High efficiency AES implementations are known to operate at 277Mb/s using 13.21mW of power. That is 163,820,000 block encryptions per watt per second. Imagine we can do 128 times better over time, say in the next 100 years (should be easy with lots of money).
Time Required To Crack Aes 256
With our 'today' efficiency we can process $2^80$ keys per second, our future efficiency would be able to do $2^88$ easy, but that still leaves $2^40$ seconds required to fully process a 128-bit key, or over 34000 years.
We will hit the limits of lithography, but I would assume we can improve our compute performance another 128-times in that time period, and maybe improve solar efficiency by double, so lets say 136 years. If we really decide to cover all land mass with solar panels to do the job, we can get maybe 4X more power, and get it done in 40 years.... BUT it will take much longer than that for process tech and buildout of the panels, and the infrastructure to get it all working, so I would still say at least a few centuries, probably under 2000 years.
Assuming that you have $2^N$ ciphertexts with different keys each, finding one of the plaintext becomes easier as $N$ increases ($2^128 - N + k$ tries - where $k$ is $2^k$ = the amount of plaintexts you want to find), making it actually feasible to find some plaintexts of AES-128 with a large amount of ciphertexts in a reasonable time.
I didn't understand the most answers here. I my view, exascale computing will be able, to easily crack 128 bit keys in near future. And in fact, 128 bit stands for random generated 16 byte masterkeys, with an security margin of 16^16 (a-f, 0-9). That masterkey is always used to encrypt the data, and is also encrypted by the user password.
A 256 bit AES key is required to be broken using the brute force method on a 2GHz computer.How long would it take to break the key in the best case and in the worst case situations? Assume that 1000 clock cycles are required to check a single AES key.
Well, using simple math: If checking one key takes 1000 clock cycles, and the computer has 2,000,000,000 cycles per second, it checks 2 million keys per second. The best case is that the first key you try is correct: total time is half a microsecond. The worst case is that the last key you try is correct: you have 2256 keys divided by around 221 checked a second (that's more like 2.1 million, but close enough), which is 2235 seconds, which according to Wolfram Alpha is around 1.75 vigintillion (that's 1.75*1063) years, or around 1.3*1053 times the age of the universe.
If running your computer for as long as the universe has existed lets you check A keys (A is absurdly huge), and a magical computer that can check A keys per second (this is running a desktop computer for 14 billion years every second) running for as long as the universe has existed would have checked B keys in that time, then if you happen to have a super-duper magical computer that checks B keys per second (keep in mind that this is as fast as a desktop running every second for 14 billion years, per second) and has been running since the Big Bang, you would only be around 68% done with your brute-force.
To put it another way: The Sun will die out in a paltry 5*109 years. In that time, the ratio of the progress you've made to the total amount of work you have to do is within a couple orders of magnitude of the ratio of the mass of one hydrogen atom to the mass of the supermassive black hole at the center of the galaxy. However, Wikipedia lists the heat death of the universe as occurring at earliest in 10100 years, so you will crack it by then.
Given that k = 1.3810-16 erg/K, and that the ambient temperature of the universe is 3.2 K, an ideal computer running at 3.2 K would consume 4.410-16 ergs every time it set or cleared a bit. To run a computer any colder than the cosmic background radiation would require extra energy to run a heat pump.
But that's just one star, and a measly one at that. A typical supernova releases something like 1051 ergs. (About a hundred times as much energy would be released in the form of neutrinos, but let them go for now.) If all of this energy could be channeled into a single orgy of computation, a 219-bit counter could be cycled through all of its states.
Let's go with the 2^235 CPU-seconds from another post. That's 2^209 18-month Moore's law cycles (not a safe assumption that the law holds that long, but people have been claiming the law was dead since the 90s and it's still going, so let's go with it...), then in 235*18 months, we'd crack that in a CPU-second. But we don't need to wait that long. There's a concept called the "Moore breakeven point", where the time-saving advantage of waiting another 18 months is less than 18 months. I think that's only 210*18 months away.
At the end of those 315 years, after investing $1000 at 5% annual, compounded monthly, you'll have the equivalent of... $4.7 billion. Woah! That's enough to buy 4,700,000 PCs! If you also invest the money you're saving in electricity by not running a desktop, about $20/month, you end up with $27Bn. So this is another, smaller log factor to take into account, as well as Moore's law: at what point, investing your initial money, plus $20/month, is it worth cashing out and buying the best network of computers you can, to crack the hash fastest?
This article describes the strength of the cryptographic system against brute force attacks with different key sizes and the time it takes to successfully mount a brute force attack factoring in future advancements in processing speeds.
Notice the exponential increase in possible combinations as the key size increases. "DES" is part of a symmetric cryptographic algorithm with a key size of 56 bits that has been cracked in the past using brute force attack.
Faster supercomputer (as per Wikipedia): 10.51 Pentaflops = 10.51 x 1015 Flops [Flops = Floating point operations per second]No. of Flops required per combination check: 1000 (very optimistic but just assume for now)No. of combination checks per second = (10.51 x 1015) / 1000 = 10.51 x 1012No. of seconds in one Year = 365 x 24 x 60 x 60 = 31536000No. of Years to crack AES with 128-bit Key = (3.4 x 1038) / [(10.51 x 1012) x 31536000] = (0.323 x 1026)/31536000 = 1.02 x 1018 = 1 billion billion years
As shown above, even with a supercomputer, it would take 1 billion billion years to crack the 128-bit AES key using brute force attack. This is more than the age of the universe (13.75 billion years). If one were to assume that a computing system existed that could recover a DES key in a second, it would still take that same machine approximately 149 trillion years to crack a 128-bit AES key.
The bottom line is that if AES could be compromised, the world would come to a standstill. The difference between cracking the AES-128 algorithm and AES-256 algorithm is considered minimal. Whatever breakthrough might crack 128-bit will probably also crack 256-bit.
In the end, AES has never been cracked yet and is safe against any brute force attacks contrary to belief and arguments. However, the key size used for encryption should always be large enough that it could not be cracked by modern computers despite considering advancements in processor speeds based on Moore's law.
KryptAll secure data utilizes Real-time encryption (virtually zero time in encrypting and decrypting the data) with Military-grade hardware encryption (not software embedded in a chip).
If a good derivation method such as PBKDF2 with a sufficient iteration count to require 100ms just multiply 94^16 * 100ms and convert to years: 10^24 years. Now divide by a faster decryptor than encryptor and the number of machines. Say 1,000 times faster and 1,000,000 machines and we are down to only 10^15 or 1,000,000,000,000,000 years.
Since the US Government considers 256 bit encryption safe enough to not be broken (by any one outside the US) for a time scale long enough to protect US security interests (last paragraph), we can assume it's a fairly long way away.
Of the currently known quantum algorithms, Grover's algorithm is the one which directly affects symmetric ciphers the most. Essentially, for a cipher that a classical computer can bruteforce in time N, a quantum computer can bruteforce it in time square root of N. This means that a 256 bit cipher (which would take at most O(2256) compexity to bruteforce on a classical computer) could be bruteforced in O(2128) on a quantum computer.
Bruteforcing even a 128 bit key is limited by the laws of physics. As this excellent answer explains, the amount of energy required to bruteforce a 128 bit key is ridiculously large (all the world's resources for 10 years straight, just for cracking one key). So, absent any other significant breakthroughs, bruteforcing a 256 bit key is out of question. In fact, Grover's algorithm has been shown to be optimal, so any further breakthroughs are extremely unlikely.
Grover's attack for AES-128 is in 264 time however that requires approximately 264 successive AES evaluations. This may not be achievable in a reasonable time. with a similar argument, we can talk about that AES-192 and AES-256 certainly not achievable.
Security experts consider AES safe against brute-force attacks. A brute-force attack is when a threat actor checks all possible key combinations until the correct key is found. The key size employed for AES encryption therefore needs to be large enough so that it cannot be cracked by modern computers, even considering advancements in processor speeds based on Moore's law.
The two standards are both symmetric block ciphers, but AES is more mathematically efficient. The main benefit of AES lies in its key length options. The time required to crack an encryption algorithm is directly related to the length of the key used to secure the communication -- 128-bit, 192-bit or 256-bit keys. Therefore, AES is exponentially stronger than the 56-bit key of DES. AES encryption is also significantly faster, so it is ideal for applications, firmware and hardware that require low latency or high throughput. 2ff7e9595c
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