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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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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292 views

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

Tamper-proofing log files

Problem Overview I want to securely store log files so the contents are secret, and they can't be modified without detection. The files will be encrypted using authenticated encryption (AES in GCM ...
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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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611 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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RSA: If n=35, show that e will equal d

Show that if $n = 35$ is used as an RSA modulus then the encryption exponent $e$ always equals the decryption exponent $d$? What I have so far: $n = 35$ Therefore $p = 5$ and $q = 7$ or vice versa, ...
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177 views

Why are we not using multiple ciphers per message?

I am aware of at least rsa, elgamal-encryption, and variations of elliptic-curves relying on different problems and that those problems are considered hard. However, if someone figures out a way to ...
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214 views

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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560 views

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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796 views

Is RSA key size the size of private key exponent in public key encryption?

I have implemented a key pair generation scheme for RSA algorithm. I have taken the length of private key exponent as RSA key size, but then I've got to know that RSA key size is the size of the ...
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644 views

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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915 views

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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636 views

How can mega store my login details and still be secure?

I understand how Mega's encryption works. For a quick summary of all those in the future looking for an answer on this... here is how it works: Upon first signing up for an account you make a ...
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891 views

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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478 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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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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1k views

ECDSA vs RSA: Performance on Android platform and surprising results

For our privacy-preserving protocol, an encrypted channel is established. In order to protect our system from man-in-the-middle attacks, signature-based approach is used. After we've implemented it ...
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678 views

RSA and ECDSA performances

Signature algorithms with elliptic curves have small output sizes compared to RSA for the same level of security. What about the processing time to generate a signature ? I've seen figures giving ...
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648 views

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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594 views

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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99 views

RSA with $\lambda(n)$ or $\varphi(n)$

The PKCS #1 v2.0 specifications suggest using $\lambda(n) = \mathrm{lcm}(p-1,q-1)$. What is the benefit of choosing $\lambda(n)$ over $\varphi(n) = (p-1)(q-1)$ in RSA key generation?
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Does RSA operate over a Finite Field (Galois Field)?

Is it correct to say that RSA operates over a Finite Field (Galois Field)? In this case GF(p)? I do understant that the modulo in RSA is not itself a prime number, but all the operations ...
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196 views

Attacking unuauthenticated RSA

In symmetric cryptography, a scheme is not considered secure if the data transmitted is only encrypted. The adversary will be able to modify messages to generate encrypted messages of his choice ...
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487 views

Why can ECC key sizes be smaller than RSA keys for similar security?

I understand how ECC is based on the discrete log problem and RSA on integer factorization. I've read several references that show how a solution to either of these problems can typically be adapted ...
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298 views

Is it possible that two distinct RSA moduli share both of their prime factors?

I am using an algorithm (can be found here1) that can compute efficiently the GCD of multiple RSA keys. It intended for RSA keys that were generated with low entropy and may have one of their primes ...
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506 views

Are RSA signatures deterministic?

If I sign the word HELLO with the mechanism "NONEwithRSA" with the same private key, do I always will have the same signature? A Java example always return ...
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254 views

RSA Without Padding?

I've been looking at the weakness with plain/textbook RSA, where the same message is encrypted and sent to multiple destinations. In this case, it is possible to recover the message. Given that an ...
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“Signing” with public key

For this question, the following caveats and assumptions hold: There exists a 2048-bit RSA key pair used exclusively for signing/verification The private key is kept completely private There exists ...
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Is it possible to figure out the public key from encrypted text?

Suppose Alice sends messages to Bob by encrypting the messages with Bob's public key. Eve knows that the data is encrypted using RSA, but does not know the public key. Can Eve figure out the public ...
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RSA cracking: The same message is sent to two different people problem

Suppose we have two people: Smith and Jones. Smith public key is e=9, n=179 and Jones public key is e=13, n=179. Bob sends to ...
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48 views

RSA: Range of public modulus

I know the public modulus is the product of two primes. For key with length L, the public modulus N should be such ...
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86 views

How often does RSA-OAEP have a leading zero?

We are working with a third party vendor who is very tight lipped about their security protocols, and one of our customers who used this vendor's products is claiming that approximately one in every ...
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220 views

Decrypt all RSA ciphertexts if you can break 1% of them

I was given a cryptography question during an interview the other day. Imagine you are given an efficient algorithm which for a given RSA public key (n,e) is able to decrypt 1% of the messages ...
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83 views

Is xgcd faster than Fermat for calculating $d$ in RSA?

I want to calculate $d$ from $e$ when generating RSA keys. What is faster? Calculating $\operatorname{xgcd}(e,p)$ and $\operatorname{xgcd}(e,q)$ and CRT. Or calculating $e^{p-2}\bmod p$ and ...
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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 ...
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421 views

RSA encryption exponent

In RSA public-key material (e, N), why must the encryption exponent e be relatively prime to $\phi(N)$? Why must any public key encryption algorithm resist CPA?
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878 views

CKM_RSA_PKCS vs CKM_RSA_X_509 mechanisms in PKCS#11

What is the exact difference between the CKM_RSA_PKCS and CKM_RSA_X_509 mechanisms in the PKCS#11 v2.20 specification (Please ...
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819 views

Extract private RSA key from USB cryptographic token using Bardou et al. attack (variant of “million message attack”)

There is a side channel attack on tamper-resistant USB cryptographic tokens using padding-oracle, described by Bardou, Focardi, Kawamoto, Simionato, Steel and Tsay, titled "Efficient padding oracle ...
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257 views

How to find an element of high-order in an RSA group?

Is this even possible? The RSA group is not cyclic, so usually you wouldn't find a generator for accessing all group elements. What happens if you use the RSA group in a scenario where you want that ...
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702 views

How much extra information is in an RSA public key?

I'm trying to calculate the size of an RSA public key in Ruby. I've retrieved the key in PEM format, and once I've decoded the base64 part from the PEM format, I get the size in bytes. What I find is ...
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500 views

RSA algorithm's license free or paid?

I checked RSA's patent application, which was registered in 1983. As patents don't last more than 20 years, it seems to me it should be free. But my friend said to use RSA I have to buy a license from ...
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When to prefer exchanging cryptographic certificates over exchanging only public keys?

Let's think of the following case: A group of peers want to exchange messages with each other. They use public-key cryptography to sign and encrypt messages. Anyone with any name can join the ...
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Calculating private keys in the RSA cryptosystem

The number $43733$ was chosen as base for an implementation of the RSA system. $M=19985$ is the message, that was encrypted with help of a public key $K=53$. What is the plaintext text? What is the ...
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89 views

Why don't use random padding in RSA?

Consider the following scenario: Sender S sends a message to receiver R. He uses a hybrid encryption scheme with RSA as key-encapsulation algorithm and AES-256-CTR (4byte-counter) and SHA256-HMAC. ...
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109 views

RSA public key recovery from signatures

Is it possible (how) to recover public (512 bit long) RSA key from multiple signatures having corresponding plain texts. Padding is not randomized. I need it to verify any future message comming from ...
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187 views

Security of RSA with $\gcd(pq, (p-1)(q-1))\ne 1$

The Congress of ThéOùÇa enacted that civilian use of any public-key encryption system is authorized on the territory of ThéOùÇa, subject to meeting certain security requirements published by the ...
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Creating a license system based on asymmetric encryption (RSA or ECDSA)

I’ve spent a couple of days researching the topic of creating a license system for my desktop software. While I fully understand that there’s no perfect copy protection, this approach seems to have ...
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Pseudocode for constant time modular exponentiation

I'm looking to implement modular exponentiation (for RSA) in constant time, but most of the examples I've found are more mathematical descriptions of the operations. Are there any references with ...
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Security Level Estimate when Cascading/Compositing Ciphers?

Way back when, DES had a theoretical security level 56-bits. 2-key TDEA provides about 80-bits of security, and 3-key TDEA provides about 112-bits of security. Obviously, those security levels are not ...
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495 views

How difficult is it to brute force d in RSA: d = (1/e) mod φ in a CPT attack?

Given that RSA key generation works by computing: n = pq φ = (p-1)(q-1) d = (1/e) mod φ If I was an attacker who wanted to brute force d, could I brute force d given just the public key, the ...