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Questions tagged [diffie-hellman]

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

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Diffie hellman: fixed modulus a risk?

In DH, are algorithms with fixed modulus p (large safe prime) to be avoided? What if it was changed every x minutes?
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is a safe prime subgroup length important?

For most cryptographers, my question may appear silly. Context: Diffie Hellman. Object: finding good primes. Code: given that NodeJS program: ...
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How to select best safe primes for DH <-> subgroups?

I run a test on some safe primes. Here is the code: ...
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Sharing secret content with multiple recipients

I have a sender and N recipients, and am thinking of using the following scheme to send secret content to those recipients. This is similar context to a group chat or email. I am no expert in crypto ...
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Simple but secure method to share secret (128 bit AES key) though an untrusted relay

I am creating an end-to-end encrypted group messenger, and am looking for a way for online members of the chat to a arrive at a shared secret that can be used as a cryptographic key. This will ...
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What's the fundamental difference between Diffie-Hellman and RSA?

What is the difference in the purpose of DH and RSA? Aren't they both public-key encryption?
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Should we use IANA groups 14 (MODP), 25, and 26 (ECP)?

By looking at SonicWall Knowledge Base article Key exchange (DH) Groups Supported - Site to Site VPN: It appears that our firewall supports DH group 25, and 26. Almost everywhere I've seen, they've ...
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Is it safe to reuse ECDH asymmetric keys for authentication?

Alice, Bob, and Carol each generate ECDH keypairs. Alice and Bob establish a communication channel and negotiate an AliceBob secret. The question is: Is it safe for Alice and/or Bob to reuse their ...
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How to select salt an IKM for HKDF

I have an application where I need to combine a Diffie-Hellman shared secret, with a user's password and derive a key. I'm investigating the possibility of using HKDF to as follows Initial Keying ...
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71 views

Problem on Elliptic Curve Point Doubling

Given an elliptical curve e.g. from “Understanding Cryptography” by Parr & Pelzl §9.2 Example 9.5: $y^2 = x^3 + 2x + 2~~~~ mod~17$ And given a primitive $P = (5, 1)$, the book indicates: We ...
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Diffie-Hellman Groups 20 vs 24 [duplicate]

Which encryption under DH has greater Encryption, it's said that the higher the number in DH the greater the encryption but I would like to verify this further. Does Anyone have inputs on this? or ...
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Discrete Logarithm within DH exchange - finding out A and B secret number [duplicate]

How would i find out Alices or Bobs private number from the details exchanged in public. prime - g = 7 primitive root - n = 3 Alice - A = 3 Bob - B = 4 The details visible in public exchange are: ...
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364 views

Diffie-Hellman (Public Key exchange)

I have read a few tutorials in regards to this. My understanding is that Diffie-Hellman is a key exchange concept that is being use everywhere in our daily lives, which is also known as the public-...
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197 views

What is Perfect forward secrecy?

I have read that when a user contacts an entity like a bank, it creates a pre-master key and then selects a master key for subsequent communications. Can the lack of PFS, create a security flaw if ...
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Why is Diffie-Hellman Insecure If Order of the Generator Has Only Small Prime Factors?

In this post from security SE, Tom Leek mentioned that, for Diffie-Hellman to be secure order of the group $g$ should have a prime factor at least $2k$ bits long, where $k$ is the security parameter. ...
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Formal Verification of DHKE protocol using ProVerif

I am new to ProVerif and trying to verify a simple DHKE protocol. The attacker is assumed as passive. The specifications are: The attacker cannot obtains the mutual key. Both participants obtain the ...
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1answer
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Public key on Server Key Exchange Generation vs Public key on Server's Certificate

To understand the distinction between TLS 1.2 and TLS 1.3. I am stuck in the past understanding for TLS and the current reference I am studying: As I know certificate goes with owner's public key, ...
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1answer
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Shamir Secret Sharing and Diffie-Hellman procedure

Alice needs to share an already generated numeric secret $s$ with Bob and she doe not want the world to see it. The problem is that she has never contacted Bob before. I thought Alice and Bob could ...
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Rational exponents on group generators

In elementary concepts, mostly scalar exponents shows up in group operations: $g^x$ As one may encounter in more advanced papers, there are rational exponents over generators. Simply seems like: $g^...
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1answer
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How to handle a lost key in Diffie-Hellman Key Exchange

I implemented the Diffie-Hellman Key Exchange algorithm but, I was wondering how to handle if one of the parties lost his key. Let's take a chat app as an example, Bob and Alice they used to have a ...
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2answers
3k views

How to derive a symmetric key from ECDH shared secret?

I am trying to implement the internal primitives of ECDH. Currently I'm able to multiply the receiver's public EC point with the sender's private key to arrive at the shared EC point. Next step is to ...
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1answer
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Does DDH hold in $Z_N^*$ where N is product of 2 large primes

I know that DDH does not hold in $Z_p^*$ because given $g, g^a, g^b, x$, we can compute legendre symbols of $g^a, g^b$ and compare it with legendre symbol of $x$. The same attack doesn't work when we ...
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How is Diffie Helman secure when the exchanged number is a power of the generator less than the modulo

I'm trying to understand how Diffie Helman is still secure when $A$ ends up being a power of $g$ less than $p$. I chose $p$, where p is prime, and $g$ is a primitive root modulo $p$. $g=2$ and $p=...
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What is a ratchet?

while reading Whatsapp's Security Whitepaper I found the term "ratchet". What does it mean in cryptography? The Message Key is derived from a sender’s Chain Key that “ratchets” forward with every ...
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1answer
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Collisions in Diffie-Hellman private keys

Given a generator $g$, a large, safe prime $P$ and a result of the DH key exchange $g^{xy} \mod P$, how would I come up with two different $x', y'$ s.t. $g^{x'y'} = g^{xy} \mod P$
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Why does DH-EKE require that public keys be indistinguishable from random?

The introduction to SPAKE pre-authentication states: Diffie-Hellman Encrypted Key Exchange (DH-EKE) is the earliest widely deployed PAKE. It works by encrypting the public keys of a Diffie-Hellman ...
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How to calculate Trace function for a point on an elliptic curve

I encountered trouble with calculating Tr (trace function) for points on an elliptic curve in polynomial basis ( $GF(2^m), m = 431$). Maybe there are any assumptions that can simplify and allow ...
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Is a Diffie-Hellman shared secret with a private and public key from the same ECSDA pair considered less secure? [duplicate]

If I generate two public / private key pairs using ECDSA - pair A and pair B. Using Diffie-Hellman, a shared secret X is generated using the public key from pair A as the public base and the private ...
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1answer
55 views

Why does the Node crypto library do Diffie Hellman this way?

I was sifting through the Node Crytpo library and I came across their Diffie Hellman utility class. Their class implements a generateKeys function that, in their ...
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2answers
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My custom handshake

I designed a custom handshake between 2 entities $\rm C$ (client) and $\rm S$ (server) which should meet the following requirements: Requirements: The handshake should make: $\rm S$ know who is $\...
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2answers
643 views

Is RSA inspired by Diffie Hellman?

I read a bit of A Method for Obtaining Digital Signatures and Public-Key Cryptosystems that introduced RSA in 1977, and, while learning the steps in RSA a few days ago, I noticed that they are similar ...
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1answer
717 views

ECDH and ECDSA in PGP with known public key

How are used ECDH and ECDSA in combination with public key ? Usually these methods are used for establish a secret themselves, ...
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1answer
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How to encrypt plain-text message using Diffie-Hellman algorithm

Let's say bob says Hi and Alice says Hello, With the knowledge of n and ...
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1answer
96 views

Solving discrete log in partially known group

Suppose I have a group $G$ of unknown order $n$ where $n=p^k\cdot s$, $\gcd(p,s)=1$, $p$ is a known prime, $k,s$ are unknown positive integers and $k,s\ge1$. (Known - $p$ and $p\mid n$, Unknown - $n,k,...
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Diffie-Hellman key exchange: Why is $(g^{k_1} \bmod n )^{k_2} \bmod n \equiv (g^{k_2} \mod n)^{k_1} \bmod n$

In a Diffie-Hellman key exchange, with a generator $g$ and a modulo $n$, and two keys $k_1$ and $k_2$, why is $(g^{k_1} \bmod n )^{k_2} \bmod n \equiv (g^{k_2} \mod n)^{k_1} \bmod n$
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1answer
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Detect MITM with hashed session-key — Is my protocol secure?

I have the following setup: An app ("client") wants to communicate securely with a device I created ("server"). The client has the public key of the server (and a hashed password) preinstalled. I use ...
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1answer
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Choosing good entropy $g$ and $p$ for a classic Diffie-Hellman Key exchange

When selecting $$g and $p$ for the Diffie-Hellman modular exponentiation: $ s= g^x \bmod p $ Which pairs of $g$ and $p$ are considered good nowadays, are recommended by bibliography? What I try ...
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Can I use NaCl's scalar multiplication functions for Diffie Hellman Key Agreement?

I want to create some software that performs diffie hellman group key agreement but I don't want to reinvent the wheel even if I know how it's done. So I came accross the NaCl library, especially the <...
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Reduction from integer factoring to computational Diffie Hellman

The computational Diffie Hellman (CDH) problem for ${\mathbb{Z}}^*_p$ is given a prime $p$, a generator $g$ of ${\mathbb{Z}}^*_p$, and a pair $(g^i, g^j)$ to compute $g^{ij}$. The value $g$ is called ...
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In the Diffie Hellman Key exchange, why is a value of $a=\frac{p-1}{2}$ a bad choice?

In Diffie Hellman key exchange, we have a large prime $p$ and non zero residue class $g \in F_p^x$ with a large order. An $a$ and $b$ are chosen in secret, and those are used to compute $A \equiv g^a ...
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1answer
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Static DH/Static ECDH certificate using OpenSSL

I've been searching for some time and have found no way to create a working certificate and private key pair with a DH or ECDH public key using OpenSSL. Once I do this, I'd like to sign it with an RSA ...
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1answer
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How Elliptic-Curve affects the Server Key Exchange parameters

In Finite Field DHE, the server sends the following parameters in the server key exchange message: $p$: prime $g$: group $g^b$: the server's public DH key In DHE_RSA (non anonymous DHE), the server ...
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1answer
73 views

Does this scheme break under a DHP adversary?

Consider the following cryptography scheme: We are given a prime $p$. Alice wants to send the plaintext $m \pmod p$ to Bob. Alice chooses $a$ s.t. $\text{gcd}(a,p-1)=1$, and sends Bob, $u = m^a \...
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1answer
7k views

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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Multiparty key exchange for end-to-end encryption

I need to make end-to-end encrypted messaging between 2 and more parties without trusting a server. Each party has it's secret and private keys. The obvious solution is to make ECDH between all of ...
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1answer
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Question About ECC Primitives (GnuPG)

In version 2.1, GnuPG featured primitives that use elliptic curves. For encryption, one option was ECDH, which confused me. I thought ECDH was for key agreement, not public key encryption. How does ...
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1answer
105 views

Restoring a point on an elliptic curve

I received a representation of a point on an elliptic curve $GF(2^m)$ (with curve coefficient A, B) in specific format and some description how to decode it but not all is clear to me. I would be ...
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1answer
126 views

The compression of the eliptic curve point coordinates

Some time ago I faced the problem of the unexpected format compression of the points on elliptic curve. I used ECDH procedure with a third party service on the base of the $\mathbb({F}_{2^m})$ curve ...
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1answer
153 views

Signal Protocol: What extra features does double ratchet algorithm add to Diffie-Hellman ratchet?

I have been reading the documentation of Signal protocol and could not find out why they came up with double ratchet instead of using Diffie-Hellman ratchet which was available at first place in OTR?
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1answer
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Tls protocols: is the simple diffie hellman key exchange still used these days?

Or did it mostly get replaced by ecdh for key exchange and rsa for authentication ?