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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Adding two RSA private key

We've constructed a new private RSA key from two known private RSA keys $Priv_1$ and $Priv_2$ as follows: $$p = next\underline{}prime\left(\frac{Priv_1(p) + Priv_2(p)}{2}\right)$$ and $$q = ...
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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 ...
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Questions about OAEP for RSA

I have two questions about OAEP for RSA. How are the number of bits to pad with 0 chosen? For example, if I'm sending a 255 byte message with RSA-2048 I have 8 unused bits (1 byte). Should I split ...
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Proof of elliptic curve difficulty

Are there any proofs that cryptographic functions on an elliptic curve are any more difficult than the analogues over modulo arithmetic? While at present, ECC appears to be more difficult, as it is ...
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152 views

low-exponent RSA

I have questions from http://link.springer.com/chapter/10.1007%2F3-540-68339-9_1 Suppose we have 2 messages $m_1$ and $m_2$ related by a known relation $m_2=m_1+1$. Suppose further the messages are ...
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Combining AEAD with RSA

'Hybrid' encryption, where we combine symmetric encryption with public-key cryptography, is pretty 'tried and tested'. To summarise, we generate a symmetric key and encrypt it using RSA. We would ...
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432 views

Question about why RSA is hard to attack

I think I understand why RSA is hard to attack but I'd like to get clarification if I actually do. Assume there are two people, Alice and Bob, who are attempting to communicate privately but that we ...
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How do ciphers change plaintext into numeric digits for computing?

For example, in RSA, we use this for encryption: $ciphertext = (m^e \mod n)$ and for decryption. If our message is "hello world", then what number do we have to ...
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Is it okay to use a variable-time RSA implementation to verify TLS certificates?

RSA as implemented by OpenSSL et al. needs to protect against side channel attacks, at a big performance penalty. However, TLS certificate validation involves no secrets. Therefore, I should be able ...
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158 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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464 views

Purpose of leading zero in PKCS1-v1_5 padding

According to this document the padded message has the following structure: $EM \;= \; 0x00 \; || \; 0x02 \; || \; PS \; || \; 0x00 \; || \; M$ What is the purpose of this null byte at the beginning ...
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How to attack RSA-CRT with large public exponent?

Suppose we have $(n,e)$ and the ciphertext $c$ where the public exponent $e$ is of the same length, 1023-bit, as the modulus $n$. It is also assumed that the factors of $n$ are balanced. The message ...
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Are there comprehensive alternatives to RSA?

If we wished to, is there a comprehensive alternative to RSA? I say comprehensive as I wonder if there is one which does both encryption and digital signature like RSA? If not, simply what ...
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How to generate a bilinear group of prime order p for key generation

I am trying to implement an IEEE Paper In Cryptography. I read many reference regarding an RSA key generation. But i am confused with above statement. Please someone explain me What it says with ...
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93 views

How to compare the efficiency of public key cryptosystems, i.e., RSA vs El Gamal?

As part of my Mathematics degree I'm taking a Discrete Mathematics module which partially covers Public Key Cryptography but does not at all enter it in depth. I'm currently working on a project that ...
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134 views

Consequence of a change on the Guillou-Quisquater Protocol

In the Guillou-Quisquater Protocol, the prover convinces the verifier that he knows an $e$-th root of an element $y \in \mathbb{Z}^*_n$ ($p, q, e$ are primes, $n = pq$ and $e$ is coprime with ...
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Factoring two RSA modulus with known $|p_1 - p_2| < \ell $

I have two 1024bit RSA modulus $N_1 = p_1q_1$ and $N_2 = p_2q_2$ such that $0 <|p_1 - p_2| < \ell$, and $\ell$ is at most 64bit integer. Can I factorise $N_1$ and $N_2$? What's the answer when ...
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How can one calculate the estimated RSA key life based on Moore's law?

How can someone estimate the number of years needed to factor an RSA key based on the advancement of technology if followed Moore's law?
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Are there any standards of multi-prime RSA key generation?

FIPS 186-3 specifies a method to generate DSA parameters. Is there anything similar (official standard or widely-accepted recommendation) that shows how to generate the primes for multi-prime RSA?
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Can you help me understand the Common Modulus Attack in a Lucas Group?

I'm trying to decrypt a message that is encrypted using a LUC encryption scheme and running into roadblocks. I know that with RSA if Alice and Bob use the same public modulus but different encryption ...
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What followed findings of A. Lenstra et al. concerning shared factors of practical RSA moduli?

A. Lenstra et al. had a paper in 2012 "Ron was wrong, Whit is right", in which one reads: "What surprised us most is that many thousands of 1024-bit RSA moduli, including thousands that are contained ...
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Ring Signature - paper/code difference in trying to solve inverse trap door function?

there is a paper on ring signatures and a python implementation of it here. The Step 4 in the paper describes $y_s = v =C_k,_v(y_1, y_2, ... y_r)$ for all $1 \leq i \leq r$ where $i \neq s$. The ...
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Generate RSA-2048 private key for a VERY fast decryption (don't care if it will be unsecure)

Given public standard RSA exponent e = 65537, is there any (d, n) pairs so that RSA decryption becomes a trivial operation? The modulus n must be no less than 2048-bit. The goal is to get a real ...
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How can I avoid calculating with huge numbers when implementing the RSA algorithm

There is 26-letter English alphabet. There is the plain text: TRYAGAINLATER. I need to encrypt it by RSA algorithm with the public key 53. What is the ciphertext? ...
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Is there any reason to use RSA or DSA when we have ECC?

I am having trouble coming up with a use case for RSA or DSA. It appears that ECC is better in every way. Is this true? I am looking for cases where RSA/DSA is superior to ECC, not where it is used ...
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Key space vs Cardinality of 1024-bit RSA

I have been trying to figure out the encryption key space, and cardinality of 1024-bit RSA. From my understanding, the key generated from 1024-bit will be primes greater than $2^{1023}$ but less than ...
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Small Prime Difference in RSA

In RSA, the $p$ and $q$ should be randomly generated, and they are the same size. The difference between $p$ and $q$ should not be small. Suppose that $u=|p-q|<20$ and $p \times q ...
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Are there any papers explaining how to port textbook RSA to realworld RSA?

Are there any papers, books, or link where it explains how the plain vanilla "textbook RSA" is actually implemented in practice with all the padding and stuff? Basically, I would like to know the ...
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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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Why is RSA encryption significantly faster than decryption?

I am designing an implementation of RSA . I recorded computation times in Java by using System.currentTimeMillis(). It returned an encryption time of 0.05 ms and ...
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Can the encryption exponent e be greater than ϕ(N)?

So I was just wondering in RSA, can the encryption exponent e be greater than ϕ(N)?? For an examples sake, lets just say N = 707, so p = 101 & q = 7. So, we have ϕ(707) = 600. Can I have e = ...
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Does RSA padding have to be unpredictable if the payload is?

I'm trying to understand the precise requirements on padding when using RSA for encryption. Suppose Alice uses RSA to encrypt a payload $M$ that cannot be guessed (say, a random nonce): Alice send ...
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RSA: Recover e given factorization of N and plaintext/ciphertext pair

Is there a way to recover the public exponent e (assume in this case it is in fact not public) used in an encryption if I know the following: Factorization of ...
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Avoiding overflow when encrypting with RSA

When encrypting with RSA one calculates $ m^e \pmod n $ by doing the following: m^e % n Where $m$ is what we encrypt. Often $e$ is a very big number to make it ...
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758 views

What's the main difference between Pohlig-Hellman and RSA?

Both Pohlig-Hellman and RSA perform encryption and decryption by exponentiation modulo some integer ($p$ prime for PH, $n$ composite for RSA). They both use a key $e$ as the exponent to encrypt a ...
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Isn't the deterministic property of (EC)DSA a security problem?

From what I read in Wikipedia's article "Elliptic Curve DSA ~ Security", the "deterministic" generation of $k$ can help prevent certain type of attacks (such as the one happened to Sony). However, ...
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Textbook-RSA meet-in-the-middle attack against other RSA based schemes?

A “meet-in-the-middle” (not “man-in-the-middle”!) attack on textbook-RSA was presented to me. The only requirements for it was that the attacker gets the output of RSA and the public key, and that the ...
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Difficulty of breaking RSA for a given key size

Is it true that breaking a 1024-bit RSA key is as difficult as breaking a 128 bit symmetric key (e.g. AES)? I know that breaking a RSA key is equivalent to factoring the modulus $N$. To factor it, you ...
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Finding Private key in RSA with public key, cipher text and plain text

Is there a known 'non-brute force' method of determining a private key in an RSA system when all other parameters are know? I found the values of a ciphertext ($C$), its corresponding plaintext ($P$) ...
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How do I attack an RSA setup where e is even?

As a challenge, we were shown an RSA setup where we have a big $n$ (617 decimal digits), $e=4$, and asked to recover three messages. (However, the messages are padded to the same length as the key ...
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HMAC SHA256 vs RSA SHA256 - which one to use

Salesforce recently announced they are moving away from HMAC SHA256 to RSA SHA256. Why did they make that move?. Any technical factors? Is HMAC really easy to break? ...
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What does an RSA signature look like?

I am using OpenSSL libs to generate signatures. Internally, I learn that a signature is a hash of the message with some padding added to it. I am trying to understand the structure of a signature. If ...
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Openssl & RSA : how many public exponents are possible?

I would like to know if it is possible to set the public exponent we want with "OpenSSL RSA" or if it is really limited to 2 possible exponents: 3 65537 If yes, why ?
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RSA by hand - did I do something wrong? (c = m on encryption)

to understand RSA better I am doing a little calculation by hand, this is what I got: Choosing: $p = 3$ $q = 5$ $n = 15$ $\phi(pq) = 2 \cdot 4 = 8$ $e > \phi(n) => e = 13$ $e \cdot d = 1 ...
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If we can find prime numbers larger than 17 milion digits, why can't we find all 1024bit primes? [duplicate]

"Largest Known Prime Number Discovered; Has 17,425,170 Digits" http://www.sciencedaily.com/releases/2013/02/130213225424.htm If we can find prime numbers larger than 17 milion digits, why can't we ...
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If RSA is limited to 117-200 bytes or so, is that a very limited use case?

Am I missing something, or is RSA very very limiting when it comes to ecrypting data when it comes to the actual message size? I have read that you can only encrypt a message of around 117 to 200 ...
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Why do we need in RSA the modulus to be product of 2 primes?

I think I roughly understand how the RSA alorithm is working. However, I don't understand why we need the $N$, which we use as a modulus, to be $pq$ for some large primes $p, q$. I vaguely know it ...
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579 views

How does the cyclic attack on RSA work?

I am trying to get the idea of cyclic attacks againts assymetric RSA encryption. Taken from Handbook of applied cryptography . Let $k$ be a positive integer such that $$c^{(e^{k})} = c\mod n ...
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Why do we need Euler's totient function $\varphi(N)$ in RSA?

After we calculated $N = p * q$, we calculate $\varphi(N)$ and use it later to determine $e$ (PR) and $d$ (PU). But why? For decryption and encryption we only use $N$ and don't need $\varphi(N)$. So ...
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Why are recomended RSA key lengths so high? [duplicate]

I was checking for authoritative sources to back up my recommendation of a minimum RSA key length of 1024 and was shocked to find that NIST 800-56Br1 and FIPS 186-4 both recommend at least 2048 bits ...