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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In RSA, do I calculate d from e or e from d?

In the original paper introducing RSA, it is implied that one should first choose $d$ and then calulate $e$ from $p$, $q$, and $d$. However, I have found in other places (such as the wikipedia article ...
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439 views

Is encrypting credit card numbers one by one with rsautl secure?

I wish to encrypt credit card numbers one by one using asymmetric encryption on the command line. My current approach is this… Encrypt: ...
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515 views

What is the key strength reduction encrypting only 160 bits of data using RSA1024 for signatures?

I am attempting to determine the strength of an incorrectly implemented 1024 bit RSA signature scheme. The weakness in the implementation is that the padding data lacks random numbers. As a result, ...
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94 views

RSA: Proving that $p+q-1 < 3 \sqrt{N}$, where N = pq and p,q are prime?

I'm doing some research into attacks on the RSA cryptosystem and have stumbled across Wiener's attack. Within the proof there exists the statement "$p+q-1 < 3\sqrt{N}$". No proof is given for ...
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279 views

RSA exhibits symmetrical properties — is it possible to form a cryptanalytic attack?

This question is broken into two sections really: Symmetry in RSA I have been analyzing raw RSA and I have noticed some interesting symmetrical properties of the algorithm. Assume that $M$ is a ...
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Why Elliptic curve cryptography are not popular in practice

RSA and ElGamal can be implemented using the technique of Elliptic curves. I am confused on why the it seems that Elliptic curves are not so popular in cryptographic applications since they provide ...
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Is a known plaintext, ciphertext, and public-key a viable attack on RSA?

Assume Alice and Bob are using RSA to create a common session key and Cindy is listening, attempting to obtain the session key. Alice and Bob each have their public- and private-key pairs ...
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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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385 views

Anonymous trust/reputation system

Suppose there are 3 persons, Alice, Bob and Peter. They are identified by their pseudonyms (public RSA keys). Alice has a key Alice, Bob has ...
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185 views

Including a “purpose” designation in a digital signature

A signature of some data can mean many different things, such as: This is a message I sent, this is a certificate I validated,... So I was surprised that common signing schemes don't include a ...
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Effect of $L_n[1/4,c]$ integer factorization on RSA-2048

Using the L-notation, integer factorization of an integer $n$ has the best known complexity of $L_n[1/3,c]$ using general number field sieve. Would discovery of an algorithm with complexity ...
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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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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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889 views

How do RSA and ECDSA differ in signing performance?

Signature algorithms with elliptic curves have smaller 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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611 views

RSA Signature Weak Padding Attack

Assume that we have a message $m$ of size $n$, and it is padded with two 01 bytes in front. Then the signature $s$ is computed using a private key $ks$. Can we ...
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7k views

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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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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5k views

Why has the RSA factoring challenge been withdrawn?

Wikipedia states that RSA challenge has been withdrawn. Does it mean that an efficient factoring algorithm is "just around the corner"? or are there some other reasons? If the challenge was still ...
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488 views

Would RSA-encrypting a private key for itself constitute a vulnerability?

I'm planning to encrypt some individual files for storage, using the GnuPG implementation of RSA. If I happened to encrypt the private key corresponding to the public key used for encrypting -- either ...
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110 views

Proof of RSA security dependent on public key exponent

I am writing a (high-school) paper on the public key exponent's (in textbook RSA - no padding is discussed!) significance in terms of time and security. The time part is done; as for the security ...
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162 views

RSA reconstructing private key knowing MSBs

PREMISE: This question is purely theoretical because usually an attacker will not know private exponent d and can't compare it with obtained MSB bytes. Suppose an RSA 1024 bit signature. An attacker ...
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943 views

Is perfect-forward secrecy achieved with RSA?

I am new to cryptography and am going through the book Understanding Cryptography by Paar and Pelzl. From what I understand Symmetric key distribution systems like Kerberos do not provide PFS ...
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How much can we compress RSA public keys?

I am wondering to what degree we can define an RSA variant, with a security argument that it is as safe as regular RSA with a given modulus size $m$ (e.g. $m=2048$), in which the public key has a ...
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300 views

What does “a 15360-bit RSA key is the equivalent to a 256-bit symmetric key” mean?

NIST key management guidelines suggest that 15360-bit RSA keys are equivalent in strength to 256-bit symmetric keys. If a 15360-bit RSA key is the equivalent to a 256-bit symmetric key, does that mean ...
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528 views

State of the art RSA key generation

I would like to know if there is an algorithm to generate a RSA key at the state of the art of the present cryptanalysis. Beside the key lenght I know there are some weakness in the choice of prime ...
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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 $p$ ...
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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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133 views

When/why is RSA (hybrid) encryption used rather than alternatives?

I've read that RSA is not meant for encrypting large plaintext because: (Are these also true for other public-key encryptions like ElGamal?) It is slow. Padding makes the ciphertext blocks much ...
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296 views

Blinding twice in RSA

I understand that if you have a message $m$, you can blind it by selecting a random $r$ and then multiplying $r^e\times m \pmod{n}$ Someone else then signs it with $d$, raising to the power of $d$: ...
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663 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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658 views

Security equivalence proofs for breaking RSA

It is my understanding that while a practical solution to the factoring problem will definitely break RSA, it has never been proven that the security of RSA is equivalent to factoring. In otherwords, ...
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RSA-based authentication and key-agreement protocol

An authentication and key-agreement protocol between devices shall mutually demonstrate their identity, and establish a shared random secret $R$ suitable for securing later communications. To that ...
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Is a private RSA key vulnerable to a chosen plaintext encrypted with that private key?

I grasp that having known plaintext encrypted with the public key doesn't provide a means of discovering the private key (that being the whole point...). But if one were in a situation where they ...
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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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590 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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107 views

Encryption scheme like RSA where encryption is the inverse of decryption

In RSA, it is basically equivalent to use the private key $d$ to encrypt as it is to use the public key $e$ to encrypt. They are exactly inverses: $e=d^{-1}$. I need to know, are there other public ...
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480 views

Prove that textbook RSA is susceptible to a chosen ciphertext attack

Given a ciphertext $y$, describe how to choose a ciphertext $\hat{y} \neq y$, such that knowledge of the plaintext $\hat{x}=d_K(\hat{y})$ allows $x=d_k(y)$ to be computed. So I use the fact that the ...
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506 views

Threshold Signatures for RSA and DSA

I have a few questions relating to threshold signatures: a scheme where $n$ participants hold a key share and any $t$ of them can conduct a protocol using their shares that results in a valid RSA or ...
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148 views

Why $e>n^{3/2}$ prevents Wiener's attack

Here's the Wiener's attack as I understand it. Suppose $n=pq$ with $q < p < 2q$, and $d < n^{1/4}/3$ where $ed=k\phi(n)+1$ and $e < \phi(n)$. $$\begin{align*} n-\phi(n) ...
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Is it possible to reduce the size of an RSA key?

The details about what an RSA key is made up of are explained succinctly here. Is it possible to reduce the amount of data that's usually packaged with the (private) key and then derive it later?
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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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709 views

RSA with modulus n=p²q

I've been wondering what would happen if the RSA modulus would be $n=p^2q$ instead of $n=pq$. I feel like there is an obvious security flaw (as there is with most modifications). Would this choise of ...
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789 views

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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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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Is RSA key size the size of private key exponent?

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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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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Cracking plain RSA without private key

I was wondering whether plain RSA encryption can be cracked given: The public key A plaintext of a known cipher text(s). In other words the decrypted message from an encrypted one (but without ...
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Is RSA encryption of a cryptographic hash with a private key the same as signature generation?

It is often said that RSA encryption with a private key is the same as signing (signature generation). Will RSA encryption with a private key over a cryptographic hash give the same result as ...
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Can an RSA private key have several public keys?

Ok, so my crpto lecturer in Uni posed this question at the end of the RSA key generation lecture as a brain teaser. I have been thinking about this and I think I have come up with a way ( I am aware ...
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Hybrid encryption with RSA and AES versus spliting into multiple RSA messages?

I've done research about this subject, but I can't find the answer I'm looking for. The problem is that the string I want to send doesn't fit into the RSA key that the client have, and during ...