ID 768738
Date 12/16/2022
Public

## ECCPSharedSecretDH

Computes a shared secret field element by using the Diffie-Hellman scheme.

Syntax

IppStatus ippsECCPSharedSecretDH(const IppsBigNumState* pPrivateA, const IppsECCPPointState* pPublicB, IppsBigNumState* pShare, IppsECCPState* pECC);

Include Files

ippcp.h

Parameters
 pPrivateA Pointer to your own private key privKey. pPublicB Pointer to the public key pubKey. pShare Pointer to the secret numberbnShare. pECC Pointer to the context of the elliptic cryptosystem.
Description

The function computes a secret number bnShare, which is a secret key shared between two participants of the cryptosystem.

In cryptography, metasyntactic names such as Alice as Bob are normally used as examples and in discussions and stand for participant A and participant B.

Both participants (Alice and Bob) use the cryptosystem for receiving a common secret point on the elliptic curve called a secret key. To receive a secret key, participants apply the Diffie-Hellman key-agreement scheme involving public key exchange. The value of the secret key entirely depends on participants.

According to the scheme, Alice and Bob perform the following operations:

1. Alice calculates her own public key pubKeyA by using her private key privKeyA: pubKeyA = privKeyA· G, where G is the base point of the elliptic curve. Alice passes the public key to Bob.
2. Bob calculates his own public key pubKeyB by using his private key privKeyB: pubKeyB = privKeyB· G, where G is a base point of the elliptic curve. Bob passes the public key to Alice.
3. Alice gets Bob's public key and calculates the secret point shareA. When calculating, she uses her own private key and Bob's public key and applies the following formula: shareA = privKeyA · pubKeyB = privKeyA · privKeyB · G.
4. Bob gets Alice's public key and calculates the secret point shareB. When calculating, he uses his own private key and Alice's public key and applies the following formula: shareB = privKeyB · pubKeyA = privKeyB · privKeyA · G.

Because the following equation is true privKeyA · privKeyB · G =privKeyB · privKeyA · G, the result of both calculations is the same, that is, the equation shareA = shareB is true. The secret point serves as a secret key.

Shared secret bnShare is an x-coordinate of the secret point on the elliptic curve.

The elliptic curve domain parameters must be hitherto defined by one of the functions: ECCPSet or ECCPSetStd.

Return Values
 ippStsNoErr Indicates no error. Any other value indicates an error or warning. ippStsNullPtrErr Indicates an error condition if any of the specified pointers is NULL. ippStsContextMatchErr Indicates an error condition if one of the contexts pointed by pPublicB, pShare, or pECC is not valid. ippStsRangeErr Indicates an error condition if the memory size of bnShare pointed by pShare is less than the value of feBitSize in the function ECCPInit. ippStsShareKeyErr Indicates an error condition if the shared secret key is not valid. (For example, the shared secret key is invalid if the result of the secret point calculation is the point at infinity.)