# 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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### Encrypt letters separately?

I am trying to encrypt the word Hello using RSA. When encrypting Hello’s integer representation, is each letter encrypted ...
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### How to calculate d in RSA for my number with this [duplicate]

I took the p&q value as 61 & 53 and n=3233 e=17 d=? How to find it? Plz help me...
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### Find private exponent in RSA [duplicate]

The other answers for this confuse me, I know the principle of d in terms of the equation it has to satisfy. However I'm not sure how I would go about finding the private exponent without trial and ...
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### Should I be concerned about padding oracle attacks if the lifespan of my key is ~1 minute?

I'm using 4096-bit RSA to encrypt a 256-bit AES key generated client-side. The RSA ciphertext is then sent to the server, and the server decrypts the RSA ciphertext to acquire the AES key. ...
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### Doubts about Authenticated Data Structures logic

I am studying the theory of authenticated data structure, like Merkle Tree and I have a doubt: why use them? I explain better: why to be sure, for example, that a cloud provider didn't modify my files ...
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### Simple RSA Key Generation example [duplicate]

I have two prime numbers: p = 37 q = 41 And I need to find whether any of these prime numbers, 5, 7 or 11, can be used as a valid encryption key e? My working ...
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Considering the following encryption scheme where RSA is used to encrypt a plaintext m and then we choose a random r and compute: $$A = r + m^e \bmod N$$ and $$B = r^e \bmod N$$ So the ciphertext is ...
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### Why is 2048-bit RSA always paired with 320-bit ECC?

You may already have noticed that most smart cards ship with 2048-bit RSA support and 320-bit ECC over GF(p) support. You may have already asked yourself "why exactly 320-bit?". Now I remember having ...
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### Does rsa-oaep provide or not plaintext integrity in addition to confidentiality?

My own understanding (possibly wrong of course) of RSA-OAEP encryption scheme is that it provides plaintext integrity (in addition to confidentiality) due to MGF function which for encryption ...
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### Comparing messages given only the ciphertext

Under RSA protocol I was wondering how a message sent could be verified under the following scenario Alice has a private (encryption key) and public key (decryption key) If Bob sends Alice cipher-...
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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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### 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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### Modular exponentiation on calculator for textbook RSA

How do you encrypt $51$ with public key $(n,e) = (91,23)$ I understand that $c = 51^{23} \bmod 91$. How can I calculate the result on a calculator?
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### Cracking plain RSA by factoring the modulus n

This is the setup: I have both public and private keys of one "instance" of RSA. And I have only the public key of another RSA cryptosystem, but this system has the same modulus as the first one. I ...
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### How secure is 'Plain Old RSA' [duplicate]

Let's say I use RSA encryption, it's 2048 bits and I use a simple character padding scheme, every character is turned into a 3 digit number and strung together, then encrypted. Saying that no message ...
16k views

### How can I use asymmetric encryption, such as RSA, to encrypt an arbitrary length of plaintext?

RSA is not designed to be used on long blocks of plaintext like a block cipher, but I need to use it to send a large (encrypted) message. How can I do this?
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### How long can a RSA public key be?

If I create an RSA of 4096 bits, what would be the range of the length in bytes of the public key in DER format? Also, will the private key always be exactly 4096 bits (512 bytes)? Does the public ...
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### RSA Attack, known public key and ciphertext. Can decrypt the message m?

I'm stuck with this problem: Assume Alice and Bob are using RSA to communicate each other. Given Bob's public key $(217,7)$, Alice send the ciphertext $c=53$ to Bob through RSA encryption. Now, Eve ...
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### How do I classify my RSA encryption strength?

So I generated 2 1024 bit prime numbers, I generated N and got a 2048 bit number, does that make my encryption 2048 bit or 1024 bit?
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### How do RSA and ECDSA differ in signing performance?

Signature algorithms with elliptic curves have smaller output sizes compared to RSA for the same level of security. What about the processing time to generate a signature ? I've seen figures giving ...
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### setting the MGF hash to a different value other than the regular hash with openssl for PSS signatures

In PKCS1's Probabilistic Signature Mode you have the Hash and the MGF Hash. Both appear to be, by default, sha1, with the OpenSSL CLI client, however, I can change it to sha256 with the following: <...
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### Theoretical decryption of RSA

I am currently looking into RSA and have some questions. I am interested in theoretical answers, assuming there is infinite time for decryption. Is it necessary to work out the private-key exponent ...
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### How to compare the efficiency of public key cryptosystems, i.e., RSA vs El Gamal?

As part of my Mathematics degree I'm taking a Discrete Mathematics module which partially covers Public Key Cryptography but does not at all enter it in depth. I'm currently working on a project that ...
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### What do numbers in a crypto algorithm stand for? Is there a convention?

What do the numbers stand for in the names of cryptographic functions, for example AES-256, RSA-1024 or ...
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### Factorizing N to derive D [duplicate]

So I have the value of N. I have to use this value of N to find the value of D. N = 265291078722948385089717069136983657793 Now I read about RSA algos and found out that ...
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### Does it make sense to have a 4000 bit long key?

My question is about the key length of a asymetric algorithm. How is it possible to memorize or remember a key that is about 4000 bits long?
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### When NIST disallows the use of 1024-bit keys, what effect will that have on SHA-3 (with max. 512 bits)?

Quoting the article Gone in 60 Months or Less: The National Institute of Standards and Technology (NIST) has disallowed the use of 1024-bit keys after 31 December 2013 because they are insecure. ...
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### RSA and difference between factors

As I understand, for RSA $n = p \cdot q$. For the key to be safe enough from getting factored, $p$ and $q$ have to be far from each other. How far do they have to be? For example, if I have two $1024$-...
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### RSA incorrectly translates for small keys [duplicate]

I've been learning about RSA and wrote my own implementation. I don't pretend to have intuitive understanding of RSA or that I understand why it works, but I believe to have some basic understanding ...
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### Message exchange with textbook RSA

I am working on this exercise but can't work out the answer to the question b. I have solved the question (a) by decrypting the ciphertext $C = 2$ using the formula:  M = C^d \bmod n = 2^{17} \bmod ...
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### Generating keys in RSA [duplicate]

I'm trying to learn how RSA works. From what I found online, I'm supposed to generate private key using Extended Euclidean algorithm. I've managed to generate the public key, but don't know how to ...
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### How much stronger is RC4 if it is keyed with an RSA private key?

My idea is to generate a RSA 2048 bit key and use RC4 with the private RSA key to encrypt a stream of data. RC4 is weak because RC4 keys are small, 256-bit. But when we use RC4 with private RSA 2048 ...
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### Attack on textbook RSA with small messages

We learned in class that if Alice wants to send a small message $m$, such that $m < N^{\frac{1}{e}}$, so we can break the system using $e$-th square of $m^e$. But what if Alice knows this flaw and ...
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### Modular Arithmetic in RSA

Consider the following the following RSA public key $pk = (N, e) = (1457, 1307)$. (a) Knowing that $187^2 \equiv 1 \pmod {1457}$ find the factorization of $N$. (b) Given the factorization of $N$ ...
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### MITM Attack on Key Exchange Protocols

I was doing research on this attack and I am wondering, why is Diffie-Hellman always associated with such an attack? ​ Aren't other public key cryptography schemes vulnerable to the same kind of ...
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### How to store keypair generated by RSA in a textfile?

I'm trying to write an encryption decryption program using Openssl-RSA. There are only two operations. User stores the data and retrieves it whenever he needs. To decrypt something, we need the ...
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### RSA enc/decryption with multiple prime modulus using CRT

Every information I found on internet about RSA-CRT encryption/decryption uses only two primes. I'm interested in my project in doing that using multiple (up to 8) primes. The general idea is to ...
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### Who first published the interest of more than two prime factors in RSA?

Multi-prime RSA is now a well known technique (described here): it uses $k>2$ distinct secret prime factors in the public RSA modulus, with the advantage that, using the CRT, we can gain a speed ...
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### Multiple-prime RSA; how many primes can I use, for a 2048-bit modulus?

In standard RSA, the modulus $n=p_1 p_2$ is a product of two primes $p_1,p_2$ of the same size. Suppose we construct the modulus as a product of multiple primes $p_1,\dots,p_k$, i.e., \$n=p_1 p_2 \...
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### RSA message integrity

I wish to send some small data that RSA alone can encrypt, and I send a shared secret along with it. ...
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### Is there a fast implementation of RSA for Microcontrollers?

Zhe Liu, Johann Großschädl, and Ilya Kizhvatov. "Efficient and Side-Channel Resistant RSA Implementation for 8-bit AVR Microcontrollers" describes a fast implementation, but only contains a sketch of ...