As a foreigner being temporarily employed in Greece you may be exempt from registering with the Greek social security. Such an exemption will depend on the type of job you do but generally will not generally apply if you’re employed permanently. If your contract is for more than a year your employer must register you with the Social Security Fund. As a citizen of an EU member state you may, in certain circumstances, be temporarily exempt from being insured by a Greek social security fund.
Your Social Security contributions are deducted from your salary at the source. Your employer must also make separate additional monthly payments for each employee. The amount of contributions is calculated according to your monthly salary and may be increased where employment is of a hazardous or physical nature.