Openssl Generate Strong Keys Using Eecdh

1. Ecdh Online
2. Openssl Generate Strong Keys Using Ecdh Key
3. Openssl Dh Key
4. Openssl Ecdsa Example

Elliptic-curve Diffie–Hellman (ECDH) is a key agreement protocol that allows two parties, each having an elliptic-curve public–private key pair, to establish a shared secret over an insecure channel.^[1][2][3] This shared secret may be directly used as a key, or to derive another key. The key, or the derived key, can then be used to encrypt subsequent communications using a symmetric-key cipher. It is a variant of the Diffie–Hellman protocol using elliptic-curve cryptography.

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• Which elliptic curve should I use? Ask Question Asked 5 years, 3 months ago. Active 3 years. Can you generate your own curve using an even bigger prime and have it work with unmodified clients? I imagine that if you picked the right and large enough prime that would be the safest. Elliptic curve cryptography and key sharing.

Diffie hellman - OpenSSL Generate ECDH Public Key - Information Security Stack Exchange I am trying to use the OpenSSL command line to generate a ECDH public key that meets the following specifications: Use a Base64 encoded X.509 SubjectPublicKeyInfo structure containing a ECDH pub.

Key establishment protocol[edit]

The following example illustrates how a shared key is established. Suppose Alice wants to establish a shared key with Bob, but the only channel available for them may be eavesdropped by a third party. Initially, the domain parameters (that is, ${\displaystyle (p,a,b,G,n,h)}$ in the prime case or ${\displaystyle (m,f(x),a,b,G,n,h)}$ in the binary case) must be agreed upon. Also, each party must have a key pair suitable for elliptic curve cryptography, consisting of a private key ${\displaystyle d}$ (a randomly selected integer in the interval ${\displaystyle [1,n-1]}$) and a public key represented by a point ${\displaystyle Q}$ (where ${\displaystyle Q=d\cdot G}$, that is, the result of adding${\displaystyle G}$ to itself ${\displaystyle d}$ times). Let Alice's key pair be ${\displaystyle (d_{\text{A}},Q_{\text{A}})}$ and Bob's key pair be ${\displaystyle (d_{\text{B}},Q_{\text{B}})}$. Each party must know the other party's public key prior to execution of the protocol.

Alice computes point ${\displaystyle (x_k,y_k)=d_{\text{A}}\cdot Q_{\text{B}}}$. Bob computes point ${\displaystyle (x_k,y_k)=d_{\text{B}}\cdot Q_{\text{A}}}$. The shared secret is ${\displaystyle x_k}$ (the x coordinate of the point). Most standardized protocols based on ECDH derive a symmetric key from ${\displaystyle x_k}$ using some hash-based key derivation function.

The shared secret calculated by both parties is equal, because ${\displaystyle d_{\text{A}}\cdot Q_{\text{B}}=d_{\text{A}}\cdot d_{\text{B}}\cdot G=d_{\text{B}}\cdot d_{\text{A}}\cdot G=d_{\text{B}}\cdot Q_{\text{A}}}$.

The only information about her key that Alice initially exposes is her public key. So, no party including Alice can determine Alice's private key (Alice of course knows it by having selected it), unless that party can solve the elliptic curve discrete logarithm problem. Bob's private key is similarly secure. No party other than Alice or Bob can compute the shared secret, unless that party can solve the elliptic curve Diffie–Hellman problem.

The public keys are either static (and trusted, say via a certificate) or ephemeral (also known as ECDHE, where final 'E' stands for 'ephemeral'). Ephemeral keys are temporary and not necessarily authenticated, so if authentication is desired, authenticity assurances must be obtained by other means. Authentication is necessary to avoid man-in-the-middle attacks. If one of either Alice's or Bob's public keys is static, then man-in-the-middle attacks are thwarted. Static public keys provide neither forward secrecy nor key-compromise impersonation resilience, among other advanced security properties. Holders of static private keys should validate the other public key, and should apply a secure key derivation function to the raw Diffie–Hellman shared secret to avoid leaking information about the static private key. For schemes with other security properties, see MQV.

If Alice maliciously chooses invalid curve points for her key and Bob does not validate that Alice's points are part of the selected group, she can collect enough residues of Bob's key to derive his private key. Several TLS libraries were found to be vulnerable to this attack.^[4]

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While the shared secret may be used directly as a key, it can be desirable to hash the secret to remove weak bits due to the Diffie–Hellman exchange.

Ecdh Online

Software[edit]

• Curve25519 is a popular set of elliptic curve parameters and reference implementation by Daniel J. Bernstein in C. Bindings and alternative implementations are also available.
• LINE messenger app has used the ECDH protocol for its 'Letter Sealing' end-to-end encryption of all messages sent through said app since October 2015.^[5]
• Signal Protocol uses ECDH to obtain post-compromise security. Implementations of this protocol are found in Signal, WhatsApp, Facebook Messenger and Skype.

See also[edit]

References[edit]

1. ^NIST, Special Publication 800-56A, Recommendation for Pair-Wise Key Establishment Schemes Using Discrete Logarithm Cryptography, March, 2006.
2. ^Certicom Research, Standards for efficient cryptography, SEC 1: Elliptic Curve Cryptography, Version 2.0, May 21, 2009.
3. ^NSA Suite B Cryptography, Suite B Implementers' Guide to NIST SP 800-56AArchived 2016-03-06 at the Wayback Machine, July 28, 2009.
4. ^Tibor Jager; Jorg Schwenk; Juraj Somorovsky (2015-09-04). 'Practical Invalid Curve Attacks on TLS-ECDH'(PDF). European Symposium on Research in Computer Security (ESORICS'15).
5. ^JI (13 October 2015). 'New generation of safe messaging: 'Letter Sealing''. LINE Engineers' Blog. LINE Corporation. Retrieved 5 February 2018.

An example of using OpenSSL operations to perform a Diffie-Hellmen secret key exchange (DHKE). The goal in DHKE is for two users to obtain a shared secret key, without any other users knowing that key. The exchange is performed over a public network, i.e. all messages sent between the two users can be intercepted and read by any other user. The protocol makes use of modular arithmetic and especially exponentials. The security of the protocol relies on the fact that solving a discrete logarithm (the inverse of an exponential) is practically impossible when large enough values are used.

Wikipedia has a description and example of DHKE. My lecture slides on public key cryptography also include a description. My description of DHKE starts at about 39m 30s into the screencast available on YouTube. It includes a simple example starting at 47m 53s. View below to go straight to the DHKE portion of the lecture.

OpenSSL provides both a library of security operations you can access from your own software, as well as a command line mode. In the past I've given examples of using OpenSSL to generate RSA keys as well as encrypt and sign with RSA. In the following I demonstrate using OpenSSL for DHKE.

DHKE is performed by two users, on two different computers. For my demo I do everything on one computer. The steps performed by each user are the same, but just with different files. In the following there is user 1 and user 2.

Steps for Diffie-Hellman Key Exchange with OpenSSL

Generate the Diffie-Hellman global public parameters, saving them in the file dhp.pem:

Display the generated global public parameters, first in the encoded form, then in the text form:

Each user now uses the public parameters to generate their own private and public key, saving them in the file dhkey1.pem (for user 1) and dhkey2.pem (for user 2):

The other user uses the same public parameters, dhp.pem, to generate their private/public key:

The users must exchange their public keys. First extract the public key into the file dhpub1.pem (and similar user 2 creates dh2pub.pem - this step is not shown below):

After exchanging public keys, i.e. the files dhpub1.pem and dhpub2.pem, each user can derive the shared secret. User 1 performs the following to output the secret, a 128 Byte binary value into the file secret1.bin:

The other user does the same using their private key and user 1's public key to produce secret2.bin:

The secrets should be the same:

Openssl Generate Strong Keys Using Ecdh Key

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Openssl Dh Key

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Openssl Ecdsa Example

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