What is the expected number of hours needed to find the password for a specific user if two salts are used and the dictionary is not used?

Steps to Solve

1. Calculate Total Possible Passwords To determine how many possible passwords can be formed with 6 characters and 16 different characters, we use the formula for combinations. The total number of combinations is given by: $$ \text{Total Passwords} = 16^6 $$

2. Adjust for Salt Values Since two salt values are included for each user, the number of unique attempts needed for that specific user doubles. Thus, the number of attempts increases to: $$ \text{Effective Total Passwords} = 2 \times 16^6 $$

3. Calculate Work Factor The attacker has a probability of $0.2$ of having the password from the password file, but since the dictionary is not used, the work is simply the total number of unique passwords computed. Thus, the expected work becomes: $$ \text{Expected Work} = \text{Effective Total Passwords} $$

4. Calculate Work Time in Seconds Since work time is defined as $3 \times \text{Work}$ in seconds, we compute: $$ \text{Work Time} = 3 \times \text{Expected Work} $$

5. Convert Time to Hours To convert seconds to hours, we use the conversion factor where 1 hour = 3600 seconds: $$ \text{Time in Hours} = \frac{\text{Work Time}}{3600} $$

6. Substitute and Calculate Now we will substitute the value of ( 16^6 ) and compute all equations step-by-step.