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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RSA cipher wrong use

Why is it foolish if you decide to use an RSA cipher to encode some message by first converting each letter of the message to an integer? So for exmaple Space=0, a=1, b=2,... After the conversion I ...
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What are some good references for the implementation weaknesses in RSA

I'm pretty sure I understand textbook RSA. Choose p and q, large primes, and compute n=pq. Choose e such that $gcd(\phi(n),e)=1.$ Publish n and e. Compute d such that $de=1$ (mod $\phi(n)$). To ...
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What are advantages of using a HMAC over RSA with SHA-1 hashes?

I am currently studying for an exam and this was a previous question: Give one advantage of using HMACs over using RSA to sign SHA-1 hashes. My thoughts are that it has something to do with the ...
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478 views

Is there a technique to confirm that a given large integer value is a product of two primes?

Given a list of 2048 bit integer values in which one or few 2048 bit integer values may be product of two prime numbers and other values may be just 2048 bit odd integers numbers. My question is - ...
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216 views

Why does OAEP have 2 rounds with 2 random oracles?

I strive into understanding why OAEP has two rounds of computations and not just one. I.e: Wouldn't it be safe to hash the random number r and XOR it with the original message?What security risks if ...
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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?
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241 views

What does “Inverting the RSA function is as hard as factoring” mean (a rigorous explanation or intuitive will do)?

I was reading that a current open problem is if inverting the RSA function is as hard as factoring. Does this mean that, its an open problem whether, if given a subroutine that computes in ...
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How much stronger is RSA-2048 compared to RSA-1024?

How much stronger is RSA-2048 compared to RSA-1024? It is hard to imagine very big numbers. So what would be your way to explain the difference to someone who doesn't know much about cryptography?
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342 views

What signature schemes allow recovering the public key from a signature?

It seems to be possible to retrieve the (public) key used for creating an ECDSA signature just from the signature alone. This seems like an interesting property; as far as I know, RSA doesn't share ...
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309 views

What do recent announcements about solving the DLP in $GF(2^{6120})$ mean for RSA

After just reading the post Do recent announcements about solving the DLP in $GF(2^{6120})$ apply to schemes proposed for cryptographic use? I was a bit confused. DSA, ElGamal and others are based on ...
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133 views

In RSA, how to make sure that $p-1$ and $q-1$ are still hard to factorize?

See this question. The comment by Brett Hale stated: On the other hand, ensuring $(p - 1)$ has a large prime factor requires very little extra effort. What's actually the 'little extra effort'?
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RSA-PSS salt size

One of the inputs of RSA-PSS signing and verification is the salt size. According to PKCS#1, you must know the salt size before the verfication is carried out. However, this makes interoperability ...
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107 views

Understanding Genkin-Pipman-Tromer's ground potential, side channel attack on RSA

I'm pretty sure that by now folks might have come across this research from Genkin-Pipman-Tromer (GPT) on extracting the RSA key used by GnuPG (GPG) just by measuring the ground potential. I'm going ...
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271 views

Adi Shamir's secret database of all primes

I was going through these presentation slides (PDF) on Crypto 2013. It summarizes the paper, Factoring RSA keys from certified smart cards: Coppersmith in the wild. In the last slide, it was ...
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934 views

Get RSA PlainText without Knowing Private Key

If I have an algorithm,RSA-Crack(), that, for a given RSA public key (n,e), is able to decrypt 1% of the messages encrypted with that key (without knowledge of the corresponding private key).Can there ...
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447 views

What is the harm if I publish an encrypted RSA private key publicly?

What is the harm if I publish an encrypted RSA private key publicly? Or in this case, what is the harm if I publish many thousands or millions of them? Assuming that the private key is encrypted ...
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686 views

Are there any MGF1 and OS2IP functions available in C?

I need MGF1 and OS2IP functions, as defined in the PKCS #1 v2.1: RSA Cryptography Standard. Is there anything available in OpenSSL, or any other open C library?
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307 views

How are trapdoor functions developed/found and where can I find existing ones?

Trapdoor functions are a fundamental part of public key cryptography. An example of the most common trapdoor is Prime Factorization, used in cryptosystems such as RSA How are these trapdoor ...
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223 views

How can I take advantage of repeated patterns in non random RSA prime factors?

I am researching vulnerable RSA moduli which are composed of primes generated with poor entropy. Having a list of these primes I searched for variable sized repeated patterns among them and I noticed ...
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306 views

Proof that padded RSA is CPA-secure

I'm referring to page 383 of J. Katz and Y. Lindell's Introduction to Modern Cryptography. The book presents a padded RSA: ${\bf Key Generation:}$ same as Textbook RSA (given security parameter ...
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306 views

In textbook RSA with low public exponent, how big does a random message needs to be?

Assume RSA with a public modulus $N$ of $n$ bits, a small odd public exponent $e$, plaintext $M$ a random non-negative integer less than $2^m$ for some integer parameter $m$, with $M\mapsto C=M^e\bmod ...
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Where does the $\varphi(n)$ part of RSA come from?

$e d \equiv 1 \pmod{\varphi(n)}$ Where does the $\varphi(n)$ part come from? How did the inventors of RSA arrive at $\varphi(n)$?
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Why $n=pq$ with $p=2p'+1$ and $q=2q'+1$ instead of just $n=p'q'$ for RSA crypto?

For RSA cryptography, we know that the modulo $n$ is a product of two big prime numbers(say $p$ and $q$). However, in some documents I see an extension of $p=2p'+1$ and $q=2q'+1$ with $q'$ and $p'$ ...
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uniqueness of the RSA public modulus

What is the probability that two separate RSA public moduli are the same? For example, consider a 2048-bit modulus. The number seems to be huge, but the choice for prime factors p and q is much more ...
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680 views

Why are RSA key sizes almost always a power of two?

I know that other bit sizes are possible, e.g. this HTTPS server seems to have a 9000 bit key https://www.ssllabs.com/ssltest/analyze.html?d=qqq.gg, but it's very rare that one sees a key not of size ...
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Subverting the key generation step in RSA public key cryptography

I am interested in the ways the implementation of an RSA key generation implementation can or cannot be subverted so that the subverter has an advantage, but the owner of the key, and the people who ...
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509 views

How to perform authentication without central server in P2P?

How can one be sure that the man who you're talking with is the one who you think he is? i.e. How can one perform authentication in P2P network without a central trust server or Certificate Authority? ...
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737 views

What is the likely cause the RSA algorithm gives back plain text in this case?

Text book question of Chapter 9 of "Crypto and Network Security" by William Stallings: When using the RSA Algorithm — if a small number of repeated encodings give back the plain text, what is the ...
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What is the length of an RSA signature?

Is it the same as the bits of the key (So a 2048 bit system will yield a 2048 bit signature)? At most as the key? Or something else entirely?
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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 ...
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Does a high exponent compensate for a low degree of certainty?

If a RSA certificate is created with a low degree of certainty, does the value of the exponent compensate for this? I'm asking because certain implementations of key generation software hide the ...
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In RSA, why is it important choosing e so that it is coprime to φ(n)?

When choosing the public exponent e, it is stressed that $e$ must be coprime to $\phi(n)$, i.e. $\gcd(\phi(n), e) = 1$. I know that a common choice is to have $e = 3$ (which requires a good padding ...
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377 views

X.509 CSR: Why does CA remove signature?

I just read this article on Wikipedia: Certificate Signing Request I'm not a PKI or Crypto expert. As I understand, a CSR (certification request) is always signed by the PKCS#10-Request creator. ...
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112 views

Should different key pairs be used for signing and encryption?

In the recent iOS Security white paper from Apple (February 2014), the section on iMessage discusses using two different asymmetric key types as part of its standard operation: When a user turns ...
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534 views

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 ...
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how to iteratively calculate a^emod n with modulus n sized 4096 bits

In most sites the exponent of the RSA public key is 24 bits. But the modulus can get to 4096 bits size. I have an accelerator that can get max. 2112 bit size modulus. It calculates ...
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713 views

What happens if an RSA key pair has identical public and private exponents?

Rather, is it possible for big prime numbers? Classroom examples usually involve smaller primes, so for example if you are given a prime number pair $p = 3$, $q = 13$ you would get $n = 39$ and $e = ...
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583 views

In RSA encryption, does the value of e need to be random?

I am a novice programmer and am just finishing up an RSA encryption program that I am writing for practice. Currently I have the program generate a relatively small random value for the public key e. ...
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Common modulus attack on RSA when the 2 public exponents differ by a single bit

This is an exam question an i have no idea how to recover the message m. John wants to send an encrypted message to mary who has a pair of RSA keys, However, John does not know Mary's public key and ...
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Why DSA cannot be used for encryption?

Here it is mentioned that DSA cannot be used for encrypt. But Both RSA and DSA can be used to generate public and private keys, right? (Or am I wrong?). Then why can't I use the DSA public key to ...
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897 views

Why is ElGamal considered non-deterministic?

One difference between RSA and ElGamal is that ElGamal isn't necessarily deterministic (while RSA is). What makes it non-deterministic? Is this advantageous to security? How else does this property ...
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173 views

When is an asymmetric scheme considered broken?

Does the following quote imply that valid encrypted data can be created and decrypted by someone other than the owner of a private key: An asymmetric encryption scheme is considered to be broken ...
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288 views

Is knowing the private key of RSA equivalent to the factorization of $N$?

Given the RSA modulus $N$ the fastest method to factor it is of sub-exponent order. But, now if I know the private key $d$ of RSA, does that mean I can factor $N$ efficiently?. It intuitively seems ...
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176 views

Solve a Modular Exponentiation

It might be common, but if we had to solve an equation like this $m=s^{e}$ mod $n$ where $m,e,n$ are known. How can we find $s$. What optimisations could be applied? And what would the complexity of ...
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Why can an RSA signature be authenticated ONLY with the signer's public key?

I'm an undergraduate Math student currently taking a cryptology course. I have a question about the RSA signature authentication mechanism. An RSA signature can be authenticated with the public key ...
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239 views

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 ...
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Difference RSA keypair creation openSSL and openPGP?

Creating a 2048bits RSA keypair I figured that doing this using openssl takes as an input 32bytes of "randomness" from /dev/urandom gpg (openGPG) takes as input ...
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Timing Attack on RSA

So far I have researched on timing attack on RSA, We all know the ransomware named Cryptolocker it uses RSA 2048 bit encryption. Now is it possible to break the encryption using timing attack. I have ...
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663 views

Recent attacks on RSA

At Blackhat 2013 this week, there was a talk saying RSA is (essentially) doomed in the near future. networkworld.com ~ “Black Hat: Elliptic curve cryptography coming as smarter algorithms threaten ...
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Why work in a subgroup QR(n) of an RSA group $Z^*_n$?

I sometimes read in papers that a (sub-)group generator $g$ is taken from $\mathrm{QR}(n)$ instead of $\mathbb{Z}^*_n$, where $n = p \cdot q$ and $p$ and $q$ are prime. Is there a reason for this? ...