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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276 views

How long does it take to decrypt an RSA/ECB encrypted message?

I am working on assignment where I have specific scenarios and I am little bit struggling with this one. Alice sends and email to Bob.For this e-mail, she uses the following method of encryption: ...
7
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2answers
384 views

Can Shor's algorithm compromise RSA when both the public and private key are secret?

If RSA is to create a public private key pair and encryption is performed on plain test P to create cipher text C, given P and C could Shor's algorithm be used to find either of the public and private ...
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2answers
3k views

How to calculate the maximum output size for data encrypted with a RSA Private Key?

I have an an encryption algorithm I am working with that looks like this: prv_key_enc(sha1_hash(data)) Where, the RSA parameters are: RSA/ECB/PKCS1Padding 1024 ...
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0answers
58 views

Name of an archaic type of RSA padding (0BBBBBBB…)

In some legacy code, I encountered RSA signature padding in the following format (hexadecimal): 0B BB BB BB BB BB BB ... BB BB <hash> Is there a name for ...
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50 views

How can I obtain the raw decimal value of an RSA key's modulus?

So maybe I'm thinking about this too hard, or maybe I'm missing a piece of information. We'll use Google for this example. Say I wanted to obtain the modulus of Google's current public key. Well I ...
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1answer
62 views

How to prove a lemma that is based on phi-hiding assumption?

Assume that the $\phi$-hiding assumption is true, i.e. that for a composite number $m$, a PPT adversary A cannot distinguish between a prime $p_0$ that divides $\phi(m)$ and another prime $p_1$ that ...
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1answer
88 views

RSA Digital Signature vs Elgamal Digital Signature

What are the advantages of RSA signatures against ElGamal signatures? Is there a situation in which it would be better e.g. to use RSA signatures?
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46 views

How to encrypt huge data using RSA? [duplicate]

Is there any way to encrypt the huge amount of data using RSA? I was supposed it is possible but when I read some articles what I saw is that, this is bad practice or they say can only encrypt bit ...
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1answer
38 views

Is there a way to turn a PGP key into its semi-prime counterpart?

From my understanding of PGP keys they use the RSA algorithms to encrypt/decrypt messages. So, I know that the RSA algorithms use a semi-prime number to encrypt/decrypt messages. So, what I was ...
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0answers
74 views

RSA PlainText without Knowing Private Key

I couldn't solve this problem for three days... In RSA, [n = 13, 19] [e = 3] c1 = m^3 = 83 mod 247 [e=5] c2 = m^5 = 97 mod 247 then, use ...
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1answer
78 views

Highest prime factor that is Safe for a particular scheme

My question is how many bits of prime number is secure so that it cannot be factored from very large number? Until today how large prime factor is found in large number? Quantum computing find ...
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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 ...
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73 views

Factoring an RSA modulus given high bits of a factor

I have {e,N,C} and part of p; can I get q from this example : ...
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1answer
128 views

Why does choosing the first coprime e greater than half of φ(n) result in the same d (private exponent)

While reading on RSA's algorithm, I attempted a simplified implementation and noticed the following: When choosing the public exponent $e$, if the value chosen is the first coprime after $φ(n)/2$ ...
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4answers
7k 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: ...
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1answer
55 views

How to use the hardcoded server's public key to register a client application?

I'm designing the security for a smartphone app that can be used to make car reservations. Clients have to register them with their driver's licence through the application and can then book a car. ...
3
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1answer
36 views

How does this solution guarantee authentication of B and privacy?

The exercise is: What could be changed on the second message " Kya(Kxb(Ra,Ks)) " to guarantee B's authenthicity and also privacy? My teacher's solution was "add a destination" , so it would be ...
3
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1answer
54 views

Need help understanding this exercise's solution

We were given this exercise, which asks us to identify the types of keys used on this diagram: The solution was Kxa -> A's private key Kya -> A's public key KxB -> B's private key My question ...
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1answer
63 views

Factorization of RSA modulus using a qubic residue

Suppose that someone uses RSA with $n = pq$, exponent $3$, also $3$ divides $\varphi(n) = (p-1)(q-1)$ and $2$ different roots $y$ and $z$ of the equation: $$x \equiv c \ (mod \ n)$$ are known (for ...
3
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2answers
82 views

Chosen-Message-Attack RSA-Signature

I know that because of the multplicative property of RSA $s =(s_1s_2) \bmod n = (m_1m_2)^d \bmod n$ If Oscar wants to sign now an own message $m$ he chooses another message $m_1$ with $\gcd(m_1,n)=...
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1answer
19 views

Digital signature with collision

Let's assume a digital signature scheme such that there's a probability of 0.2 for two random messages to have the same signature. How can I exploit this sheme? I'm having difficulties in finding an ...
0
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1answer
25 views

X509 Cert exploit CA check

Assumptions Let's theoretically assume that a browser skips the check that a certificate it receives belongs to the stated CA (that's an exercise). How could I exploit this in order to impersonate ...
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1answer
55 views

Why is it better to have the private key as the multiplicative inverse mod phi(n) in RSA?

I'm studying the RSA algorithm and the theory says to select $d$ to be the multiplicative inverse of. $$ e \mod \phi(n) $$ If we take this approach I know that it is important that $e$ and $\phi(...
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0answers
39 views

Issue Factorization Quadratic Sieve

Good evening, I'm about to write my own quadratic sieve implementation in C using GMP library for large numbers. I'm facing an issue while attempting to do the last factorization step for the number: ...
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3answers
116 views

Can $d$ and $e$ be the same number in RSA?

I'm reading about RSA and I have doubts: 1) To choose $e$, this value have to be between $1$ and $\phi=(p-1)(q-1)$, with $\gcd(\phi, e) = 1$, right? 2) In my example, $p = 139$ and $q = 491$. So $n =...
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4answers
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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 ...
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2answers
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Why is padding the plaintext with a random string before encryption worse than OAEP / PKCS#7?

I'm reading about OAEP / PKCS padding used for PGP to turn deterministic algorithms like RSA from deterministic encryption to probabilistic encryption (randomness in the resulting output). That way ...
4
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1answer
432 views

How to sign a large file for random-access reading?

I need to write an "Authoring" application which produces large files. These files must be signed so that the "Consuming" application knows that it was authored with a matching key. The consuming ...
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9answers
5k 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 ...
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4answers
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Why does RSA need p and q to be prime numbers?

This is a clarifying thread after finding: What makes RSA secure by using prime numbers?. Despite the fact that this question was answered already, I am still struggling to really grasp the ...
3
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0answers
102 views

How to generate an RSASSA-PSS signature with MGF1-SHA256?

As part of rooting a device, I need to generate a 256-byte RSASSA-PSS signature using SHA256 as the hash and MGF1-SHA256 as the mask function, for an update file I created. I can choose any 32-byte ...
3
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3answers
117 views

Can an adversary distinguish a private key from a pseudo-random string of the same length?

Apologies if this is a dumb question but allow me to describe the dilemma I have: Suppose that I am protecting a private key on a device using a password & PBKDF2. The obvious attack would be an ...
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2answers
706 views

Calculate the RSA private exponent from the CRT parameters

I am trying to make the RSA structure of Openssl manually, knowing the public key ($n$, $e$) and the CRT parameters $p$, $q$, $d_P$, $d_Q$, and $u = q^{-1} \mod p$. That is, I want to get the $d$ ...
4
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2answers
125 views

RSA 3072 is 65,536 more difficult to factor than 2048?

If RSA 3072 is equal to 128 bit symmetric and 2048 is equal to 112 bit symmetric then 128-112= 16 and 2^16= 65,536. In that case wouldn't this make 3072 more future proof against quantum computers or ...
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2answers
11k 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 $p$ ...
4
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1answer
133 views

What is the major difference between FIPS 186-2 and FIPS 186-4?

Can anyone please tell me the major difference between FIPS 186-2 and FIPS 186-4? I know with FIPS 140-2 they want the DSS standard to be FIPS 186-4, but what difference does it make?
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1answer
91 views

New Improved Probabilistic version of RSA

On the 2nd page of "New probabilistic public-key encryption based on the RSA cryptosystem" by Roman'kov (PDF), at last it says Alice can find "f" of order "l" with least probability of (1-1/l). I ...
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1answer
31 views

How to add passphrase to an RSA key?

If I want to protect a private RSA key, do I just XOR the password into the key, or do I do something else? Is it secure? Edit: I got a good answer from a comment - Hash the password/passphrase with ...
3
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1answer
188 views

What is the probability of attacking SHA1 used in RSA signature with small exponent?

There is RSA signature check which has following properties: RSA modulus N which is 2048-bit RSA public exponent equal 41 (0x29) Genuine Signature uses EMSA-PKCS1-v1_5 padding of SHA1 hash, however ...
21
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2answers
2k views

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 ...
0
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1answer
46 views

How do you work out the private key in a RSA cryptosystem knowing a certain public key?

The public key: n = 85 and e = 19 I know that n is the product of two prime numbers, now is it right of me to figure them out by process of elimination which I got p or q equals 17 and 5. Or is ...
2
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1answer
99 views

RSA Encryption problem for Discrete Math

I am doing practice problems for my upcoming final exam, and am having trouble with this RSA encryption problem. If any one could check to see if i did these correctly, it would be greatly appreciated....
2
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1answer
59 views

How can I show RSA OAEP IND-CPA secure

How can I show, that RSA with OAEP is IND-CPA secure by using G,H one way function?
5
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2answers
178 views

Should RSA primes p and q differ in length by “a few digits”?

When generating RSA keys in the original RSA paper it is stated: to gain additional protection against sophisticated factoring algorithms, p and q should differ in length by a few digits Why is ...
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Encrypting/Decrypting using RSA and AES; standards?

I'm looking for a standard way of encrypting and signing a message using RSA and AES. I understand that in pseudo code the actions taking place are like this: Alice's actions for sending a secret, ...
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2answers
72 views

RSA: select $e$ given $n$ and $\varphi(n)$

I have a question for a course I am doing. In an RSA question, it asks "Is it possible to select $e$ in such a way that it coincides with the corresponding private key $d$? If it is possible, provide ...
7
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1answer
224 views

How many qubits are required to break RSA 2048 or 4096 with a universal quantum computer?

So in the news this week, IBM have created a universal quantum computer with 5 fully functional qubits. Logic and Moore's law dictates they will be able to scale this up to a lot more qubits within a ...
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1answer
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How to find $e$ when $p,q,d$ are given?

I have solved till here ..... $$n=p*q$$ $$n=5*11$$ $$\varphi(n)=(p-1)*(q-1)=4*10=40$$ Now, how to find $e$, when $d$ is given as $27$ and message for encryption is $\text{abcdefghij}$. We have to take ...
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1answer
122 views

Decrypting an RSA message given $a^2 \equiv 1 \pmod n$

I need help with a practice problem for an upcoming test. I've learned the answer to the problem is "well done", but don't know how to get there. Any help is greatly appreciated. Suppose that the ...
6
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3answers
12k 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 ...