Hardware Security

1. "Montgomery Reduction", what is the necessary condition:

• gcd (R,N) = 1

2. For e=1001010110, when we compute ae(mod n) with the left to right "square and multiple algorithm (I)", the total number of multiplication (both b*b and b*a) we will do is:

• 15

2 multiplications for the leading bit 1: one b*b and one b*a, both are trivial operations, 1*1 and 1*a. If we replace line 2 by b=a; and start the for loop in line 3 with i=s-1; these 2 multiplications can be saved.
  
3. When we use the "iterative exponentiation and modular" method to compute 24(mod 5), starting from 21, we will have 21=2(mod 5); 2×2=4(mod 5); 4×2=3(mod 5); 3×2=1(mod 5). The results we will see are 2, 4, 3, 1. If we use the same method to compute 37(mod 5), starting from 31, the results we will see are

• 3, 4, 2, 1, 3, 4, 2

4. Which of the following statements is true for data remanence on SRAM?

• It is possible to freeze data and read it at temperature higher than -20 degree.

5. Passive non-invasive attacks:

• Side channel attack: side channel attack itself is passive, but it can be combined with other method (such as fault injection) to become active.