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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Why is elliptic curve cryptography not widely used, compared to RSA?

I recently ran across elliptic curve crypto-systems: An Introduction to the Theory of Elliptic Curves (Brown University) Elliptic Curve Cryptography (Wikipedia) Performance analysis of identity ...
31
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5answers
4k views

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 ...
28
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3answers
7k 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 message. How can I do this?
28
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4answers
15k views

How can I generate large prime numbers for RSA?

What is the currently industry-standard algorithm used to generate large prime numbers to be used in RSA encryption? I'm aware that I can find any number of articles on the Internet that explain how ...
28
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10answers
5k views

Now that quantum computers have been out for a while, has RSA been cracked?

D-wave systems has released a commercially viable quantum computer. This means in theory, that all asymmetric encryption algorithms — such as RSA — are now useless due to the speed at which quantum ...
26
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3answers
2k views

How are primes generated for RSA?

As I understand it, the RSA algorithm is based on finding two large primes (p and q) and multiplying them. The security aspect is based on the fact that it's difficult to factor it back into p and q. ...
22
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2answers
726 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 ...
15
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5answers
875 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 ...
15
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5answers
1k views

Does RSA work for any message M?

I decided to read the original RSA paper A Method for Obtaining Digital Signatures and Public-Key Cryptosystem because of a question I had about RSA (which is not the question I'm about to ask, but ...
15
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4answers
944 views

Is Wiener's attack on RSA extendable to larger keys with low hamming weight?

Using small private exponents with RSA improves performance. However, it has been shown (Wiener, 1990) that if $\log d \leq \frac14 \log N$, the private exponent $d$ can be reconstructed from the ...
13
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8answers
2k views

RSA with small exponents?

Just to establish notation with respect to the RSA protocol, let $n = pq$ be the product of two large primes and let $e$ and $d$ be the public and private exponents, respectively ($e$ is the inverse ...
11
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6answers
5k views

Is Diffie-Hellman mathematically the same as RSA?

Is the Diffie-Hellman key exchange the same as RSA? Diffie Hellman allows key exchange on a observed wire – but so can RSA. Alice and Bob want to exchange a key – Big brother is watching everything. ...
11
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2answers
8k views

Signatures: RSA compared to ECDSA

I'm signing very small messages using RSA, and the signature and public key are added to every message, which requires a lot of space compared to the actual content. I'm considering switching to ...
10
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4answers
2k views

Why RSA encryption key is based on modulo $\varphi(n)$ rather than modulo $n$

While calculating RSA encryption key we take modulo $\varphi(n)$ rather that modulo $n$. I couldn't understand why its so?
10
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2answers
638 views

Why RSA can't handle numbers above 76?

I'm going to encrypt the characters Zhu, and decrypt them using RSA. I'm using the public key $\{e, n\}$ and private key $\{d, n\}$. The values of $e$, $d$ and $p$ ...
10
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4answers
516 views

Is there an intuitive explanation as to why only the private key can decrypt a message encrypted with the public key?

I have just learned about using PGP/GPG for email encryption and one thing has always bugged me: How is it possible that a message encrypted with somebody's public key can be decrypted only with that ...
10
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4answers
2k views

Encrypting small values with RSA private key

I'm looking for best practices when it comes to encrypting small (< 128 bytes) amounts of data with the RSA private key. Signing it would make the resulting payload too large.
10
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3answers
905 views

Are any of the major asymmetric ciphers distinguishable (EG, RSA, ECC)?

Related to "Is it possible to derive the encryption method from encrypted text?". Given ciphertexts generated by any of the major asymmetric ciphers (RSA, ElGamal, ECC, etc..) can these ciphertexts ...
10
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1answer
4k views

Calculating RSA private exponent when given public exponent and the modulus factors using extended euclid

When given $p = 5, q = 11, N = 55$ and $e = 17$, I'm trying to compute the RSA private key $d$. I can calculate $\varphi(N) = 40$, but my lecturer then says to use the extended Euclidean algorithm to ...
10
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1answer
2k views

Security strength of RSA in relation with the modulus size

NIST SP 800-57 §5.6.1 p.62–64 specifies a correspondence between RSA modulus size $n$ and expected security strength $s$ in bits: ...
9
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2answers
2k views

Can two different pairs of RSA key have the same modulus?

Can $n=pq$ be part of two different pairs of RSA keys? If such keys exist, say $(e_1,n)$ and $(e_2,n)$, how are they related? What will be the security concerns for the two users?
9
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3answers
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What is the relation between RSA & Fermat's little theorem?

I came across this while refreshing my cryptography brain cells. From the RSA algorithm I understand that it somehow depends on the fact that, given a large number (A) it is computationally ...
9
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1answer
2k views

Why do all SSH-RSA Keys begin with “AAAAB3NzaC1yc”?

My Friend and I have been generating a few ssh2-rsa keys and noticed that all the public keys began with "AAAAB3NzaC1yc". The similarity extended to "AAAAB3NzaC1yc2EAAAABIwAAAQEA" between two keys I ...
9
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2answers
3k views

Are there practical upper limits of RSA key lengths?

Suppose one wanted to use RSA encryption for the sole purpose of sending key bits for use in symmetric crypto systems, a dedicated key exchange system so to speak. And say you didn't think that the ...
9
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3answers
300 views

Is it possible to create an asymmetric cryptosystem where the private keys are not easily verifiable as such?

Plaintext that consists of an RSA key is easily recognizable as such, because it satisfies certain mathematical properties, in particular (See the answer for Why can an encrypted private key be brute ...
9
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3answers
448 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, ...
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2answers
8k views

When to use RSA and when ElGamal asymmetric encryption

If i am not wrong in cryptography there are 2 basic cryptographic schemes for public key cryptography. RSA encryption whose security is based on the infeasibility of solving the factoring of big ...
9
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1answer
445 views

What changed in PKCS#1 v2.2, and why?

PKCS#1 is one of the most used (de-facto) standard for real-world use of RSA. That's for good reasons: PKCS#1 is well thought, versatile, understandable, has been relatively stable for over two ...
9
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0answers
279 views

Who first published the interest of more than two prime factors in RSA?

Multi-prime RSA is now a well known technique: 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 boost in ...
8
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3answers
13k 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?
8
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3answers
444 views

Is it reasonable to assure that p-1 and q-1 aren't smooth?

I came across the requirement that, in RSA, $p-1$ and $q-1$ shouldn't be smooth, shouldn't consist of lots of small factors. Therefore my question: How complicated is it to check whether $p-1$ is ...
8
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5answers
435 views

RSA leak bits to factor N

Suppose you randomly generate large primes p and q as in RSA, and then tell me N=pq but not p or q. Then, you would like to actually let me factor N, except you should tell me as few bits of ...
8
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3answers
2k views

Is it possible to validate a Public Key in RSA?

If I have a 1024-bit number, and someone is telling me that it is in fact a valid RSA public key, is there any way I can quickly validate that it is indeed so (without cracking RSA)? (I suppose I am ...
8
votes
2answers
396 views

Given a message and signature, find a public key that makes the signature valid

Given a message $M$ and a signature $S$, is it feasible to find a RSA public key $(n,e)$ such that $S$ verifies as a valid signature on $M$ (using this public key)? What if we're given one public key ...
8
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2answers
3k views

Impacts of not using RSA exponent of 65537

This RFC says the RSA Exponent should be 65537. Why is that number recommended and what are the theoretical and practical impacts & risks of making that number higher or lower? What are the ...
8
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2answers
7k views

What's the fundamental difference between Diffie-Hellman and RSA?

What is the difference in the purpose of DH and RSA? Aren't they both public-key encryption?
7
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3answers
802 views

Is RSA padding needed for single recipient, one-time, unique random message?

I want a way to encrypt files using this process: http://crypto.stackexchange.com/a/15 . That is: generate a random password, use that to AES-encrypt a file, and use an RSA public key to encrypt the ...
7
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3answers
2k views

Why hash or salt when signing?

I've seen an example of how to sign using RSA. Besides the signing itself (s = m^d mod n) it also hashes and adds an IV. Why is that needed?
7
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2answers
4k views

Definition of Textbook RSA

What is the definition of Textbook RSA? What are some of the properties of textbook RSA? How does it differ from other RSAs?
7
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2answers
206 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 ...
7
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3answers
2k views

What are some disadvantages of homomorphic encryption schemes?

I'm doing some self-teaching / research for my own benefit in homomorphic cryptography. I've studied both additive and multiplicative schemes (Pallier and RSA respectively), but all I can seem to ...
7
votes
2answers
228 views

RSA: Letting $p$ and $q$ have different bit-size

I am aware that there are concerns if $p$ and $q$ are close i.e. $\Delta=|p-q|$ can't be too small. But I would like to know if there are any known attacks for cases where $p$ and $q$ take on ...
7
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2answers
1k views

Cycle attack on RSA

I originally posted this question in the mathematics section, you can see it here. Let $p$ and $q$ be large primes, $n=pq$ and $e : 0<e<\phi(n), \space gcd(e, \phi(n))=1$ the public encyption ...
7
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3answers
1k views

Would the ability to efficiently find Discrete Logs have any impact on the security of RSA?

This answer makes the claim that the Discrete Log problem and RSA are independent from a security perspective. RSA labs makes a similar statement: The discrete logarithm problem bears the same ...
7
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1answer
351 views

Exposing RSA private-key data… bad?

We know that exposing $p$, or $q$ or $\phi(n)$ results in trivial attacks on RSA since they allow us to factor $n$ and to compute the private exponent $d$. In OpenSSL (and most RSA implementations) ...
7
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1answer
2k views

Why does the PKCS1 RSA private key structure contain more than just exponent and modulus?

The ASN.1 spec for the PKCS1 RSA private key format is as follows: ...
7
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490 views

How to argue to a paranoid that RSA is safe?

From today's standpoint, most people would claim RSA to be secure. However, to my knowledge, this is purely based on the speculation that no one knows a computational feasible way to find a $d$ for ...
7
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4answers
515 views

Is an RSA variant with public exponent $e=f+(p-1)\cdot(q-1)$ safe (for $f$ random in some small interval)?

Alice is going to use some existing RSA scheme (employing industry-standard signature or/and encryption with proper padding), which she can't change, or influence beyond her choice of key. In this ...
7
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2answers
1k views

RSA and prime difference

It is known that the two prime factors $p$ and $q$ of an RSA modulus $n$ should not be too close to each other, otherwise an attacker may factor the modulus. In other words, $\Delta = \left| p - q ...
7
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1answer
522 views

How can I determine the GPG/PGP key ID from the RSA modulus?

According to http://www.pgp.net/pgpnet/pgp-faq/pgp-faq-keys.html#key-public-key-forgery, key ID is some lower bits sequence from the modulus (i.e. the $n$ variable): A PGP key ID is just the ...