Discovering average salary without disclosing your own to another

To determine the average salary among a group of friends, you need to encode your own salary by adding a random number to it. These encoded salaries are added together and the random numbers are subtracted.

Example:

Salary A = $50,000

Salary B = $55,000

Salary C = $53,000

A adds 25,776 (random number) to his salary ($50,000) and provides the sum to B. $75,776

B adds 15,899 (random number) to his salary ($55,000) and provides the sum to C. $146,675

C adds 13,499 (random number) to his salary ($53,000) and provides the sum to A. $213,174

A subtracts his random number (25,776) from the sum received from C ($213,174) and provides the result to B. $187,398

B subtracts his random number (15,899) from the sum received from A ($187,398) and provides the result to C. $171,499

C subtracts his random number (13,499) from the sum received from B ($171,499) and provides the end result to everyone. $158,000

($50,000 + $55,000 + $53,000) / 3 = $52,667.

But strategy this requires everyone to be truthful! Participants need to be guaranteed some useful information so they want to participate. Participants need to be given a reason to be honest or else whey will free ride on other people's honesty. The process should be anonymous so that no one fears revealing their personal salary to others face to face.