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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3
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1answer
791 views

Theoretical attack on RSA

The high security of RSA is granted, because it is very hard to factorize $$ N = p * q $$ Nevertheless, there is actually no need of factorizing $N$, in order to generate the $Private$ $Key$, but the ...
6
votes
2answers
203 views

Is perfect-forward secrecy achieved with RSA?

I am new to cryptography and am going through the book Understanding Cryptography by Paar and Pelzl. From what I understand Symmetric key distribution systems like Kerberos do not provide PFS ...
4
votes
1answer
135 views

Using Lattice-based cryptography for TLS\SSL

Given the general benefits of Lattice-based cryptography, such as: Post quantum Security Security from worst case scenario Efficiency What could the outlook of shifting from RSA \ ECC-based ...
1
vote
2answers
127 views

Public key Issue - same key pair as existing one? [duplicate]

My question is a bit naive, but what if someone generates the same RSA key pair as someone else? This person would have the same private key and so would be able to decrypt messages not intended to ...
2
votes
2answers
100 views

ECDH anonymous key exchange to avoid PKI

I want to use TLS to encrypt the communication between peers in a P2P network. Each peer has a well known 256bit peer identifier (the public key of a 256bit elliptic curve keypair). Both peers need ...
-2
votes
1answer
52 views

Textbook RSA with exponent e=3 [duplicate]

I remember $e=3$ is a bad choice for textbook RSA. But I can't really recall why. What happens if I choose $e=3$? Can I retrieve the message by simply calculating $\sqrt[3]{c}$? Why can't I do that ...
5
votes
3answers
604 views

RSA with modulus n=p²q

I've been wondering what would happen if the RSA modulus would be $n=p^2q$ instead of $n=pq$. I feel like there is an obvious security flaw (as there is with most modifications). Would this choise of ...
2
votes
2answers
181 views

In RSA, why does $p$ have to be bigger than $q$ where $n=p \times q$?

In openSSL – during RSA key generation – if $q$ is bigger than $p$, they exchange them. Why is that?
-5
votes
1answer
85 views

RSA Key and RSA Security

Is there any relationship between the RSA keypair standard and RSA security? Keypair: http://en.wikipedia.org/wiki/RSA_(cryptosystem) Security: http://en.wikipedia.org/wiki/RSA_Security If not, ...
2
votes
2answers
449 views

The modulus of RSA public key

I am studying the RSA cryptosystem. The public key consists of $(n, e)$, the modulus (product of two large primes), and the encryption exponent. I want to separate the modulus $n$ and exponent $e$. A ...
5
votes
1answer
263 views

Adi Shamir's secret database of all primes

I was going through these presentation slides (PDF) on Crypto 2013. It summarizes the paper, Factoring RSA keys from certified smart cards: Coppersmith in the wild. In the last slide, it was ...
3
votes
1answer
84 views

Client authentication on limited hardware

I'm developing a authentication and authorization protocol for a Bluetooth device. The device should communicate with an Android app and needs to be able to authenticate the app during the connection ...
-2
votes
1answer
55 views

moduli in SSL certificates [closed]

this is normally seen in a typical SSL certificate. For the modulus, I know that it is represented in hexadecimal form, but why is there a semicolon (:) after every group of 2 digits? ...
3
votes
1answer
425 views

RSA example-calculation: Public Key = Private Key (e = d)

I am a bit confused. I just calculated manually the single steps of RSA for an implementation with small numbers and suddenly $d$ was equal $e$. Please help me understand what I am doing wrong. ...
1
vote
0answers
59 views

Coppersmith method for factorisation

Is anyone familiar with the Coppersmith method? Does anyone know how is the $3\times3$ basis matrix obtained in this case?
1
vote
0answers
41 views

Minimum length of PKI key for signature [duplicate]

I am looking for data which shows how time it would take to brute force (or crack by any other method) different sizes of RSA/DSA keys used for a digital signature. I am looking to use as small a ...
1
vote
1answer
81 views

Public and private key lengths

I am generating RSA Public and Private keys with node.js instead of reading them from pem/crt files as I can hide them inside a private object using this module https://www.npmjs.org/package/private ...
-1
votes
1answer
85 views

How to calculate bit strength of Integer Factorization Cryptography (IFC) such as RSA using Python

I would like to know how to calculate the bit-strength of Integer Factorization Cryptography (IFC) such as RSA by using Python. I gathered it is based off the complexity of factorizing the modulus ...
0
votes
0answers
68 views

RSA: Common modulus attack problem [duplicate]

I understand in theory how the common modulus attack works (as described here: how to use common modulus attack?) Though, I did not understand completely how it worked with a negative $s_i$. Since ...
0
votes
2answers
186 views

RSA decrypting of a huge file by parts [closed]

I need to decrypt a huge file that I own previously encoded by myself with a RSA public key (it's possible for this step using a symmetric algorithm key). Problem is that I can't load it in my ...
1
vote
1answer
115 views

Brute force RSA cracking

Suppose one had a complete list of primes up to $2^{n+1}-1$. Then wouldn't one be able to crack an $n$-bit RSA public key in time $O(\pi(2^{n+1}-1))$, making RSA insecure? Thanks, René
1
vote
1answer
69 views

How can a digital signature algorithm incorporate a random data if it is to be authenticated on a separate system

I am trying to understand how RSA digital signatures can incorporate any data from a PRNG into the final signature. Does this mean that separate implementations might fail to verify each others ...
1
vote
1answer
118 views

Are those RSA keys flawed?

I used rsa-json.native to generate RSA keys for a node.js application that will use secure-peer later to connect two clients with each other. Now I have 2 questions: In secure-peer/index.js I've ...
1
vote
2answers
80 views

Sender and receiver having different moduli conflicts with encryption and signing in RSA

I should implement a security protocol as a part of which I need to: Encrypt the message with receiver public key. Sign it with my private key. Send it to receiver. Suppose that the system uses a ...
3
votes
1answer
95 views

Multiplication-homomorphic schemes

I'm looking into multiplication-homomorphic schemes now and basically I see that there are 3 options: RSA, Boneh-Goh-Nissim and ElGamal. RSA was proved to be insecure unless message is randomly ...
2
votes
0answers
123 views

RSA encryption and signature padding flaw

This is Oxford's computer security exam question: Suppose that Bob has published an RSA encryption key $ke$ (retaining in secret the corresponding decryption key $kd$), and Alice has published a ...
1
vote
0answers
136 views

Commutative Encryption with RSA scheme?

I wanted to know how I could manage to do what I'm going to tell you next, with the RSA encryption/decryption scheme. So Alice and Bob each have a public key $(n, e)$ and a private key $(p, q, d)$; ...
2
votes
1answer
119 views

Pick faster private exponent

I recently tried to send 1536-bit modulus CSR to COMODO. They refused to sign the certificate. I later found out that it's because NIST mandated 2048-bit modulus on the SSL certificate. I think it's ...
1
vote
2answers
119 views

Three different numbers with x³=x mod p

p is a prime greater than 2 and $a \in \mathbb{Z}_p$. Why are there exactly three solutions for a³ = a mod p? Obviously 0 and 1 are both in $\mathbb{Z}$ and valid solutions, but that still means, ...
1
vote
1answer
92 views

Modulo properties of two prime numbers

I am supposed to prove that x = y mod (p*q) <=> x = y mod p and x = y mod q with p and q are prime numbers. It somewhat sounds reasonable to me, but unfortunately I don't have any clue how to prove ...
2
votes
1answer
338 views

Precomputation attacks on RSA

Are precomputation attacks - such as outlined in RFC 3610 chapter 5 - possible on RSA PKCS#1 v1.5 signature generation? If yes, are such attacks taken into account when calculating the cryptographic ...
2
votes
1answer
247 views

Montgomery Ladder vs Double-and-Add

I would like to know what (if any) are the advantages of using Montgomery Power ladder over the Double-and-Add-Always algorithm. I think that firstly, Monty would be slightly faster than DoubleAndAdd. ...
3
votes
2answers
202 views

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 ...
2
votes
1answer
163 views

RSA: Fermat's Little Theorem and the multiplicative inverse relationship between mod n and mod phi(n)

I'm learning about the proof of the RSA encryption algorithm, and I'm clearly fudging or missing something, because for me it doesn't add up. When generating keys for RSA encryption, we make sure ...
-1
votes
1answer
55 views

How small are we talking about when defining the small public/private key exponent [duplicate]

I've been wondering about the 'small' part of the attacks on RSA, like the small public key exponent and the small private key exponent and what's not really clear is how small are we talking about? ...
-1
votes
1answer
48 views

The improvement of the private key exponent in the M.Weiner Attack

I am working on attacks on RSA and came across the M. Weiner attack. The limit for $d$ in order for the attack to apply is $d <= (\frac{1}{3})N^{0.25}$. The paper states that Boneh and Durfee ...
3
votes
2answers
265 views

Is RSA key size the size of private key exponent in public key encryption?

I have implemented a key pair generation scheme for RSA algorithm. I have taken the length of private key exponent as RSA key size, but then I've got to know that RSA key size is the size of the ...
-2
votes
1answer
49 views

How to write the encrypted message after using RSA

I have created a RSA encryption/decryption program but how do i write out the results after doing a encryption? Right now I have it so that it will just print out the decimal value of one character ...
1
vote
2answers
108 views

Understanding math behind RSA key derivation [duplicate]

I was reading through the key derivation for RSA. Here are the steps per wiki - Select strong primes $p$ and $q$ such that $pq = n$ $\phi(n)$ = $(p-1)(q-1)$ select $e$ such that $e$ and $\phi(n)$ ...
4
votes
2answers
155 views

How can one encrypt with RSA (or ElGamal) without revealing whom the ciphertext is intended for?

Imagine Alice wants to encrypt for Bob and post this encryption publicly, so that only Bob can decrypt but no one can other than Alice or Bob tell that the message was encrypted for Bob. The naive ...
4
votes
1answer
201 views

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 ...
1
vote
1answer
86 views

Low level explanation of how a message is sent via RSA

I understand that RSA encryption uses this formula: C = M^e (mod N) public key is e and N N is pq - p and q are private key. mod N makes above function one-way ...
1
vote
1answer
229 views

modulo operations in crypto algorithms

Am not a mathematician. Every crypto specification I see uses the modulo operation. For example RSA - If $e$ is the public key and $m$ is the plaintext with a modulus $n$ - the cipher text is $c = ...
2
votes
1answer
89 views

RSA private exponent primality

I know that the public exponent is always a prime, but what about the private exponent? Is it always a prime too?
1
vote
1answer
146 views

Breaking RSA when some bits of one prime are known

RSA primes are 100 bit. You know first 80 bits of one of the primes. In this system, come up with an efficient way to decrypt the cipher-text. This was the question on my quiz. I'm not sure how ...
3
votes
1answer
449 views

ECDSA vs RSA: Performance on Android platform and surprising results

For our privacy-preserving protocol, an encrypted channel is established. In order to protect our system from man-in-the-middle attacks, signature-based approach is used. After we've implemented it ...
1
vote
0answers
49 views

RSA Key Blinding

I was looking the answer to the following question (Timing attack on modular exponentiation), discussing the Private Key Blinding as a countermeasure for timing attacks. Therefore I'm asking if ...
0
votes
1answer
145 views

RSA, finding p,q [duplicate]

If the public key $(e,n)$ and the private key $(d,n)$ are known, what is the easiest way to find the primes $p$ and $q$? When $n$ and $\phi(n)$ are given this is easy to solve. But I can't manage it ...
1
vote
1answer
61 views

Symmetry between a public and a private key

I know that the private and public key in assymetric cryptography are different and the public is used for encryption while the private for decryption. My question is if they are symmetrical to each ...
0
votes
0answers
72 views

Cryptodefense ransom use RSA-2048. Any chance with known plaintext attack? [duplicate]

The "new" kind of ransomware invade your computer and crypt all your files using the RSA-2048. Personally, I have been victim of cryptodefense: 40000 files encrypted... I'm not going to pay anything ...