Developer Reference for Intel® Integrated Performance Primitives Cryptography 2019

GFpECSharedSecretDH

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

Syntax

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

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 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.

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 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 one of the contexts pointed to by pPublicB, pPrivateA, 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 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.)