# Questions tagged [rsa]

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 with proper paddings.

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### Can or can not D-Wave's quantum computers use Shor's and Grover's Algorithm to find encryption keys? Why?

I read that a company called D-Wave Systems has and is manufacturing quantum computers of 128 qubits. Can they or can they not use Shor's and Grover's algorithms for finding RSA-keys? If they can't ...
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### What motivated the creation of RSA and ECDH?

Recently I've been learning about cryptography and so far I am loving it. However, there are some things I do not comprehend. As far as I know, RSA was published in 1979 while New Directions on ...
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### Is it reasonable to assure that p-1 and q-1 aren't smooth?

I came across the requirement that, in RSA, $p-1$ and $q-1$ shouldn't be smooth, shouldn't consist of lots of small factors. Therefore my question: How complicated is it to check whether $p-1$ is ...
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### How long does it take to crack RSA 1024 with a PC?

Using an Intel Core i5 CPU, how long does it take to crack RSA using a key size of 1024 bit (generated using a secure key pair generation function)? Suppose for instance that we have thousands of ...
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### Why has the RSA factoring challenge been withdrawn?

Wikipedia states that RSA challenge has been withdrawn. Does it mean that an efficient factoring algorithm is "just around the corner"? or are there some other reasons? If the challenge was still ...
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### 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 ...
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### Is RSA padding needed for single recipient, one-time, unique random message?

I want a way to encrypt files using this process: https://crypto.stackexchange.com/a/15 . That is: generate a random password, use that to AES-encrypt a file, and use an RSA public key to encrypt the ...
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### RSA private key integrity check

I am working on a device whose OS provides an RSA Private primitive, where the inputs are the message, and the usual components of a private key. Unfortunately it is bugged so that in some cases of ...
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### What are some disadvantages of homomorphic encryption schemes?

I'm doing some self-teaching / research for my own benefit in homomorphic cryptography. I've studied both additive and multiplicative schemes (Paillier and RSA respectively), but all I can seem to ...
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### 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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### 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 $n_B$ ...
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### How to perform authentication without central server in P2P?

How can one be sure that the man who you're talking with is the one who you think he is? i.e. How can one perform authentication in P2P network without a central trust server or Certificate Authority? ...
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### Why do crypto tools display key components in such an unusual format?

openssl x509 (v1.0.1f) displays public key moduli as arrays of hex-encoded bytes, 15 columns wide, starting with a leading 00:: ...
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### Is it possible to get an RSA encryption key by comparing the unencrypted and encrypted file?

Exactly what the title says. If I have a RSA encrypted file, and the exact same file but decrypted, can I tell the key that was used from that information?
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### 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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### 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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### 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 ...
1k views

### RSA & DH at risk due to math advances, will this eventually affect elliptic curves too?

I was looking into the predictions by some researchers that RSA and Diffie-Hellman may not be secure in the next few years due to advances in math and being able to calculate the discrete logarithm ...
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### RSA encryption using multiplication

Generally in RSA we encrypt as $m^e \pmod n$. Will RSA work if we replace the power by normal multiplication? $E = (m \times e) \mod n$ and decryption as $c \times d \mod n$. What will be $d$ ...
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### Why do we need Euler's totient function $\varphi(N)$ in RSA?

After we calculated $N = p * q$, we calculate $\varphi(N)$ and use it later to determine $e$ (PR) and $d$ (PU). But why? For decryption and encryption we only use $N$ and don't need $\varphi(N)$. So ...
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### How are random numbers for RSA generated? [duplicate]

The RSA public key encryption requires two very large prime numbers as part of its encryption process that serve as secrets. These are typically generated with cryptographically secure random number ...
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### 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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### Why can’t DSA be used for encryption?

This question at StackOverflow mentions that DSA cannot be used for encryption. But both RSA and DSA can be used to generate public and private keys, right? Then why can't I use the DSA public key to ...
11k views

### RSA-PSS salt size

One of the inputs of RSA-PSS signing and verification is the salt size. According to PKCS#1, you must know the salt size before the verification is carried out. However, this makes interoperability ...
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### Safe primes in RSA

It's my understanding that there's no longer a requisite of safe primes for $q$ and $p$ when choosing a RSA modulus. How is it that this does not change the hardness of factoring $N$?
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### At what stage is DHE and RSA used during the SSL/TLS handshake?

At what stage of the SSL/TLS handshake is the DHE and RSA used and what is the purpose of using a pre-master secret when you could just use RSA to exchange the symmetric key (i.e. AES) for further ...
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### Is it possible to create an asymmetric cryptosystem where the private keys are not easily verifiable as such?

Plaintext that consists of an RSA key is easily recognizable as such, because it satisfies certain mathematical properties, in particular (See the answer for Why can an encrypted private key be brute ...
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### What's the difference between rsa_pss_pss_* and rsa_pss_rsae_* schemes?

I'm trying to understand the difference between rsa_pss_pss_ and rsa_pss_rsae_. The picture shows the extension of TLS1.3's ...
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### What are advantages of using a HMAC over RSA with SHA-1 hashes?

I am currently studying for an exam and this was a previous question: Give one advantage of using HMACs over using RSA to sign SHA-1 hashes. My thoughts are that it has something to do with the ...
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### Given enough RSA signature values, is it possible to determine the public key value?

Given enough RSA signature values, is it possible to determine which public key is required to verify the values? Could there be enough information to establish which key is required? Is there ...
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### RSA key such that pi deciphers to your name per RSA-OAEP

Can you efficiently construct an RSA public/private key pair with $8k$-bit public modulus such that $C=\left\lfloor\pi\,2^{8k-2}\right\rfloor$ deciphers per RSA-OAEP to your name as a bytestring in ...
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### What is the minimum and maximum value of an RSA private exponent?

Is it possible to calculate the minimum and maximum value of the private exponent for an RSA key, for example for a 1024 key size? In other words, what is the range of values in which the private ...
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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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### Why hash or salt when signing? [duplicate]

EDIT: Just wondering why was this question closed as a duplicate of a question asked almost 2 years after this one... I've seen an example of how to sign using RSA. Besides the signing itself (s = m^d ...
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### 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 ...
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### 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 ...
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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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### Why is RSA encryption significantly faster than decryption?

I am designing an implementation of RSA . I recorded computation times in Java by using System.currentTimeMillis(). It returned an encryption time of 0.05 ms and ...
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### Should RSA primes p and q differ in length by “a few digits”?

When generating RSA keys in the original RSA paper it is stated: to gain additional protection against sophisticated factoring algorithms, p and q should differ in length by a few digits Why is ...
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### Why Static RSA and Diffie-Hellman cipher suites have been removed in TLS 1.3?

Why Static RSA and Diffie-Hellman cipher suites have been removed in TLS 1.3? How keys can be exchanged then? https://tools.ietf.org/html/draft-ietf-tls-tls13-28
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### What signature schemes allow recovering the public key from a signature?

It seems to be possible to retrieve the (public) key used for creating an ECDSA signature just from the signature alone. This seems like an interesting property; as far as I know, RSA doesn't share ...
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### Is this definition of an RSA modulus safe?

Suggested definition A positive integer is a safe RSA modulus if, after removing all its prime factors less than 512 bits, it is composite and has size at least 2048 bits. Discussion I want to ...
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### 33c3ctf beeblebrox RSA Sign challenge: any tipps? [closed]

I recently participated in the 33c3 ctf competition and tried to solve the beeblebrox challenge but could not crack it and nobody posted a writeup/exploit of it so far so I want to get help solving it ...
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### Anatomy of an RSA private key

I'm learning about OpenSSL and public key infrastructure and am curious about the structure of an RSA key and how it's related to its corresponding public key. I can generate a private RSA key with ...
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### When/why is RSA (hybrid) encryption used rather than alternatives?

I've read that RSA is not meant for encrypting large plaintext because: (Are these also true for other public-key encryptions like ElGamal?) It is slow. Padding makes the ciphertext blocks much ...
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### Good entropy source for generating openssl keys

I need to generate a CA (4096-bit RSA) and server keys for openvpn and I want them to be "top quality". Here is my plan: gather entropy from multiple sources (saving individual files): FreeBSD Yarrow,...
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### RSA-based authentication and key-agreement protocol

An authentication and key-agreement protocol between devices shall mutually demonstrate their identity, and establish a shared random secret $R$ suitable for securing later communications. To that ...
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### Collision resistance of hash function built on modular exponentiation

Consider the following hash function family for hashing integers: $Gen(1^k)$: generate 2 $k$-bit primes p,q. Let $n = pq$. Choose random $y \rightarrow QR_n$ and output $n,y$. \$H_{(n,y)}(x) = y^x \...