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I have been trying to understand the cryptography behind emv in a better way but without mathematics. I really want to know how it does SDA,DDA and CDA for offline data authentication, as well as offline enciphered pin verification and online authentication including all the keys types involved in the process. it would be very helpful if you can explain this in plain English, Though i tried goggling the information was too formal and for me its not required to bog down to such a detailed level.

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For knowing about ODA - offline data authenticaton (SDA and DDA) you can read my answer here_1. and here_2

For detailed description you can download doc from EMV Co Book 2 - Security_and_Key_Management

hope this information helps you to understand better about ODA concept of EMV.

[Explanation - SDA] - edit 1

In simple term, SDA is like calculate and store hash of some data (X) in the card and calculate hash again at terminal during SDA perform with data (X),

if Hash matched it means data (X) is not changed else data is altered (X BECOME Y) because hash of same data will be always same.

[Explanation DDA ] -edit 2

In DDA we have X + Y - random no generated by Terminal, Y is random so everytime it will have a different value so X+Y is always different when DDA if performed,

Can say data used in DDA is different every time while SDA perform on same data X.

I tried to explain in simple way, to get more follow link given above.