# Tagged Questions

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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### 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? ...
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### Extract private RSA key from USB cryptographic token using Bardou et al. attack (variant of “million message attack”)

There is a side channel attack on tamper-resistant USB cryptographic tokens using padding-oracle, described by Bardou, Focardi, Kawamoto, Simionato, Steel and Tsay, titled "Efficient padding oracle ...
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### Why is it a security problem that two RSA moduli are not co-prime?

I found this security problem, for example: Alice has an RSA public key: $e = 37$ and $\phi$ (totient, $N_A = (pa-1)(qa-1)$) is $55$, so the key is $(37, 55)$. Bob has an RSA public key: $e = 37$ ...
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### using random encrypted RSA challenge as key material

Assume a simple protocol for authentication - one side sends a randomly generated challenge string and encrypts it with RSA. The receiver decrypts it and replies with a hash of the challenge, proving ...
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### Is it possible to determine the group order by knowing the “public” and “private” key exponents in an RSA group?

I have an RSA group with modulus $n = p \cdot q$, two safe primes $p=2p'+1$ and $q=2q'+1$ and the "public" and "private" key exponents $d$ and $e$. $\phi(n) = 4p'q'$ is the order of the RSA group. If ...
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### is this authenticated key exchange protocol sound? too complicated? obviously flawed?

(significantly reworded this question to fit better into crypto.se). I have static RSA keypairs for both sides and an encrypted transport that needs symmetric keys, and need to exchange session keys. ...
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### RSA padding: what is it and how does that work?

If I am not mistaken, plaintext RSA is not secure. So, I have read that padding and hashing is needed to make the RSA algorithm secure. However, I am confused on what does padding or armoring mean in ...
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### DSA, RSA, ECDSA etc - which one is cheapest for signing?

For a protocol where the server presents its signature to prove authenticity (e.g. IKE/SIGMA/STS with only one party authenticated), it's essential that the signing is extremely cheap, while ...
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### Given a message and signature, find a public key that makes the signature valid

Given a message $M$ and a signature $S$, is it feasible to find a RSA public key $(n,e)$ such that $S$ verifies as a valid signature on $M$ (using this public key)? What if we're given one public key ...
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### What's the fundamental difference between Diffie-Hellman and RSA?

What is the difference in the purpose of DH and RSA? Aren't they both public-key encryption?
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### risk of attacker decrypting RSA ciphertext without public or private key

As I describe in my previous question I am trying to decide if it's worth it for me to use the Offline Private Key Protocol in creating some long term private archives, instead of just going with a ...
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### RSA - Ecrypting the same data with the same public key = same ciphertext?

If an adversary knows my public key and guesses what was my plaintext, can he test for it somehow? The most obvious way is encrypting the guessed plaintext with my public key and the same parameters ...
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### implementing long term archive encryption

Let's say I want to create private archives for the long term (e.g. more than 30 ). The archives' sizes could be anywhere from 1 GB to 30 GB. As far as I understand I could go down two ways: The ...
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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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### How to learn the first bit of m in padded RSA

Consider the following version of padded RSA encryption, where encryption of $m$ is done by setting $m′ = (0^k~||~r~||~00000000~||~m)$ for a random $r$ (of length 8 btyes = 64 bits) and then computing ...
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### Comprehension question on a signature protocol based on the RSA assumption

We have the following two-party protocol between Alice and Bob. Alice sends messages $m_1, m_2, \ldots \in_R \mathbb{Z}_n^*$ to Bob and Bob signs these values by calculating \$v_1, v_2, \ldots \in_R \...
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### What is the relation between RSA & Fermat's little theorem?

I came across this while refreshing my cryptography brain cells. From the RSA algorithm I understand that it somehow depends on the fact that, given a large number (A) it is computationally ...