Non-dictionary known-plaintext brute force attack on AES-256

Maximal duration of Intel Advanced Encryption Standard (AES) New Instructions (NI) cycles in a non-dictionary known-plaintext brute force attack against a ciphertext encrypted with AES, using a 256-bit key, operating in Electronic Codebook (ECB) mode, with one million cores @ 3.1 GHz supporting Intel AES NI

Version 6, November 26, 2011

Copyleft 2011 Neven Lovrić <[email protected]>. Released under the GNU Free Documentation License; latest version applies. Link to this page for the latest version of this table.

This was calculated with the assumption that a Cray XE6 with one million Opteron 6282 SE cores @ 3.1 GHz has equivalent computing power. May contain miscalculations.

"a-z" and "A-Z" denote the letters of the English alphabet.

Pass phrase length	Possible characters	Maximal duration of Intel AES NI cycles

10			a-z			~2.55 seconds
11			a-z			~66.30 seconds
12			a-z			~28.73 minutes
13			a-z			~12.45 hours
14			a-z			~13.49 days
15			a-z			~350.68 days <-- infeasible
16			a-z			~24.96 years
17			a-z			~649.04 years
18			a-z			~16,874.96 years
19			a-z			~438,748.84 years
20			a-z			~11,407,469.74 years

10			a-z (+ SPACE)		~3.72 seconds
11			a-z (+ SPACE)		~100.42 seconds
12			a-z (+ SPACE)		~45.19 minutes
13			a-z (+ SPACE)		~20,34 hours
14			a-z (+ SPACE)		~22.88 days
15			a-z (+ SPACE)		~1.69 years <-- infeasible
16			a-z (+ SPACE)		~45.66 years
17			a-z (+ SPACE)		~1,232.84 years
18			a-z (+ SPACE)		~33,286.65 years
19			a-z (+ SPACE)		~898,739.61 years
20			a-z (+ SPACE)		~24,265,969.60 years

10			a-z0-9			~66.05 seconds
11			a-z0-9			~39.63 minutes
12			a-z0-9			~23.78 hours
13			a-z0-9			~35.67 days
14			a-z0-9			~3.52 years <-- infeasible
15			a-z0-9			~126.55 years
16			a-z0-9			~4,555.78 years
17			a-z0-9			~164,007.94 years
18			a-z0-9			~5,904,285.91 years
19			a-z0-9			~212,554,292.87 years
20			a-z0-9			~7,651,954,543.49 years

10			a-zA-Z			~43.52 minutes
11			a-zA-Z			~37.72 hours
12			a-zA-Z			~81.72 days <-- infeasible or
13			a-zA-Z			~11.63 years <-- infeasible
14			a-zA-Z			~605.02 years
15			a-zA-Z			~31,461.00 years
16			a-zA-Z			~1,635,971.99 years
17			a-zA-Z			~85,070,543.59 years
18			a-zA-Z			~4,423,668,266.45 years
19			a-zA-Z			~230,030,749,855.59 years
20			a-zA-Z			~11,961,598,992,490.65 years

10			a-zA-Z0-9		~4.21 hours
11			a-zA-Z0-9		~10.88 days
12			a-zA-Z0-9		~1.85 years <-- infeasible
13			a-zA-Z0-9		~114.50 years
14			a-zA-Z0-9		~7,099.14 years
15			a-zA-Z0-9		~440,146.96 years
16			a-zA-Z0-9		~27,289,111.64 years
17			a-zA-Z0-9		~1,691,924,921.78 years
18			a-zA-Z0-9		~104,899,345,150.51 years
19			a-zA-Z0-9		~6,503,759,399,331.78 years
20			a-zA-Z0-9		~403,233,082,758,570.59 years

10			a-zA-Z0-9 (+ 22 other)	~3.66 days
11			a-zA-Z0-9 (+ 22 other)	~307.17 days <-- infeasible
12			a-zA-Z0-9 (+ 22 other)	~70.64 years
13			a-zA-Z0-9 (+ 22 other)	~5,934.08 years
14			a-ZA-Z0-9 (+ 22 other)	~498,462.36 years
15			a-zA-Z0-9 (+ 22 other)	~41,870,838.40 years
16			a-zA-Z0-9 (+ 22 other)	~3,517,150,425.18 years
17			a-zA-Z0-9 (+ 22 other)	~295,440,635,715.48 years
18			a-ZA-Z0-9 (+ 22 other)	~24,817,013,400,100.47 years
19			a-zA-Z0-9 (+ 22 other)	~2,084,629,125,608,439.36 years
20			a-zA-Z0-9 (+ 22 other)	~175,108,846,551,108,906.01 years

Conclusion: Keys derived from up-to-10-usually-used-pass-phrase-character pass phrases might be determined on a Cray XE6 with one million Opteron 6282 SE cores @ 3.1 GHz using a non-dictionary known-plaintext brute force attack within 3.66 days (only equivalents of Intel AES NI cycles taken into account).

1			(255 characters)	~4.61 picoseconds
2			(255 characters)	~1.17 nanoseconds
3			(255 characters)	~299.53 nanoseconds
4			(255 characters)	~76.38 microseconds
5			(255 characters)	~19.48 miliseconds
6			(255 characters)	~4.97 seconds
7			(255 characters)	~21.11 minutes
8			(255 characters)	~3.74 days
9			(255 characters)	~2.61 years <-- infeasible
10			(255 characters)	~665.46 years

Conclusion: Keys derived from up-to-8-character pass phrases might be determined on a Cray XE6 with one million Opteron 6282 SE cores @ 3.1 GHz using a non-dictionary known-plaintext brute force attack within 3.74 days (only equivalents of Intel AES NI cycles taken into account).