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 blind signatures in practice

Hi I have a problem with moving my blind signature implementation from educational (textbook RSA) to more practical (padded RSA) side. David Chaums paper gives a following figure: $r$ - blinding ...
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RSA least significant bit oracle attack

I have been reading up on RSA attacks and came across one that could be called a least-significant-bit (LSB) oracle attack. For the sake of clarity lets define RSA primes $(p, q)$, private key $d$ ...
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783 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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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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How do institutions like banks do RSA with big primes?

When encrypting with RSA it is often infeasible to decrypt by just doing c^d mod n, because for example when using the primes $(p,q)=(12553,1233)$, which are small ...
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662 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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678 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 $1^...
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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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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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85 views

What does Shor's algorithm tell us about the complexity class of RSA and the DLP?

If quantum computers operate in BQP and (using Shor's algorithm) they are able to factor large integers and break the discrete log problem, what does that tell us about the complexity class of these ...
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535 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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564 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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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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750 views

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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753 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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883 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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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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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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How to calculate the time it'll take to crack RSA or DH?

Sometimes the easiest way to describe security of a type of cryptography is to say that "the time it takes to solve for an x-bit key would be y years". How would one go about doing such a calculation ...
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Should RSA primes p and q differ in length by “a few digits”?

When generating RSA keys in the original RSA paper it is stated: to gain additional protection against sophisticated factoring algorithms, p and q should differ in length by a few digits Why is ...
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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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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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967 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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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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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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How do I solve this RSA instance for m?

How we can solve this equation and get the value of M? $$8 = M^{13} \mod 33$$ not a computer program, but a mathematical operation.
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Is a RSA-signature of some identifying data a safe way to implement a license key?

I have this idea of implementing a license key: After the user downloads the program, he connects to a website and sends his Windows product ID. The website, then, sends this back to him with a ...
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119 views

Leading 00 in RSA public/private key file

I found these following values ALWAYS have the leading 00 in public/private key, public key: modulus private key: modulus, p,q, d mod (p-1), d mod (q-1), coefficient e.g., modulus ...
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269 views

lcm versus phi in RSA

In textbook RSA, the Euler $\varphi$ function $$\varphi(pq) := (p-1)(q-1)$$ is used to define the private exponent $d$. On the other hand, real-world cryptographic specifications require the ...
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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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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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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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309 views

Why does RSA give better security on longer messages?

I am trying to understand the notion of RSA security. Choosing a public exponent where $e = 3$ facilitates the calculations, considering that it is secure if the plaintext or message is long. If the ...
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Signing MD5 hashes with RSA? [duplicate]

Lets say I need to update a project and allow anyone to distribute the updates, however I need it to be secure, so I hash the data and sign the hash, this project uses MD5. How likely would it be ...
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123 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 part,...
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268 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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236 views

Trapdoor and RSA (Schneier)

Disclaimer: I'm new to cryptography. Background: From Applied Cryptography (Bruce Schneier), page 30 of 2nd edition A trapdoor one-way function is a special type of one-way function, one with a ...
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71 views

Can RSA-PSS signing be made deterministic without loss of security?

Is it possible to make RSA-PSS signing deterministic without loss of security? Specifically, I would use Blake2b of the key and message to generate the salt.
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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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RSA example-calculation: Public Key = Private Key (e = d)

I am a bit confused. I just calculated manually the single steps of RSA for an implementation with small numbers and suddenly $d$ was equal $e$. Please help me understand what I am doing wrong. Here’...
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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? ...
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Given a private RSA key, how do we get the public key?

Is it possible to pre-choose a private RSA key, then obtain a public key from it?
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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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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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In PKCS#1 V2.2, should MGF be based on the same hash function that RSA-OAEP-ENCRYPT uses?

In Section 7.1.1 of PKCS#1 v2.2 there are two options for RSAES-OAEP-Encrypt given: Hash MGF Appendix B.2.1 of the same document states that MGF1 is based on a hash function. Is MGF1 based on the ...