A Robust and Effective Smart-Card-Based Remote User Authentication Mechanism Using Hash Function

Algorithm 2

𝐸𝑋𝑃2^{𝐻𝐴𝑆𝐻}_{𝒜,𝑅𝐸𝑈𝐴𝑆}.

(1) Extract all the secret information (𝑟_𝑖,𝑒_𝑖,𝑇𝐷_𝑖,𝐷_𝑖,𝐾) from the memory of the stolen or lost smart

 card 𝐶_𝑖 of the user 𝑈_𝑖 using the power analysis attacks [23, 24].

(2) Call 𝑅𝑒𝑣𝑒𝑎𝑙 oracle on input 𝑟_𝑖 in order to retrieve 𝐼𝐷_𝑖 and 𝑅𝑃𝑊_𝑖 as (𝐼𝐷^′_𝑖,𝑅𝑃𝑊^′_𝑖) ←𝑅𝑒𝑣𝑒𝑎𝑙(𝑟_𝑖).

(3) Call 𝑅𝑒𝑣𝑒𝑎𝑙 oracle on input 𝑅𝑃𝑊^′_𝑖 to retrieve 𝐼𝐷_𝑖, 𝐾 and 𝑃𝑊_𝑖 as (𝐼𝐷_𝑖^′′‖𝐾^′′‖𝑃𝑊^′_𝑖) ←𝑅𝑒𝑣𝑒𝑎𝑙(𝑅𝑃𝑊^′_𝑖).

(4) if (𝐼𝐷^′_𝑖=𝐼𝐷_𝑖^′′) and (𝐾=𝐾^′′) then

(5)  Accept 𝑃𝑊_𝑖^′′ as the correct password 𝑃𝑊_𝑖 of the user 𝑈_𝑖.

(6)  return 1 (Success)

(7) else

(8)  return 0 (Failure)

(9) end if