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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Feasible attacks on ECRSA cryptosystem

In ECRSA cryptosystem, I want to know the feasible attacks. For illustrations we have two prime $p$ and $q$ such that $p \equiv 2 \pmod 3$, $q \equiv 2 \pmod 3$ and generate key pair as follows: $$n = ...
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30 views

Do RSA keys contain a checksum mechanism? [duplicate]

I'm new to cryptography, and I was making an experiment a few minutes ago, but I want to have some deeper knowledge about RSA public and private keys. I have a set of keys One begins with ...
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53 views

Why is RSA still being used? [duplicate]

In hybrid encrytion, I still see that some site's use RSA in their https connection, so now I wonder, why do they not use ECC instead of RSA, ECC requires less computational power and encrypt's and ...
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1answer
123 views

How does DH work when combined with ECC or RSA?

I know that Diffie-Hellman is used to create keys in a secure way over an insecure channel. But there is one thing which I cannot understand: I see that a lot of sites use ECC or RSA alongside DH. ...
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59 views

Questions about length key of RSA 2048 bit

I use putty gen to generate RSA key, I choose length of key is 2048 bit, it generate public key: ...
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104 views

Forgery attack against Textbook RSA with simple redundancy

I know how to forge vanilla Textbook RSA message signatures (easy). I've learnt that by adding a good redundancy to the message, it cannot be forged anymore. How can one add redundancy so that the ...
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Diffie-Hellman combined with DSA/RSA

we have learned Diffie-Hellman, RSA and DSA (Digital Signature Algorithm) in university. Because DH is vulnerable of Man-in-the-Middle we had the task to program the DH combined with RSA to protect ...
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33 views

factorization of an integer $N$ that is in special format

Suppose $p_0$ and $q_0$ are known prime numbers and define $p_i$ and $q_i$ as follows: $$p_{i+1} = next\_prime(p_i^2 + q_i^2), \qquad i \ge 0$$ and $$q_{i+1} = next\_prime(2p_iq_i), \qquad i \ge 0$$ ...
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Are public key and private key exchangeable? [duplicate]

If I get a key pair from RSA algorithm, can I make Private-Key public, and keep Public-Key secret without breaking the security of encryption and signature?
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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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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
60 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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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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366 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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71 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
36 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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1answer
84 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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126 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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1answer
76 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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71 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
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 ...
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1answer
53 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
62 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 ...
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23 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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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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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 ...
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1answer
54 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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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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In RSA, how does the CPU deal with this huge modulus (8192 bits)?

Whilst I understand how the RSA algorithm works, I don't understand how the CPU operates when it needs to use the mod function with a huge number $n$, for example. ...
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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
429 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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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 ...
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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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3answers
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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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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 ...
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1answer
99 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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56 views

What is proper size of window Using RSA Window method?

I want to Use Window method for RSA modular Exponentiation. because of SCA. But I don`t know what is proper window size.
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2answers
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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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1answer
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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 ...
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1answer
89 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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45 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 ...
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1answer
64 views

How to decrypt an RSA ciphertext given an oracle providing the lower 8 bits of decryptions?

I have access to an oracle that can encrypt and partially decrypt a number with RSA-1024 algorithm. For encryption: \begin{equation} C = M^e\bmod n \end{equation} But for decryption, result will ...
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1answer
175 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 ...
2
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1answer
95 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....
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1answer
58 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?
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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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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 ...
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1answer
191 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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68 views

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
91 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 ...