Contents

# ECCPSharedSecretDH

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

## Syntax

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
.
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.)

#### Product and Performance Information

1

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