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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96 views

Plaintext and ciphertext block sizes

How can you determine the largest plaintext block size and smallest ciphertext size if you used RSA with $n=59768553302699443$ using an alphabet with $27$ characters?
2
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1answer
77 views

Preserving Confidentiality and Integrity in a Public channel

Let's say I've got two people that are trying to talk in a public channel $A$ and $B$ and they want to preserve their confidentiality and integrity. Which cryptographic algorithm would they want to ...
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0answers
122 views

Complexity using RSA

You encrypt a message using the RSA encryption system as $t^e \pmod n$ , where $t, e < n$ and $t$ is the numerical equivalent of the message. The message is written in a $27$-letter alphabet and is ...
5
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1answer
139 views

Encryption scheme like RSA where encryption is the inverse of decryption

In RSA, it is basically equivalent to use the private key $d$ to encrypt as it is to use the public key $e$ to encrypt. They are exactly inverses: $e=d^{-1}$. I need to know, are there other public ...
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0answers
71 views

Diffie-Hellman, RSA and the types of public key cryptography

Are these schemes fundamentally different? Are other schemes fundamentally different in the sense that you can do different operations with them (or the same operations, but needing different ...
0
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0answers
103 views

splitting the plaintext and ciphertext into blocks

Say I was to use RSA with a given value of n. I choose to split the plaintext and ciphertext written in a 27 letter alphabet into blocks with k and m characters resp. How would I find the largest ...
1
vote
1answer
52 views

Computing the cardinality of the co-domain of specific modular exponentiations

Consider the following function: $f: \mathbb{Z}_n \rightarrow Y,~x \mapsto x^e \bmod n$, where $n = p \cdot q$ is an RSA modulus and $gcd(\varphi(n),e) \neq 1$ (different as required for a public ...
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vote
1answer
150 views

Session key Exchange, some doubt

I have to find a solution to this problem: I have a network composed by 1 server and some client. The server has a couple of keys (public and private) and it shares a secret key with each client. My ...
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3answers
62 views

Defining Symmetric vs Asymmetric cryptosystems

I'm writing a project on the advantages and disadvantages of symmetric vs asymmetric cryptosystems. At the moment I am trying to define both systems using mathematical notation. Under the heading "...
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1answer
258 views

Should I use RSA encryption since RSA is said to be broken by NSA? [closed]

I am developing a simple web app that uses asymmetric encryption, but I am not sure whether to chose RSA for the reasons mentioned above. What are your suggestions? Also if I decided to go with RSA ...
8
votes
1answer
101 views

Could this “symmetric RSA” scheme provide key compromise resistant communications?

This question, and fkraiem's answer to it, made me wonder about the security and practicality of using "symmetric RSA" to provide a partially compromise-resistant secure channel. Specifically, assume ...
2
votes
1answer
214 views

Lattice based attack on RSA

Let $n=pq$ be the RSA module and at least one of $p,q$ is a weak prime.It is proved that the number of such $1024$bit $n$ is at least $2^{759}$. With lattices we can factor these $n$ in a second (I ...
2
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1answer
240 views

$m ∈ Z_n \backslash Z^*_n$, RSA works but not secure

If you happen happen to have a message $m ∈ Z_n \backslash Z^*_n$, RSA works but not secure. How likely is it going to happen? $|n|=1024$ bits $|p| = 512$ bits $|q| = 512$ bits.
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0answers
51 views

compact rsa private key format

As shown in Why does my SSH private key still work after changing some bytes in the file? a typical RSA private key file contains. The public modulus $n$ and exponent $e$; The private ...
6
votes
2answers
120 views

RSA: Proving that $p+q-1 < 3 \sqrt{N}$, where N = pq and p,q are prime?

I'm doing some research into attacks on the RSA cryptosystem and have stumbled across Wiener's attack. Within the proof there exists the statement "$p+q-1 < 3\sqrt{N}$". No proof is given for this,...
6
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4answers
564 views

Why can’t the public key exponent in RSA be negative?

I am looking at why certain public keys in RSA can't be used, such as: 2 and all other even numbers (since $\gcd(\phi,e)$ must equal 1) 1 (since the cipher text would equal the message) 0 (since the ...
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vote
2answers
129 views

Encrypt letters separately?

I am trying to encrypt the word Hello using RSA. When encrypting Hello’s integer representation, is each letter encrypted ...
-3
votes
1answer
59 views

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...
0
votes
1answer
546 views

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 ...
3
votes
1answer
110 views

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. ...
0
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1answer
79 views

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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0answers
26 views

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 ...
3
votes
1answer
195 views

Homemade Randomized RSA

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 ...
6
votes
2answers
122 views

Effect of $L_n[1/4,c]$ integer factorization on RSA-2048

Using the L-notation, integer factorization of an integer $n$ has the best known complexity of $L_n[1/3,c]$ using general number field sieve. Would discovery of an algorithm with complexity $L_n[1/4,c]...
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6answers
2k views

Is it feasible to build an index of prime factors?

Would it be possible to break an RSA key, in for example 1 week of time, if the cracker have already spent X number of years building an index of primes by performing every permutation of existing ...
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0answers
28 views

Finding Private Key $d$ using RSA [duplicate]

I'm a RSA n00b when it comes to the mathematics for RSA. After spending some time reading, watching lectures, etc. I pretty much have everything down, except for how to figure out the equation for ...
5
votes
1answer
120 views

Proof of RSA security dependent on public key exponent

I am writing a (high-school) paper on the public key exponent's (in textbook RSA - no padding is discussed!) significance in terms of time and security. The time part is done; as for the security part,...
32
votes
3answers
453 views

How does RSA compute such enormous numbers?

So I have been reading and learning a lot about cryptography lately and in particular asymmetric ciphers such as RSA. One thing that I am curious about but never seems to be mentioned is how the ...
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1answer
124 views

How “hard” it is to take an e'th root mod p?

I know it's hard to find the $e$th root of a number mod $n=p_1*p_2$, and if it would be possible we could break RSA. But how hard it is to take an $e$th root mod $p$ where $p$ is a prime and $\gcd(e,p-...
4
votes
2answers
251 views

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 ...
4
votes
1answer
100 views

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 ...
0
votes
1answer
97 views

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-...
5
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1answer
179 views

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 ...
11
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4answers
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 ...
4
votes
1answer
250 views

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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votes
2answers
310 views

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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0answers
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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 ...
47
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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
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1answer
123 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 ...
-1
votes
1answer
197 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
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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
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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 ...
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1answer
72 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: <...
3
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1answer
142 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
104 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
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3answers
390 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
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3answers
160 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
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4answers
624 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
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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
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2answers
100 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 $1024$-...