Utilizing the Double-Precision Floating-Point Computing Power of GPUs for RSA Acceleration

Algorithm 2

DPF-based parallel Montgomery multiplication () algorithm: Computing Phase.

Input:

: Thread ID, where ;

: Loops num, where ;

: Multiplicand, where ;

: Multiplier, where ;

: Modulus, where ;

: Integer, where ;

Output:

Redundant-format sub-result

, where ;

(1)

(2) for     do

(3)

 Step ( 1):     

(4)for    to   do

(5)

(6)end for

 Step ( 2):   

(7)if      then

(8)

(9)

(10)

(11)end if

(12)

 Step ( 3):   

(13)for    to   do

(14)

(15)end for

 Step ( 4):   

(16) ?

(17) ?()

(18)for    to   do

(19)

(20)end for

(21)

(22) end for