I have read that the credit protection seller is assuming long credit risk and the protection buyer is assuming short credit risk.

I think of it as the opposite. For example, if I have bought a CDS (the protection buyer) I would benefit from it if credit risk becomes wider.

Yes, buying CDS = buying protection against default = even if it doesnt default and credit quality deteriorates, you make money

then if i am a cds protection buyer i would be long credit risk not short credit risk???

I think you have to look at it as about credit quality instead of credit risk, that way you get your long and shorts right. From the CFAI book:

Because of these CDS characteristics, there is potential confusion regarding which party is long and which is short. Normally, we think of buyers as being long and sellers as being short, but in the CDS world, it is the opposite. Because the credit protection buyer promises to make a series of future payments, it is regarded as being short. This is consistent with the fact that in the financial world, “shorts” are said to benefit when things go badly. Credit quality is based on the underlying debt obligation, and when it improves, the credit protection seller benefits. When credit quality deteriorates, the credit protection buyer benefits. Hence, the CDS industry views the credit protection seller as the long and the buyer as the short. This point can lead to confusion because we effectively say the credit protection buyer is short and the credit protection seller is long.

Could I understand it as “The protection buyer is natural long short credit risk as he/she is better of if credit risk narrows”.

Similar as to buyer of an option stock being natural long as he/she benefits if price goes up.

One question to your comment pmond:

You mentioned “Because the credit protection buyer promises to make a series of future payments, it is regarded as being short”.

I think credit protection buyer are the lender of monet who buy CDS to hedge the potential default of a borrower. How does so a credit protection buyer make a promise to make a series of future payments?

Thanks for the help.