The Diffie–Hellman key agreement is an anonymous, non-authenticated key-agreement protocol.

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Show How to Efficiently Solve the Computational Diffie-Hellman Assumption given an Algorithm that Solves the Square-DH Problem

Let $q$ prime number, $G$ a cyclic group with order $q$ and let $g \in G$ be a generator of $G$. Suppose that you have an algorithm $A$ who takes input the element $g^a$ of $G$ and gives as output the ...
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Why does encryption in STS protocol protect against identity attacks?

The basic STS protocol contains encryption of the signature as shown in Wikipedia. https://en.wikipedia.org/wiki/Station-to-Station_protocol If we would like to defend against MITM attack, this ...
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curious DHE implementation for key exchange

I have made some reverse engineering on proprietary software and came up with some DHE algorithm that works like this: First and foremost, the client and the server shares some public parameters (g, ...
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Why we need ECDSA when we have ECDH?

ECDSA and ECDH give us the following methods: ...
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Is this a secure method of encrypting with authentication?

My goal is to allow two clients to send files securely over an untrusted network without the need for more than one block of information to be sent. Both clients have ECDSA keys of size 256 bits. I'd ...
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Diffe-Helman Exchange result is always 1

I watched a video on Khan Academy explaining the Diffe-Hellman exchange. When I try to do an example problem, I get 1 all the time. Does the generator and prime modulus (or base on Wikipedia) have to ...
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What is a man-in-the-middle attack (for instance in Diffie-Hellman)?

I'm new to cryptography and I just started learning about the Diffie-Hellman key agreement. I read that this system is vulnerable to a man-in-the-middle attack when used alone. What kind of attack is ...
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22 views

SSH rekey security implications

When an SSH session is rekeyed due to either the time limit or data limit for rekeying having passed, does the Diffie-Hellman exchange take place within the encrypted channel provided by the existing ...
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Relationship between an elements order and the DLP [closed]

How can I use these properties to attack the DHKE? I know that the order of $a$ is always $2$ for $a = P - 1$ in $Z_p$. The subgroups generated by a will be $\{1,a\}$.
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Session key Exchange, some doubt

I have to find a solution to this problem: I have a network composed by 1 server and some client. The server has a couple of keys (public and private) and it shares a secret key with each client. My ...
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45 views

Supersingular Isogeny Key Exchange Software [closed]

Are there any optimised implementations of the Supersingular Isogeny Key Exchange by Defeo, Jao, and Plut. It seems like this would be a great drop-in replacement for Diffie-Hellman in both OpenSSL ...
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Can we reduce Diffie-Hellman problem to “Discrete-log inversion” problem?

Let $G$ be a cyclic multiplicative group of order $n$. Let $g$ be a (public) generator of $G$. The Diffie-Hellman (DH) problem asks: Given $g^x, g^y\in G$ for $x, y\in \mathbb{Z}^*_n$, to compute ...
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Deriving 2 shared secrets from one private key and 2 different public keys

I have a key pair, say $(d, Q)$. I send my public key $Q$ to 2 different people. I also get their public keys $Q_1$ and $Q_2$. Now I can derive 2 shared secrets, $d*Q_1$ and $d*Q_2$. The 2 other ...
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Solving discrete logarithm when p is not a safe prime

If you have the cyclic group of integers modulo $p$, where $p$ is not a safe prime, as well as a generator $g$ with which for all factors $q$ of $(p-1)$, $g^{(p-1)/q} \ne 1$, This answer says that ...
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Property of Multiplicative group of integers mod n

While practising on paper I've realized of a property of multiplicative group of integers mod $n$. First, let's define $G$ being $p$ a prime and $g$ a primitive root mod n or a generator of a ...
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My attempt of combining socialist millionaire and Diffie-Hellman. Is it any good?

I've come up with an algorithm to solve the socialist millionaire problem, but I'm not sure if the algorithm is secure. I wasn't able to find any flaw in it, but it seems too simple to be secure, so ...
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110 views

About Primitive roots mod n in Diffie-Hellman [duplicate]

I'm on the study of Diffie-Hellman and its related math (multiplicative group of integers $\mod n$). In some crypto papers and documents I've read that $g$ needs to be a primitive root mod $n$ ($g$ ...
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possible MITM attack against servers that used to support weak DH?

from reading the TLS 1.1 RFC, it looks like it would be possible to break a previously recorded TLS <1.2, 512-bit DHE ServerKeyExchange and then send it (unmodified, with the original, valid ...
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162 views

Logjam on Elliptic Curves?

I think we're all aware of the Logjam attack. From now on we know that re-using primes for DH is a bad idea. But we also say that elliptic curves are safe from the attack (relying on the NFS), ...
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Can a TLS client perform any DH regeneration?

I have only the barest understanding of cryptography, but I've been following the Logjam issue; some posts and articles (elsewhere) imply that a client can regenerate DH keys. Is Logjam solely a ...
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Logjam: “composite order subgroups” explained for TLS developers and system admins?

I have read the recent logjam paper Imperfect Forward Secrecy: How Diffie-Hellman Fails in Practice. On page 11 in the Recommendations section, they state: ...
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RSA_DH vs ECDH implementation

In ECDH protocol is possible, naturally, to use the same algorithm for calculate a secret key for both communication parties (Alice and Bob for example). It is possible to design also a same algorithm ...
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Ephemeral Diffie-Hellman in a symmetric crypto context

I'd like forward secrecy in a case where the two sides have a shared long-term symmetric key. I intend to use AES in GCM. It looks like ephemeral Diffie-Hellman is the best way to generate the session ...
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what is recommended x length in Diffie Hellman algorithm

According to rfc documents http://tools.ietf.org/html/rfc2412#appendix-E.2 & http://tools.ietf.org/html/rfc3526#section-3, it has defined the prime and the ...
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DH with AES - is that an acceptable security scheme over UPnP?

I'm trying to devise a good security scheme to protect comms over Wi-Fi. Right now, I have 2 devices that already communicate via UPnP but I need to secure this communication. I've come up with this: ...
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Diffie Hellman Exponentiation Implementation Problem

im trying to work on key agreement schemas on embeded systems. for diffie hellman, ive written a 256 bit multiplication, on AVR core it takes about 2 seconds on 1Mhz frequency, lets say my algorithm ...
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Understanding Diffie-Hellman Key Exchange [closed]

Help me understand the Diffie-Hellman Key Exchange From what I understand: Agreed upon numbers: Both parties agree on the value of a large prime number $p$ and a generator $g$. The users each ...
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117 views

Why does Diffie-Hellman need be a cyclic group?

Why is Diffie-Hellman defined on a cyclic group? Doesn't it work for any commutative operation which the inverse is hard to find? Say Alice and Bob agree in a public prime $c$ and both choose a ...
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Why does spiped use both nonces and ephemeral keys?

Colin Percival's spiped utility uses a pre-shared key and Diffie-Hellman with ephemeral keys to provide forward secrecy. The protocol is summarized in the ...
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Why is it a bad idea to use Diffie-Hellman with a prime such that $p - 1$ is smooth?

I recently stumbled upon another question in which somebody menitoned that using custom primes for DH is safe if you keep in mind, that $p-1$ should not be a smooth number. Why is that?
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41 views

DHKE choice of private keys

In some literature it is written that the private key should be chosen random from {2,3, ..., p-1} and in some it says {2,3, ..., p-2} I guess p-1 is a weak private key, but why is that so? The ...
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dh parameters someone else generated

Am am auditing some software that includes compiled in DH parameters (2048 bits). I can't be sure who generated the DH parameters or how they were generated. Question: Can DH parameters be weak ...
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Rationale of “r” AES key use in OTR version 3 AKE protocol?

I just tried to review & understand AKE (Authenticated Key Exchange) protocol as defined in OTR secure messaging protocol version 3 here , and aiming to achieve Perfect Forward Secrecy I am a ...
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How to encypt/decrypt messages after ECDH key agreement

I am using Diffie-Helman key exchange to generate the shared secret. But how will can a message be encrypted using this shared key?
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133 views

Is only one shared secret generated by ECDH per key pair?

I'm confused about ECDH. Using their public keys and private keys, two entities can arrive on a shared secret. But from the equations I've seen, it looks like ONLY the numbers present in their key ...
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Why is diffie-hellmangroup1-sha1 used instead of diffie-hellman?

For SSH why is diffie-hellmangroup1-sha1 used instead of just diffie-hellman? In other words, why is the hash function used?
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Workaround to implementing Forward Secrecy

In the case where I am self-signing my digital certificates, if I just change my certificate (generate a new one) every week or month, will this have (sort of similar to) the same effect as ...
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DH and PKI for KeyExchange

My question is fairly simple. I have more than two nodes which needs to communicate very efficiently from computational point of view. One of the nodes can become a coordinator between the nodes. ...
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How does $g$ being a generator imply Diffie-Hellman's correctness?

In the Diffie-Hellman protocol for key exchange over an unsecured channel, we choose $p$ and $g$, where $g$ is a generator of $\mathbf{Z}_p^*$. However I want to know why this assumption makes the ...
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Requirement for the exponent generation during DH protocol [duplicate]

The setting is classic DH protocol. Alice computes $A = g^a \bmod p$. Alice then sends $A$ to Bob. Then Bob will send $B = g^b \bmod p$ to Alice. Are there any requirements for the values $a$ and ...
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Diffie-Hellman Application

Alice and Bob want to perform a Diffie-Hellman key exchange using the group $G$, a primitive root $g$, Alice’s secret key $k_A$ and Bob’s secret key $k_B$. In each case below compute the element of ...
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Given $g^a, g^b, g^c, g^{1/b}$, is it hard to distinguish $e(g, g)^{abc}$ from a random value?

where $g$ is a group element in bilinear group $\mathbb{G}$. I understand it is very similar to the conventional DBDH problem, but $g^{1/b}$ is also known, possibly making it easier? Does anyone know ...
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Is it possible to perform one-way Diffie-Hellman MITM?

Here's something that is bugging me recently: suppose that me and my friend establish an OTR session and - as a result of that - DH key exchange is performed. My friend verifies my key, but I cannot ...
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Diffie-Hellman on infinite groups

The most common groups to be used as examples for the DH protocol are modular multiplication and elliptic curves. But I've realised that the groups doesn't need to be finite, a suitable infinite group ...
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How does ECDH arrive on a shared secret?

I read a brilliant, three part article on Elliptic Curve cryptography (one, two, three). It was able to explain Elliptic Curves to me in a way that didn't require a math degree to understand. The ...
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Relations between RSA and DLOG, factoring and DLOG

Definition: (The generalized Diffie-Hellman problem) Let $n=pq$ for two large primes $p,q$. Given $x, x^a, x^b,n$, find $x^{ab}\pmod{n}$. (1) Is there a known reduction from the GDH problem ...
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Post-quantum hybrid encryption

Assume the following simplified protocol: seed = curve25519SharedKey(theirPublicKey, myPrivateKey) sharedKey = scrypt(seed, salt, sufficientlyHardWorkFactors...) cipherText = aes256(sharedKey, ...
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ECC - ElGamal with Montgomery or Edwards type curves (curve25519, ed25519) - possible?

I know the usual way of using getting shared secrets for encryption with ECC is DH, however, this only works with two keypairs of exactly the same kind, for example two curve25519- or two ...
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101 views

Building a pad for OTP on-the-fly with Diffie-Hellman

Through repeated DH attempts, could Alice and Bob build a large random key for use as a one-time pad? My intuition is that this protocol would be as hard as breaking DH (discrete logarithm).
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Addition / Multiplication modulo 13

I am currently studying Diffie-Helman protocol. In my lecture notes I have a generator g=2 and I'm in group $Z_{13}^*$ . There I calculate a remainder cycle from 1 to 12 with $r =g^i \mod 13 \forall ...