The cryptographic algorithm used between your PC and the payment server is secure enough that I offered a free membership to anyone who could crack it... I even provided some tips. There were a few attempts but no winners. ;)
Of course, use your personal computer, not a public computer, to make such transactions if you're concerned about security. Alternate forms of payment are listed here:
http://www.chess.com/membership.html
Would my relevant fees be deducted in EUROS.
How else can I pay besides Credit Card.
If credt card only how secure is it.