Contents

# GFpECSharedSecretDHC

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

## Syntax

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.)

#### Product and Performance Information

1

Performance varies by use, configuration and other factors. Learn more at www.Intel.com/PerformanceIndex.