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.

learn more… | top users | synonyms

45
votes
4answers
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?
0
votes
1answer
116 views

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 ...
-2
votes
1answer
185 views

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 ...
2
votes
2answers
81 views

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?
5
votes
1answer
1k views

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 ...
1
vote
1answer
65 views

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: ...
2
votes
1answer
134 views

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 ...
4
votes
1answer
98 views

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 ...
2
votes
3answers
385 views

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 ...
0
votes
3answers
156 views

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 ...
2
votes
4answers
613 views

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?
2
votes
1answer
3k views

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. ...
2
votes
2answers
98 views

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 ...
2
votes
1answer
115 views

textbook RSA signature scheme security

Are textbook RSA signatures secure if an Adversary does not have access to ask signing oracle queries?
1
vote
0answers
17 views

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 ...
1
vote
4answers
322 views

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 ...
1
vote
0answers
24 views

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 ...
0
votes
1answer
98 views

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 ...
2
votes
1answer
86 views

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 ...
1
vote
1answer
162 views

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 $N$ ...
2
votes
0answers
66 views

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 ...
1
vote
1answer
48 views

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 ...
3
votes
1answer
227 views

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 ...
10
votes
0answers
686 views

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 ...
9
votes
2answers
1k views

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 ...
1
vote
3answers
84 views

RSA message integrity

I wish to send some small data that RSA alone can encrypt, and I send a shared secret along with it. ...
1
vote
0answers
55 views

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 ...
2
votes
1answer
5k views

What is the meaning of “trapdoor” in cryptography?

I do not really understand the meaning of a "trapdoor" in cryptography, so here are my questions: What is the meaning of trapdoor and how can I convert a word or string using a trapdoor in ...
2
votes
0answers
83 views

Deletion in RSA Accumulator

I am studying RSA Dynamic Accumulator and I have a question: why is simpler to calculate the new accumulator value after a deletion if is known the secret ϕ(n)? Is possible to calculate the deletion ...
1
vote
1answer
37 views

Deletion complexity in a RSA accumulator

My question is about the existence of a dynamic RSA accumulator with deletion of an element in O(1) time. Do you know some practical implementation?
0
votes
0answers
23 views

How to calculate Private Key in RSA using Extended Euclidean Algorithm [duplicate]

I have googled for about 2 hours now and still haven't found an explanation. The wiki article just makes me more confused and so has every other similar question I've found on StackExchange. Here's an ...
0
votes
2answers
149 views

Random Coin Flip

Quoting an old question: Consider the following protocol for two parties A and B to flip a fair coin (more complicated versions of this might be used for Internet gambling): A trusted ...
0
votes
2answers
134 views

Could Riemann hypothesis solve certainly RSA?

I don't have the background for dealing with Riemann hypothesis but is well known that covers the prime distribution below a specified number. In order to solve the RSA problem you have to factor the ...
1
vote
1answer
67 views

RSA Optimal Asymmetric Encryption Padding Beginner

I'm new to the OAEP scheme. I learn it from the Wikipedia page. Link The page does not explain a proper setup for of the system. So I'm not sure if the output of the padding scheme which contains ...
0
votes
1answer
55 views

help understanding part of Wiener's attack on RSA w/ small d

In this paper, the author writes: Now $k\phi(N) = ed - 1 < ed$. Since $e < \phi(N)$, we see that $k <d < \frac{1}{3}N^{\frac{1}{4}}$. Hence, we obtain: $\mid \frac{e}{N} - ...
1
vote
0answers
23 views

Does OEAP padding limit the size of my modulous to the size fo the hash function?

im looking at wiki at the moment as how to use oeap padding and it appears, help me out if im wrong as G(r) - expands r to the size of the padded message, I am then limited by the size of my hash ...
2
votes
1answer
157 views

Checking the integrity of RSA public key

Let's say I need to verify a digital signature and the public key is stored in untrusted storage which I need to fetch before I verify the digital signature. However, I can store the cryptographic ...
3
votes
1answer
175 views

RSA: Most significant key bit always 1?

Is it possible to say that the most significant bit of an RSA private exponent is always 1? Wouldn't that weaken the key strength by exactly that one bit? I refer to the paper "Timing Attack: What ...
1
vote
0answers
89 views

Does the RSA algorithm use repeated squaring?

Simple question: in order to reduce such huge exponents in modular arithmetic, is repeated squaring used in RSA or is there a better way to implement it?
4
votes
1answer
122 views

Are there comprehensive alternatives to RSA?

If we wished to, is there a comprehensive alternative to RSA? I say comprehensive as I wonder if there is one which does both encryption and digital signature like RSA? If not, simply what ...
1
vote
1answer
98 views

RSA: must $d$ be an integer?

I am only taking baby steps in RSA. If $p=11$, $q=7$ and $e=3$, $$\phi(n) = 10*6 = 60$$ Then: $$d = (2 (\phi(n)) + 1 ) / 3 = 121/3$$ Should $d$ be kept as a non-integer or is such a $d$ invalid? ...
1
vote
1answer
77 views

Which hash function is usually used in RSA?

I know there are several available, however I can't seem to find whether there is one standard one or not. I think I understand the process of digital signatures, just wondering which has function is ...
2
votes
2answers
77 views

Find plaintext of RSA by solving extended euclidean algorith for two encrptions with two different exponents for same plaintext

This is my homework question (but I am not asking the answer to it): Suppose two users Alice and Bob have the same RSA modulus n and suppose that their encryption exponents eA and eB are ...
1
vote
1answer
58 views

how to calculate maximum data size of an RSA signature

I am reading a content, and am not sure if I follow how they come up with the maximum data size which can be signed by an RSA key. The author states: "...if you are trying to sign a message using a ...
4
votes
0answers
52 views

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 ...
2
votes
1answer
88 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 ...
1
vote
1answer
93 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 ...
4
votes
1answer
201 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 ...
6
votes
3answers
6k views

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 ...
1
vote
1answer
261 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 ...