Question: What is the relationship between the **EMV** **ODA**, **CA** and issuer certificate during the transaction?

Answer: 
Offline data authentication is the process to verify the cards authenticity.
Terminals are loaded with CA Public key.

* SDA(Static Data Authentication) can assure you the card data has not
been altered after the issuance. SDA card contains Signed Static
Application Data and Issuer Public Key certificate. CA Public key in
the terminal is used to verify the Issuer Public key certificate and issuer Public key is used to verify the signed static application data in
the card.
* DDA(Dynamic Data Authentication) can assure the card data has not
been altered and that the card as a whole is not cloned. DDA Card
Contains ICC Private Key, ICC Public key certificate and Issuer Public Key Certificate. CA Public Key in terminal is used to verify the  

Issuer Public Key certificate. Issuer Public key used to validate the
ICC Public Key certificate. ICC Public key used to verify the dynamic
signature generated by the card using its ICC Private key.
* CDA/AC(Combined Data Authentication with Cryptogram generation) -
Same as DDA card, only difference being Cryptogram Generation
and Dynamic signature happens together assuring that
Cryptogram came from a valid card.
Data Authentication is used for validating authenticity of an EMV payment card when the request for payment is received on POC. The [EMV CA](https://emvca.com/index.html#EMV-CA) is used for generating EMV root certificates and issuing EMV Issuer certificates for banks that issue payment cards to their customers. Index of CA Public key, issuer certificate, and SDA signature with card holder data are sent to the POC, which can then get the CA public key from the POS storage, use the CA Public key to verify the Issuer RSA key in Issuer Certificate, and use the issuer RSA key to decrypt the SDA Signature and verify that what was signed is the same to the card data. In this process also EMV CA CRL, and EMV Issuer CRL is used for validating whether the certificates are not revoked.