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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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 ...
2
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1answer
641 views

ABC Conjecture's Impact on RSA Encryption

A recent proof of the ABC Conjecture has been released by one Shinichi Mochizuki. Now, I'm not well versed in mathematics but it would appear that this proof implies that finding prime factors could ...
9
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3answers
521 views

Can we ensure the security of a crypto-algorithm and -implementaton against acoustic cryptanalysis?

Like people always say: “Attacks only get worse…” — which is why I'm asking early. I have been reading the paper “RSA Key Extraction via Low-Bandwidth Acoustic Cryptanalysis” published December 18, ...
6
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2answers
201 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 ...
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1answer
789 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 ...
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1k views

How many RSA keys before a collision?

I was wondering how many possible private/public keys exist? If a million people – for whatever reason – would try to generate 5 keys each in the same minute (on the same date and time) is there a ...
4
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1answer
132 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 ...
2
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1answer
143 views

Where can I download a database of RSA keys?

I'm looking to do some research into how RSA is used in the wild. I've read through a few papers and it seems other researchers have had no trouble collecting millions of keys to perform analysis on. ...
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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
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2answers
98 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 ...
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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, ...
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2answers
829 views

What security authorities and standards reject $e=3$ in RSA, when, and with what rationale?

In RSA, some security authorities and/or standards allow the public exponent $e=3$, others require or recommend $e>2^{16}$ (or perhaps some other minimum). I gathered the following: PKCS#1 allows ...
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1answer
51 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 ...
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3answers
601 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 ...
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4answers
572 views

RSA with composite numbers

It has been said that RSA uses a modulus product of two prime numbers for security reasons. But does RSA even work correctly if we allow composite integers instead? I think that the answer is "NO". ...
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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?
4
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2answers
478 views

Attacks on the RSA Cryptosystem

I was reading some articles about attacks on RSA system and I wonder about some generalization of the following theorem. Theorem (Coppersmith). Let $N=pq$ be an $n$-bit RSA modulus, where ...
3
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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 ...
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2answers
1k views

RSA-based authentication and key-agreement protocol

An authentication and key-agreement protocol between devices shall mutually demonstrate their identity, and establish a shared random secret $R$ suitable for securing later communications. To that ...
5
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1answer
262 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 ...
2
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2answers
387 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 ...
2
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1answer
277 views

RSA 896 vs 1024 vs 2048 in Javascript?

I am currently working on a secure messaging website and I had been using RSA 2048 for encryption, decryption and signing of messages but I found it to be EXTREMELY LAGGY so i've moved to 1024. I did ...
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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? ...
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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?
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0answers
40 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 ...
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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 ...
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0answers
95 views

Unblind a RSA blinded signature

I have blinded $m = 16$ with $r= 13$, $e = 7$ and $n = 209$. This resulted in $m' = 464$, which led to a $s' = 8$. Now, I want to unblind this $s'$ by using $s = s' \times r^{-1}$ but im stuck at ...
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5answers
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How big an RSA key is considered secure today?

I think 1024 bit RSA keys were considered secure ~5 years ago, but I assume that's not true anymore. Can 2048 or 4096 keys still be relied upon, or have we gained too much computing power in the ...
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1answer
80 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 ...
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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
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2answers
168 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
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1answer
114 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
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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 ...
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1answer
116 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 ...
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2answers
79 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 ...
8
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3answers
15k views

RSA encryption with private key and decryption with a public key

When using the RSA cryptosystem, does it still work if you instead encrypt with the private key and decrypt with the public key? What about in the case of using RSA for sender authentication?
2
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0answers
122 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
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1answer
203 views

Prime factorization of RSA modulus

Consider RSA public-key encryption with public modulus $N=3953$. Suppose we know that the public keys $e_1=337$ and $e_2=23$ correspond with the decryption information $d_1=3385$ and $d_2=2663$. ...
6
votes
1answer
358 views

Prove that textbook RSA is susceptible to a chosen ciphertext attack

Given a ciphertext $y$, describe how to choose a ciphertext $\hat{y} \neq y$, such that knowledge of the plaintext $\hat{x}=d_K(\hat{y})$ allows $x=d_k(y)$ to be computed. So I use the fact that the ...
2
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0answers
107 views

Rabin/RSA four possible messages?

Given this encryption method: $$f_{N,e} : Z^{*}_{N} \to QR(N)^{*};\quad f_{N,e}(x) = x ^{2e} \bmod N$$ I need to show that, for any $x_{0} \in Z^{*}_{N}$, there are four elements $x \in Z^{*}_{N}$ ...
3
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1answer
170 views

Is differential calculus related to RSA?

I'm writing a high school math paper on RSA and I'm wondering if it's possible to relate calculus to RSA. Is calculus used for any part of RSA? It can be for proving equations/theorems, for generating ...
2
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3answers
309 views

RSA assumption and cryptography

The RSA assumption states that it is hard to find $m$, given $c = m^e \bmod{n}$, $e$, and $n$ (for appropriate choice of $n,e$). Suppose that there exists an algorithm, $D(c,e,n)$, that finds $m$ in ...
0
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1answer
120 views

Digital signatures under plain RSA

Show that digital signatures under plain RSA are insecure (Plain RSA means that signing is done by calculating $m^d\bmod n$, with $0\le m<n$, and no padding or hashing of $m$). Write an algorithm ...
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3answers
157 views

Question on RSA trapdoor permutation

You plan to use a public-key cryptosystem based on the RSA trapdoor permutation in three different real-life applications, in which the attacker has, respectively, only one of the following resources: ...
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0answers
101 views

m ∈ Zn \Z*n, RSA works but not secure

If you happen happen to have a message m ∈ Zn \ 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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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
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1answer
94 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 ...
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0answers
124 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 $(p, q, d)$; ...
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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 ...
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2answers
118 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, ...