Applied Cryptography
On a certain machine, a brute-force search trying every 56-bit key takes about 20 hours. Which of the following is closest to the time the same machine needs to try every 64-bit key?
- AAbout 23 hours
- BAbout 160 hours
- CAbout 213 days
Show answer and explanation
Answer: C. About 213 days
A key of n bits has 2ⁿ candidates, so adding 8 bits to the key length multiplies the candidates by 2⁸ = 256. Therefore 20 hours × 256 = 5,120 hours = about 213 days. Each additional bit doubles the brute-force effort, and AES-128 has 2⁷² times (about 4.7 × 10²¹ times) as many key candidates as a 56-bit key.
- A. About 23 hours is 20 × 64/56, the value obtained by assuming that the effort is proportional to the key length.
- B. About 160 hours is 20 × 8, the value obtained by counting the 8 extra bits as a factor of 8.
- C. Correct. 20 × 2⁸ = 5,120 hours, about 213 days.