ID 768738
Date 12/16/2022
Public

## GFpECSharedSecretDHC

Computes a shared secret field element by using the Diffie-Hellman scheme and the elliptic curve cofactor.

Syntax

IppStatus ippsGFpECSharedSecretDHC(const IppsBigNumState* pPrivateA, const IppsGFpECPoint* pPublicB, IppsBigNumState* pShare, IppsGFpECState* pEC, Ipp8u* pScratchBuffer);

Include Files

ippcp.h

Parameters
 pPrivate Pointer to your own private key privKey. pPublic Pointer to the public key pubKey. pShare Pointer to the secret number bnShare. pEC Pointer to the context of the elliptic curve. pScratchBuffer Pointer to the scratch buffer.
Description

The function computes a secret number bnShare which is a secret key shared between two participants of the cryptosystem. Both participants (Alice and Bob) use the cryptosystem for getting a common secret point on the elliptic curve by using the Diffie-Hellman scheme and elliptic curve cofactor h.

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 = h · privKeyA · pubKeyB = h · privKeyA · privKeyB · G, where h is the elliptic curve cofactor.
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 = h · privKeyB · pubKeyA = h · privKeyB · privKeyA · G, where h is the elliptic curve cofactor.

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

The elliptic curve domain parameters must be hitherto defined by the functions: GFpECInitStd, GFpECInit, GFpECSet, or GFpECSetSubgroup.

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 any of the contexts pointed to by pPrivate, pPublic, pShare, or pEC does not match the operation. ippStsRangeErr Indicates an error condition if the memory size of bnShare pointed to by pShare is less than the size of the GFp modulus that is the base for the specified elliptic curve. 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.)