An asymmetric cipher is an encryption scheme using a pair of keys, one to encrypt and a second to decrypt a message. A special class of asymmetric ciphers are public-key ciphers, in which the encrypting key need not be kept secret to ensure a private communication.

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Random Coin Flip using ElGamal and a Trusted Party

An old exam question I am trying to figure out: Consider the following protocol for two parties to flip a fair coin. Trusted party T publishes her public key pk A chooses a random bit $...
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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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How can I remove my personal data from my PGP public key?

According to this Q&A-discussion it is possible to remove all personal data (name and mail address) that is attached to a public key. What steps do I have to follow in order to remove all ...
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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 ($\left[...
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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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Why can’t DSA be used for encryption?

This question at StackOverflow mentions 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 ...
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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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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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Why can't Diffie-Hellman be used for signing?

I understand that signing is often a case of hashing data and then encrypting the hash with the private key. What properties keep Diffie-Hellman from being useful for this?
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Is there a theorem to determine the elliptic curve parameters based on the group order?

By Hasse's theorem we know that range of the group order of the elliptic curve. And similarly, there exist a theorem on the admissible order of elliptic curves. Suppose by the theorem on the ...
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Authentication by hardcoding public key in client software

It would seem to me that mobile applications could reduce network traffic by hardcoding the server's public key into the app. The idea being that they could then encipher a secret to share with the ...
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For public-key encryption, why does COA resistance imply CPA resistance?

My professor told me: If a public-key crypto-system is secure against ciphertext-only attacks, then it is also secure against a chosen-plaintext attack. Why is this true? Is there a proof that ...
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The difficulty of computing discrete logs

I understand that in Diffie-Hellman it should be hard to compute $a$ given $g$ and $g^a$. In computational Diffie-Hellman, it appears to be hard to compute $(g^{ab})$ from $g^a$ and $g^b$. As for ...
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Do asymmetric signatures require constant-time verification?

To avoid a timing attack, HMAC signatures are usually compared in constant-time (every byte is compared, and the results aggregated). Is the same necessary for asymmetric signature algorithms such ...
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What is the difference between RCCA and CCA2?

Well, I know it's easy to tell CCA1 from CCA2, but I failed to find the difference between RCCA and CCA2. What is the difference?
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Are there groups where the computational Diffie Hellman problem is easy but the discrete log problem is hard?

I know that there are elliptic curve groups, used in pairing-based cryptography, where the decisional Diffie Hellman problem (ie. given $g$, $g^a$, $g^b$ and $c$, determine if $c = g^{ab}$ is easy but ...
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Can an RSA public key be generated without ever knowing the factors? [duplicate]

Context: http://blog.cryptographyengineering.com/2013/12/a-few-more-notes-on-nsa-random-number.html Assume I wanted to use RSA as the basis for a hash function or DRBG. Also assume that my construct ...
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Single Party Encryption, Multi Party Decryption

I am looking for an adequate protocol for public key decryption, which would allow $n$ parties to jointly decrypt a cipher text. The usage scenario for such a protocol would be a mixnet that wouldn't ...
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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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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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In a lattice, how can one define a good basis and a bad basis?

When it comes to lattice based cryptographic systems, all the literature talks about, good bases and bad bases. How does one define what a good basis is and what a bad basis is?
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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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Finding the subgroup in isogeny-based cryptography

Isogeny-based cryptography is one of the newest post-quantum cryptography. Hardness of this system is based on finding isogeny between two elliptic curves. Also this is theorem: Elliptic curves ...
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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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What is Identity-Based Encryption (IBE) and why is it “better”?

Most CS/Math undergrads run into the well-known RSA cryptosystem at some point. But about 10 years ago Boneh and Franklin introduced a practical Identity-Based Encryption system (IBE) that has ...
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How can one sign with NTRU?

I am looking at implementing NTRU, but I noticed that while the encryption/decryption algorithm seems to be mature and well-documented, there is comparatively little information about how to sign ...
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Is there an authenticated encryption scheme where the recipient can attribute the message to a single sender?

With a standard authenticated encryption scheme (or MAC), Alice and Bob share a symmetric key. When Alice sends something to Bob, Bob can check that it is authentic. At that point, Bob can deduce ...
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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 it possible to create an open-source SecurID?

As far as I understand it, the hardware key-fob two-factor systems such as RSA SecurID depend on secret algorithms, and employ tamper-resistant hardware to prevent reverse engineering. Is there some ...
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What other one-way functions are used in cryptosystems?

For RSA and El Gamal (and most other public key cryptosystems), one of the key ideas is that factoring and finding discrete logarithms are hard. There are other systems that rely on certain properties ...
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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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Is it possible to pick your Ed25519 public key?

Is it possible to generate an Ed25519 keypair that has a very similar public key as another keypair (fooling a casual visual comparison) or is this as hard as solving one of SHA-512 or the discrete ...
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Can we use elliptic curve cryptography in wireless sensors?

Can we use elliptic curve cryptography in wireless sensors? If so, how do you map points to message characters?
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ECDSA key recovery - floating point values

I'm currently attempting to recover an ECDSA key. I have $m$, $m'$ and signatures $(r, s)$, $(r', s')$, and I know that $k$ is constant, the curve is NIST P-192 and the hash function of the. As such,...
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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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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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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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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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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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Can I remove new lines in a public key?

Can I remove new lines from the rsa public key file to get a one line string? So the question is if the key looks like this AAA BBB CCC or ...
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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 can ssh-keygen export a public key in PEM PKCS8 format?

In the documentation of ssh-keygen (man ssh-keygen) it says for the option -m that an export ...
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Discovering private exponent from public key

I'm going to assume this isn't possible, but I have to ask because I'm trying to fundamentally understand what I've thus far been trying to implement by following an RFC. SRP-6a starts off with ...
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Client and server using same SSL certificate - any issues?

I'm working on software where multiple components will communicate with each other using SSL. There would be one central component acting as a server, which would also require the clients to present ...
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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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Using ECDSA keys for encryption

I know that ECDSA is used for signature only, but I wonder if I can use the public/private Elliptic Curve keys for encryption too. I have ECDSA SSH public keys and I wonder if I can use them to ...
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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 ...