Key generation. In Merkle–Hellman, the keys are two knapsacks. The public key is a 'hard' knapsack A, and the private key is an 'easy', or superincreasing, knapsack B, combined with two additional numbers, a multiplier and a modulus. The multiplier and modulus can be used to convert the superincreasing knapsack into the hard knapsack.

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Definition

  • Walkthrough of Diffie-Hellman Key Exchange. Walkthrough of Diffie-Hellman Key Exchange. If you're seeing this message, it means we're having trouble loading external resources on our website. If you're behind a web filter, please make sure that the domains.kastatic.org and.kasandbox.org are unblocked.
  • I need to generate an EC Diffie Hellman key pair. I am using the secp256r1 named curve, and OpenSSL. This is what I have with me so far: unsigned char.ecdh(sizet.secretlen) EVPPKEYCTX.

Provides a Cryptography Next Generation (CNG) implementation of the Elliptic Curve Diffie-Hellman (ECDH) algorithm. This class is used to perform cryptographic operations.

Inheritance
ECDiffieHellmanCng

Examples

The following example shows how to use the ECDiffieHellmanCng class to establish a key exchange and how to use that key to encrypt a message that can be sent over a public channel and decrypted by the receiver.

Remarks

The ECDiffieHellmanCng class enables two parties to exchange private key material even if they are communicating through a public channel. Both parties can calculate the same secret value, which is referred to as the secret agreement in the managed Diffie-Hellman classes. The secret agreement can then be used for a variety of purposes, including as a symmetric key. However, instead of exposing the secret agreement directly, the ECDiffieHellmanCng class does some post-processing on the agreement before providing the value. This post processing is referred to as the key derivation function (KDF); you can select which KDF you want to use and set its parameters through a set of properties on the instance of the Diffie-Hellman object.

Key derivation functionProperties
HashHashAlgorithm - The hash algorithm that is used to process the secret agreement.
SecretPrepend - An optional byte array to prepend to the secret agreement before hashing it.
SecretAppend - An optional byte array to append to the secret agreement before hashing it.
HmacHashAlgorithm - The hash algorithm that is used to process the secret agreement.
SecretPrepend- An optional byte array to prepend to the secret agreement before hashing it.
SecretAppend - An optional byte array to append to the secret agreement before hashing it.
TlsLabel - The label for key derivation.
Seed - The seed for key derivation.

The result of passing the secret agreement through the key derivation function is a byte array that may be used as key material for your application. The number of bytes of key material generated is dependent on the key derivation function; for example, SHA-256 will generate 256 bits of key material, whereas SHA-512 will generate 512 bits of key material.The basic flow of an ECDH key exchange is as follows:

  1. Alice and Bob create a key pair to use for the Diffie-Hellman key exchange operation

  2. Alice and Bob configure the KDF using parameters the agree on.

  3. Alice sends Bob her public key.

  4. Bob sends Alice his public key.

  5. Alice and Bob use each other's public keys to generate the secret agreement, and apply the KDF to the secret agreement to generate key material.

Constructors

ECDiffieHellmanCng()

Initializes a new instance of the ECDiffieHellmanCng class with a random key pair.

ECDiffieHellmanCng(CngKey)

Initializes a new instance of the ECDiffieHellmanCng class by using the specified CngKey object.

ECDiffieHellmanCng(ECCurve)

Creates a new instance of the ECDiffieHellmanCng class whose public/private key pair is generated over the specified curve.

ECDiffieHellmanCng(Int32)

Initializes a new instance of the ECDiffieHellmanCng class with a random key pair, using the specified key size.

Fields

KeySizeValue

Represents the size, in bits, of the key modulus used by the asymmetric algorithm.

(Inherited from AsymmetricAlgorithm)
LegalKeySizesValue

Specifies the key sizes that are supported by the asymmetric algorithm.

(Inherited from AsymmetricAlgorithm)

Properties

HashAlgorithm

Gets or sets the hash algorithm to use when generating key material.

HmacKey

Gets or sets the Hash-based Message Authentication Code (HMAC) key to use when deriving key material.

Key

Specifies the CngKey that is used by the current object for cryptographic operations.

KeyDerivationFunction

Gets or sets the key derivation function for the ECDiffieHellmanCng class.

KeyExchangeAlgorithm

Gets the name of the key exchange algorithm.

(Inherited from ECDiffieHellman)
KeySize

Gets or sets the size, in bits, of the key modulus used by the asymmetric algorithm.

Label

Gets or sets the label value that is used for key derivation.

LegalKeySizes

Gets the key sizes that are supported by the asymmetric algorithm.

(Inherited from AsymmetricAlgorithm)
PublicKey

Gets the public key that can be used by another ECDiffieHellmanCng object to generate a shared secret agreement.

SecretAppend

Gets or sets a value that will be appended to the secret agreement when generating key material.

SecretPrepend

Gets or sets a value that will be added to the beginning of the secret agreement when deriving key material.

Seed

Gets or sets the seed value that will be used when deriving key material.

SignatureAlgorithm

Gets the name of the signature algorithm.

(Inherited from ECDiffieHellman)
UseSecretAgreementAsHmacKey

Gets a value that indicates whether the secret agreement is used as a Hash-based Message Authentication Code (HMAC) key to derive key material.

Methods

Clear()

Releases all resources used by the AsymmetricAlgorithm class.

(Inherited from AsymmetricAlgorithm)
DeriveKeyFromHash(ECDiffieHellmanPublicKey, HashAlgorithmName)

Performs key derivation using a specified hash algorithm.

(Inherited from ECDiffieHellman)
DeriveKeyFromHash(ECDiffieHellmanPublicKey, HashAlgorithmName, Byte[], Byte[])

Performs key derivation using a specified hash algorithm with optional prepended or appended data.

DeriveKeyFromHmac(ECDiffieHellmanPublicKey, HashAlgorithmName, Byte[])

Performs key derivation using a specified HMAC (Hash-based Message Authentication Code) algorithm.

(Inherited from ECDiffieHellman)
DeriveKeyFromHmac(ECDiffieHellmanPublicKey, HashAlgorithmName, Byte[], Byte[], Byte[])

Performs key derivation using a specified HMAC (Hash-based Message Authentication Code) algorithm with optional prepended or appended data.

DeriveKeyMaterial(CngKey)

Derives the key material that is generated from the secret agreement between two parties, given a CngKey object that contains the second party's public key.

DeriveKeyMaterial(ECDiffieHellmanPublicKey)

Derives the key material that is generated from the secret agreement between two parties, given an ECDiffieHellmanPublicKey object that contains the second party's public key.

DeriveKeyTls(ECDiffieHellmanPublicKey, Byte[], Byte[])

Performs key derivation using the TLS (Transport Layer Security) 1.1 PRF (Pseudo-Random Function).

DeriveSecretAgreementHandle(CngKey)

Gets a handle to the secret agreement generated between two parties, given a CngKey object that contains the second party's public key.

DeriveSecretAgreementHandle(ECDiffieHellmanPublicKey)

Gets a handle to the secret agreement generated between two parties, given an ECDiffieHellmanPublicKey object that contains the second party's public key.

Dispose()

Releases all resources used by the current instance of the AsymmetricAlgorithm class.

(Inherited from AsymmetricAlgorithm)
Dispose(Boolean)

Releases the unmanaged resources used by the AsymmetricAlgorithm class and optionally releases the managed resources.

(Inherited from AsymmetricAlgorithm)
Equals(Object)

Determines whether the specified object is equal to the current object.

(Inherited from Object)
ExportECPrivateKey()

Exports the current key in the ECPrivateKey format.

(Inherited from ECDiffieHellman)
ExportEncryptedPkcs8PrivateKey(ReadOnlySpan<Byte>, PbeParameters)

Exports the current key in the PKCS#8 EncryptedPrivateKeyInfo format with a byte-based password.

(Inherited from AsymmetricAlgorithm)
ExportEncryptedPkcs8PrivateKey(ReadOnlySpan<Char>, PbeParameters)

Exports the current key in the PKCS#8 EncryptedPrivateKeyInfo format with a char-based password.

(Inherited from AsymmetricAlgorithm)
ExportExplicitParameters(Boolean)

Exports the key and explicit curve parameters used by the ECCurve object into an ECParameters object.

ExportParameters(Boolean)

Exports the key used by the ECCurve object into an ECParameters object.

ExportPkcs8PrivateKey()

Exports the current key in the PKCS#8 PrivateKeyInfo format.

(Inherited from AsymmetricAlgorithm)
ExportSubjectPublicKeyInfo()

Exports the public-key portion of the current key in the X.509 SubjectPublicKeyInfo format.

(Inherited from AsymmetricAlgorithm)
FromXmlString(String)

This method is not implemented.

FromXmlString(String, ECKeyXmlFormat)

Deserializes the key information from an XML string by using the specified format.

GenerateKey(ECCurve)

Generates a new ephemeral public/private key pair for the specified curve.

GetHashCode()

Serves as the default hash function.

(Inherited from Object)
GetType()

Gets the Type of the current instance.

(Inherited from Object)
ImportECPrivateKey(ReadOnlySpan<Byte>, Int32)

Imports the public/private keypair from an ECPrivateKey structure, replacing the keys for this object.

(Inherited from ECDiffieHellman)
ImportEncryptedPkcs8PrivateKey(ReadOnlySpan<Byte>, ReadOnlySpan<Byte>, Int32)

Imports the public/private keypair from a PKCS#8 EncryptedPrivateKeyInfo structure after decrypting with a byte-based password, replacing the keys for this object.

(Inherited from ECDiffieHellman)
ImportEncryptedPkcs8PrivateKey(ReadOnlySpan<Char>, ReadOnlySpan<Byte>, Int32)

Imports the public/private keypair from a PKCS#8 EncryptedPrivateKeyInfo structure after decrypting with a char-based password, replacing the keys for this object.

(Inherited from ECDiffieHellman)
ImportParameters(ECParameters)

Imports the specified parameters for an ECCurve object as a key into the current instance.

ImportPkcs8PrivateKey(ReadOnlySpan<Byte>, Int32)

Imports the public/private keypair from a PKCS#8 PrivateKeyInfo structure after decryption, replacing the keys for this object.

(Inherited from ECDiffieHellman)
ImportSubjectPublicKeyInfo(ReadOnlySpan<Byte>, Int32)

Imports the public key from an X.509 SubjectPublicKeyInfo structure after decryption, replacing the keys for this object.

(Inherited from ECDiffieHellman)
MemberwiseClone()

Creates a shallow copy of the current Object.

(Inherited from Object)
ToString()

Returns a string that represents the current object.

(Inherited from Object)
ToXmlString(Boolean)

This method is not implemented.

ToXmlString(ECKeyXmlFormat)

Serializes the key information to an XML string by using the specified format.

TryExportECPrivateKey(Span<Byte>, Int32)

Attempts to export the current key in the ECPrivateKey format into a provided buffer.

(Inherited from ECDiffieHellman)
TryExportEncryptedPkcs8PrivateKey(ReadOnlySpan<Byte>, PbeParameters, Span<Byte>, Int32)

Attempts to export the current key in the PKCS#8 EncryptedPrivateKeyInfo format into a provided buffer, using a byte-based password.

(Inherited from ECDiffieHellman)
TryExportEncryptedPkcs8PrivateKey(ReadOnlySpan<Char>, PbeParameters, Span<Byte>, Int32)

Attempts to export the current key in the PKCS#8 EncryptedPrivateKeyInfo format into a provided buffer, using a char-based password.

(Inherited from ECDiffieHellman)
TryExportPkcs8PrivateKey(Span<Byte>, Int32)

Attempts to export the current key in the PKCS#8 PrivateKeyInfo format into a provided buffer.

(Inherited from ECDiffieHellman)
TryExportSubjectPublicKeyInfo(Span<Byte>, Int32)

Attempts to export the current key in the X.509 SubjectPublicKeyInfo format into a provided buffer.

(Inherited from ECDiffieHellman)

Explicit Interface Implementations

IDisposable.Dispose()

For a description of this member, see Dispose().

(Inherited from AsymmetricAlgorithm)

Applies to


Dh Public Key Generation C Code Download

Hi,

I'm trying to generate and exchange keys using the functions in the dhm.c file. The code is compiled using EWARM for an STM32F407.

I'm not setting up the parameters correctly as my function calls are returning immediately with errors.

Can someone please point me to an example that uses these functions or list the steps I need to make in order to generate my private and shared secret keys?

Thank you

I think the point is that you need to load Diffie-Hellman parameters before you can generate a DH key. DH parameters define the playground in which you'll be able to generate keys and perform a key exchange. (You need to make sure both parties are using the same parameters.)

One way to load them is to use mbedtls_dhm_parse_dhm() if you got your parameters encoded as a DER or PEM string (this is the format you'll get using openssl dhparam for example). Another way is to directly set them in the context using mpi_read() just as we do in mbedtls_ssl_conf_dh_params(). For that you can use standard parameters provided in dhm.h, such as MBEDTLS_DHM_RFC3526_MODP_2048_P and the corresponding G.

Dh Public Key Generation C Code List

Hope this helps!

Thank you for your quick response. After more searching, I found that I should be using the functions in ecdh.c rather than dhm.c

Note that there is still a similar thing here: before you can generate a key or do a key exchange, you need to pick an elliptic curve and set it with mbedtls_ecp_group_load( &ecdh_ctx.grp, MBEDTLS_ECP_DP_xxx );.

Thanks Manuel for the tip.

I'm still have issues though. The shared secret key I am generating doesn't match the server's key. This is my code, can you tell me if I'm missing something?

Sorry, &ctx.z should be &z in there, but either way it makes no difference.

Sorry, I think you need to tell me more about how your code is used, here I see only one side and I don't see how the pubic keys of both parties are exchanged: can you be more explicit on that?

Hi Manuel,

The exchange as best as can explain it:

Dh Public Key Generation C Code Download

  • 1) The server creates a public and secret key.
  • 2) I receive the server's public key into tcpbuffer.
  • 3) I create a public and secret key using - mbedtls_ecdh_gen_public().
  • 4) I store my public key to send to the server later.
  • 5) I combine the server's public key and my secret using - mbedtls_ecdh_compute_shared() - to generate our shared secret key.
  • 6) I send my public key to the sever.
  • 7) For debugging purposes, I check my shared secret against the server's shared secret. It does not match when I believe it should.
  • 8) I SHA512 my shared secret.
  • 9) I copy over bytes 16 to 23 of the result to get my session key for use with future decryptions.
  • 10) Obviously, the session key I create does not match the sever's session key either.

I hope that's all clear, thank you for your time helping me with this.

Hi Manuel,

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Is there any update you can give me on my problem, it's becoming critical now.

Key Generation Software

Thanks

I just wrote an example program that I hope will help you: https://github.com/ARMmbed/mbedtls/blob/3eb8c34e6a761b3f1f5fce01e31c70b1560e70b5/programs/pkey/ecdh_curve25519.c

Dh Public Key Generation C Code List

PS: worry for not getting back to you earlier, and thanks for pinging us.

Free Key Generation Software

Thanks Manuel! I'll check out the example.