Frequent 'public-key' Questions

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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 ...

asked Mar 3 '12 at 2:51

Inaimathi

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6answers

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Should we sign-then-encrypt, or encrypt-then-sign?

Frequently, we want to send messages that are (a) encrypted, so passive attackers can't discover the plaintext of the message, and (b) signed with a private-key digital signature, so active attackers ...

encryption public-key signature protocol-design hash-signature

asked Nov 22 '12 at 16:55

David Cary

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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 ...

public-key rsa

asked Oct 20 '11 at 19:13

mikeazo

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52

votes

3answers

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Definition of textbook RSA

What is the definition of textbook or "raw" RSA? What are some of the properties of textbook RSA? How does it differ from other schemes based on RSA?

rsa public-key cryptanalysis terminology

asked Dec 12 '11 at 19:36

Bobby S

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23

votes

2answers

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Is RSA encryption with a private key the same as signature generation?

It is often said that RSA encryption of a cryptographic hash with a private key is the same as signing (signature generation). And that verification consists of decryption using a public key. Is RSA ...

encryption rsa public-key signature

asked May 4 '14 at 16:43

Maarten Bodewes♦

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66

votes

1answer

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Can you explain Bleichenbacher's CCA attack on PKCS#1 v1.5?

I've studied that the Bleichenbacher's CCA attack on PKCS#1 v1.5. is a base to many versions of attacks in the area. I'm trying to understand that attack, but every explanation I saw starts with the ...

encryption rsa public-key chosen-ciphertext-attack

asked Jan 2 '14 at 14:24

Bush

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69

votes

4answers

38k 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?

encryption rsa public-key

asked Jul 12 '11 at 19:27

samoz

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56

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8answers

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How does asymmetric encryption work?

I've always been interested in encryption but I have never found a good explanation (beginners explanation) of how encryption with public key and decryption with private key works. How does it ...

public-key

asked Aug 3 '11 at 10:18

Senad Meškin

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18

votes

3answers

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Why does key generation take an input $1^k$, and how do I represent it in practice?

In my lecture, the lecturer said: Let $K$ be the key generation algorithm. Given a security parameter represented in unary, $1^k$, $K(1^k)$ will output a keypair $(pk; sk)$, known as the public ...

public-key notation

asked Apr 29 '13 at 21:09

juaninf

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16

votes

1answer

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After ECDH with Curve25519, is it pointless to use anything stronger than AES-128?

Is the following reasoning correct: After ECDH with Curve25519, the resulting shared secret will be an EC public key with a bit strength of 128 bits. This public key would then be hashed (let's say ...

aes public-key elliptic-curves diffie-hellman symmetric

asked Jun 3 '18 at 22:00

knaccc

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52

votes

3answers

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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?

encryption rsa public-key authentication

asked Mar 18 '12 at 16:53

Humam Shbib

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74

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5answers

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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. ...

public-key rsa prime-numbers

asked Mar 1 '12 at 12:54

Vilx-

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25

votes

5answers

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Why is it important that phi(n) is kept a secret, in RSA?

Why is it important that $\phi(n)$ is kept a secret, in RSA?

rsa public-key

asked Dec 20 '12 at 11:59

johankj

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27

votes

2answers

31k views

Why is asymmetric cryptography bad for huge data?

I've been told that asymmetric cryptography requires that the message to be encrypted be smaller than its key length. Why is this? I know about hybrid encryption, which uses symmetric encryption to ...

encryption public-key symmetric

asked Dec 19 '12 at 20:31

K_X

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13

votes

1answer

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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 $n_B$ ...

rsa public-key

asked May 20 '14 at 16:17

Shankha Jana

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68

votes

3answers

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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 ...

public-key rsa

asked Jul 1 '12 at 4:25

Christopher Jon Mankowski

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1answer

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Verbatim of early work on public-key cryptography?

In late 1997, the history of public-key cryptography was turned around with the announcement (then extended) that public-key cryptography was theorized in a 1970 note [1] by James Henry Ellis: The ...

public-key history

asked Nov 20 '14 at 14:42

fgrieu♦

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25

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2answers

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Why is PuTTYgen-created RSA public exponent(e) not in {3,17,65537}?

As far as I know, RSA public exponent(e) should be one of {3,17,65537}. However, I found PuTTYgen-created RSA public exponent(e) is 0x25(37) by default,as follows, (PuTTYgen version: 0.66) I am ...

encryption rsa public-key

asked Nov 25 '15 at 15:17

Matt Elson

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votes

2answers

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Can a computationally unbounded adversary break any public-key encryption scheme?

Assume there is a public-key encryption scheme $(KeyGen, Enc, Dec)$ with perfect correctness (i.e., for all messages M and valid key-pairs (PK,SK), we have $Dec_{SK}(Enc_{PK}(M))=M$). Will there ...

public-key brute-force-attack

asked Sep 24 '11 at 21:25

huyichen

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26

votes

9answers

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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 ...

cryptanalysis public-key rsa

asked Jul 14 '11 at 0:39

Elliott

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169

votes

4answers

113k views

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 ...

rsa public-key elliptic-curves computational-complexity-theory

asked Nov 15 '11 at 6:19

Vineet Menon

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45

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3answers

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Why is public-key encryption so much less efficient than secret-key encryption?

I'm currently reading Cryptography Engineering. After giving a high level explanation of the difference between secret-key encryption and public-key encryption, the book says: So why do we bother ...

public-key symmetric

asked Sep 2 '11 at 2:12

user670

27

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2answers

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How much computing resource is required to brute-force RSA?

It's been over 30 years since Rivest, Shamir and Adleman first publicly described their algorithm for public-key cryptography; and the intelligence community is thought to have known about it for ...

cryptanalysis public-key rsa brute-force-attack

asked Jun 25 '12 at 6:14

eggyal

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36

votes

4answers

30k views

How can one securely generate an asymmetric key pair from a short passphrase?

Background info: I am planning on making a filehost with which one can encrypt and upload files. To protect the data against any form of hacking, I'd like not to know the encryption key ($K$) used for ...

encryption public-key key-derivation pbkdf-2 host-proof

asked Jan 13 '12 at 21:23

Flumble

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11

votes

2answers

2k views

More than one private key for RSA

In an RSA-encryption scenario, Bob's public key pair $(n, e)$ is $(143, 43)$. An attacker Mallory tries brute-force and comes to $d = 7$ as the private key. The value of $φ(143) = 120$ is not known to ...

encryption rsa public-key

asked Jan 17 at 17:40

user86295

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10

votes

1answer

442 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 ...

rsa public-key signature authenticated-encryption

asked Jan 3 '16 at 19:23

Ilmari Karonen

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83

votes

10answers

17k views

In end-to-end encryption, doesn't the server need to be trusted?

Applications like WhatsApp use end to end encryption. WhatsApp says that only the users share a specific key and no third party can view the messages. But I do not understand how the two users agree ...

encryption public-key key-exchange

asked Dec 19 '17 at 14:30

AV94

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22

votes

4answers

12k views

Is sharing the modulus for multiple RSA key pairs secure?

In the public-key system RSA scheme, each user holds beyond a public modulus $m$ a public exponent, $e$, and a private exponent, $d$. Suppose that Bob's private exponent is learned by other users. ...

rsa public-key modular-arithmetic

asked Feb 16 '13 at 9:15

Mohammed Fathi

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62

votes

1answer

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Why does my SSH private key still work after changing some bytes in the file?

I (for a test) just randomly altered a private RSA key by opening it up in Vim and changing a few bytes. It is the private part of an SSH key pair used for logging in on a remote system. Puzzlingly, ...

rsa public-key authentication ssh

asked Jan 9 '16 at 19:15

PhilPotter1987

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25

votes

2answers

31k views

How does a chosen plaintext attack on RSA work?

How can one run a chosen plaintext attack on RSA? If I can send some plaintexts and get the ciphertexts, how can I find a relation between them which helps me to crack another ciphertext?

cryptanalysis rsa public-key chosen-plaintext-attack

asked Apr 10 '12 at 4:24

user1829

21

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1answer

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Security of RSA for paranoids with padding?

RSA for Paranoids (RSAP) (in CryptoBytes v1n3), also known as Unbalanced RSA, is a variant of RSA proposed in 1995 by Adi Shamir, as a mean to increase the RSA public modulus size while keeping ...

rsa public-key rsap

asked Apr 12 '14 at 23:07

fgrieu♦

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7

votes

1answer

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Is a known plaintext, ciphertext, and public-key a viable attack on RSA?

Assume Alice and Bob are using RSA to create a common session key and Cindy is listening, attempting to obtain the session key. Alice and Bob each have their public- and private-key pairs ($\left[...

rsa public-key protocol-design known-plaintext-attack

asked Mar 7 '13 at 18:19

geofflittle

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16

votes

1answer

14k views

How does encryption work in elliptic curve cryptography?

So I think I understand a good amount of the theory behind elliptic curve cryptography, however I am slightly unclear on how exactly a message in encrypted and then how is it decrypted. So my ...

encryption public-key elliptic-curves

asked Dec 30 '15 at 21:58

Ali

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14

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2answers

3k views

Is it safe to reuse a ECDSA nonce for two signatures if the public keys are different?

We denote the s value of an ECDSA signature $(r, s)$ on a message $m$ as: $s=\frac{H(m)+xr}{k}$ Assume two ECDSA signatures sharing the same nonce $(r, s_1) , (r, s_2)$ on two messages $m_1, m_2$, ...

public-key elliptic-curves cryptanalysis signature dsa

asked Jul 5 '19 at 17:04

Ethan Heilman

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4

votes

2answers

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Why is hybrid encryption more effective than other encryption scheme?

Currently I am learning about Hybrid Encryption but I was not able to find any good study material. Below is my understanding: One of the reason why we use ...

encryption public-key symmetric key-exchange hybrid-encryption

asked Dec 13 '15 at 7:36

python

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How to compute $m$ value from RSA if $phi(n)$ is not relative prime with the $e$?

Here is some information we got : We know the value of $n$, with size $1043$. We know the value of $p$ (size $20$) and $q$ (size $1023$) as the factors. $e = 65537.$ $\varphi(n)$ = $(q-1)(p-1)$ When I ...

rsa public-key modular-arithmetic

asked Jul 17 '20 at 12:39

user81147

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18

votes

2answers

34k views

What makes RSA secure by using prime numbers?

I am just learning about the RSA algorithm. Looking at the first two steps: Choose two distinct prime numbers $p$ and $q$. Compute $n = pq$. I have some probably stupid questions: Why do $p$ and $...

rsa public-key prime-numbers

asked Sep 27 '13 at 5:19

Joark

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14

votes

2answers

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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 ...

cryptanalysis public-key rsa group-theory

asked Jan 4 '12 at 22:17

Emilio Ferrucci

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10

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5answers

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Why do we need asymmetric algorithms for key exchange?

In SSL protocols, both symmetric and asymmetric algorithms are used. Why is it so? The symmetric algorithms are more secure and easier to implement. Why are asymmetric algorithms usually preferred in ...

public-key tls symmetric key-exchange

asked Feb 6 '12 at 6:37

user5507

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10

votes

3answers

4k views

Is RSA in a ECB-like-mode safe for bulk encryption?

Let's say I would like to communicate with my friend using asymmetric/public-key encryption, e.g. RSA. (Note: I do realize that in practice this is done through an intermediate symmetric key, but ...

encryption public-key rsa key-reuse

asked Jun 4 '12 at 16:42

user541686

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4

votes

1answer

2k views

How to calculate RSA CRT parameters from public key and private exponent

Given the public key (n, e) and private exponent (d), how to calculate CRT parameters (p, q, dP, dQ, and qInv) of this RSA key pair?

rsa public-key keys modular-arithmetic

asked May 25 '15 at 14:02

user1563721

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Factors of RSA modulus

In the article A Method for Obtaining Digital Signatures and Public-Key Cryptosystems, the original RSA article, it is mentioned that Miller has shown that n (the modulus) can be factored using any ...

rsa public-key prime-numbers factoring

asked Jan 13 '15 at 17:11

user3343768

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11

votes

3answers

23k views

Using ECDSA keys for encryption

I know that ECDSA is used for signature only, but I wonder if I can use the public/private Elliptic Curve keys for encryption too. I have ECDSA SSH public keys and I wonder if I can use them to ...

public-key elliptic-curves dsa

asked Feb 23 '14 at 23:34

jcea

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votes

1answer

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What does the $\|$ operation mean in cryptographic notation?

I am studying elliptic curves problems, which also includes study of related protocols such as ECIES. The problem is that I don't understand the notation $\|$. What does this operation mean? Some ...

encryption public-key elliptic-curves notation

asked May 16 '12 at 10:13

eXPi

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4

votes

1answer

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ECC vs RSA: how to compare key sizes?

I know and I have understood the details of RSA, elliptic curve cryptography, (EC)DH and (EC)DSA. I keep reading everywhere that (if we don't consider non-deterministic computers) "ECC can achieve ...

rsa public-key elliptic-curves key-size

asked May 11 '15 at 14:30

user16538

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Definition of Short Authentication String

I am studying for my cryptography final and I passed by the following term: short authentication string. Please, can anyone explain it to me, thank you very much.

public-key authentication

asked Jan 2 '19 at 10:33

okm02

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16

votes

5answers

11k views

Why does the recommended key size between symmetric and asymmetric encryption differ greatly?

In various articles it is mentioned that for secure communications, the recommended key sizes are 128-bit key size for symmetric encryption (which makes it $2^{128}$ possible keys?) and 2048-bit key ...

encryption public-key symmetric key-size

asked Feb 4 '13 at 22:04

Bailala

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10

votes

4answers

4k views

Why should the RSA private exponent have the same size as the modulus?

Consider the generation of an RSA key pair with a given modulus size $n$ and a known, small public exponent $e$ (typically $e = 3$ or $e = 65537$). A common method is to generate two random primes ...

public-key rsa

asked Jul 18 '12 at 18:14

Gilles 'SO- stop being evil'

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4

votes

2answers

503 views

Bruce Schneier, encryption, public keys and digital-signature.

In his book "Applied Cryptography" Bruce Schneier, when talking about public key cryptography, says that: If the same algorithm is used for both encryption and digital-signature verification there ...

encryption public-key signature

asked Jul 26 '17 at 19:53

Jean Pacher

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8

votes

0answers

334 views

Are there groups where the computational Diffie Hellman problem is easy but the discrete log problem is hard? [duplicate]

I know that there are elliptic curve groups, used in pairing-based cryptography, where the decisional Diffie Hellman problem (ie. given $g$, $g^a$, $g^b$ and $c$, determine if $c = g^{ab}$ is easy but ...

public-key elliptic-curves group-theory

asked Jan 20 '14 at 10:57

Vitalik Buterin

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