman Key Exchange, the used modulus is the same throughout the process. Is it possible to use 2 different for both sides? For example, $A \gets M^{d_1} \pmod{n_1} $ $B\gets M^{d_2} ...
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1answer
2k views

how to use common modulus attack?

I am struck with the following problem: Let Alice, Bob, Chris and Eve communicate over a public network. They encrypt all messages they send using RSA system. Bob and Chris have the RSA modulus ...
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Why is it important that phi(n) is kept a secret, in RSA?

Why is it important that $\phi(n)$ is kept a secret, in RSA?
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Is using same key pair for both encryption and signing secure in RSA [duplicate]

In GPG, we can use same key pair for encryption and signing. Can't/Shouldn't we do this in RSA. I am using RSAES-OAEP and RSASSA-PSS, not raw RSA btw.
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How to decrypt RSA cipher text? [closed]

How can I decrypt an RSA cipher text in which I am only provided with a public key and the cipher text. The person who encrypted it made a mistake in taking the exponent.
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2answers
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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Usefulness of ability to calculate $m^{p+q}$ with RSA

I noticed that with only an RSA public key, it is possible/tractable to calculate $m^{p+q} \pmod n$ for any $m$ without knowing $p$ or $q$. Namely, $m^{p+q} \equiv m^{n+1} \pmod n$. (This follows ...
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1answer
144 views
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2answers
105 views

How do you communicate the hash function used with RSA signing?

When it comes to RSA signing, I understand why you need to hash the data before signing it, but don't you need to communicate what hash algorithm you use to whoever will need to verify the signature? ...
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2answers
125 views

Possible to guess RSA public key $e$ using $n$ and $\phi$

We know that if $n$ and $\phi$ is known, then it is possible to find $p$ and $q$ (initial prime numbers). I have following the questions: Assume the public key $e$ is not known, how difficult would ...
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3answers
722 views

Is it possible to reduce the size of an RSA key?

The details about what an RSA key is made up of are explained succinctly here. Is it possible to reduce the amount of data that's usually packaged with the (private) key and then derive it later?
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1answer
260 views

Large primes p and q for RSA

I am writing a high-school paper on textbook RSA (the mathematical aspect only). Many definitions of the RSA method start off with saying that one should: Generate two large random (and distinct) ...
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249 views

File encryption using per-user-encrypted shared key

So I'm looking to encrypt files using AES CTR, using a shared key which would be accessed via a per-user password. My two main concerns are: - making sure that the algorithms in use are appropriate ...
2
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1answer
52 views

What is the most an adversary can do in the context of public key masquerading?

Suppose two parties A and B are using a public-key encryption scheme in order to communicate securely. A and B both have a public/private key pair: $$ A: (P_A, S_A), B: (P_B, S_B)$$ and A already ...
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1answer
227 views

RSA reconstructing private key knowing MSBs

PREMISE: This question is purely theoretical because usually an attacker will not know private exponent d and can't compare it with obtained MSB bytes. Suppose an RSA 1024 bit signature. An attacker ...
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0answers
87 views

public/private key: is it possible to have master public/private key

This may be a very primitive question which might not be possible but I have this question to understand. Assume Yahoo provides a messenger where yahoo users can chat in secure way (end-end ...
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Fingerprint RSA public key in PKCS1 format

I can't find anywhere details on how to fingerprint a public RSA key in PKCS1 format. There are a lot of examples on the internet on how to fingerprint an RSA public key in openssh format using ...
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2answers
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Is RSA key size the size of private key exponent?

I have implemented a key pair generation scheme for RSA algorithm. I have taken the length of private key exponent as RSA key size, but then I've got to know that RSA key size is the size of the ...
5
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2answers
239 views

lcm versus phi in RSA

In textbook RSA, the Euler $\varphi$ function $$\varphi(pq) := (p-1)(q-1)$$ is used to define the private exponent $d$. On the other hand, real-world cryptographic specifications require the ...
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29 views

Understanding RSA [duplicate]

I'm reading RSA in Cryptography Course. There is portion of RSA that's confusing me. In Handbook of Applied Cryptography its written Represent the message $M$ as ...
2
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1answer
243 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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5answers
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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. ...
2
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2answers
175 views

Does it necessarily mean that an RSA moduli generated with poor randomness is not random?

In 2012 a group of researchers collected a large amount of RSA moduli and calculated their greatest common divisor in order to find common factors between them. By finding a common factor they could ...
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104 views

Values of p and q when e = 3 (RSA)?

I am doing a paper on textbook RSA (this is for high school btw) and in my example I need two very large primes, but I want my $e = 3$. Is there a short way to calculate the values of $p$ and $q$ ...
2
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1answer
124 views

Verify a RSA signature using only RSA encryption

I'm trying to verify a RSA signed message, however, the API that I have access to in that environment only has encrypt and decrypt. I think I understand that verification and encryption with public ...
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10answers
8k views

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 ...
2
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1answer
240 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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1answer
139 views

Wanted: Simple ring signature example

I spent all day trying to figure ring signature schemes out but apparently I wasted time. I read the original ring signature paper (Rivest's How to leak a secret). I'm having numerous problems. Let's ...
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396 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 ...
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1answer
169 views

RSA 1024 bit forge a new matching signature from a chosen message

I have an RSA signature scheme with 1024-bit key where I know the following: Public modulus $N$ Public exponent $e=3$ A lot of signatures Summary: To compute a signature, an MD5 hash is ...