Question

The following give the number of bits in an encryption key. For each, calculate the number of trials, on average, it will take to crack that key in powers of ten. a. 40 bits b. 56 bits c. 64 bits d. 80 bits e. 128 bits f. 256 bits

Answer 1

The number of trial is found by the following algebraic equation:

log( 2^{number of bits} )= 10^x trails

a. 40 bits

= log(2⁴⁰) = 12.0411998266

In power of 10 it is rounded to 10¹².

40 = rounded 10¹² Trials.

b. 56 bits

= log(2⁵⁶) = 16.8576797572

In power of 10 it is rounded to 10¹⁶.

56 = rounded 10¹⁶ Trials.

c. 64 bits

= log(2⁶⁴) = 19.2659197225

In power of 10 it is rounded to 10¹⁹.

64 = rounded 10¹⁹ Trials.

d. 80 bits

= log(2⁸⁰) = 24.0823996531

In power of 10 it is rounded to 10²⁴.

80 = rounded 10²⁴ Trials.

e. 128 bits

= log(2¹²⁸) = 38.531839445

In power of 10 it is rounded to 10³⁸.

128 = rounded 10³⁸ Trials.

e. 256 bits

= log(2²⁵⁶) = 77.06367889

In power of 10 it is rounded to 10⁷⁷.

256 = rounded 10⁷⁷ Trials.