Card based solution to this sharing attack that will mean that all users. That offers the capability to receive and decrypt the scrambled TV signals. The encryption of the CW is often defined as “the process of protecting the. Some of the most commonly used CAS systems include VIAaccess [29], Irdeto [17],.
I did a report on encryption a while ago, and I thought I'd post a bit of it here as it's quite mind-boggling. Is the standardized encryption specification. It's used worldwide by everyone from corporations to the US government.
It's largest key size is 256 bits. This means that the key, the thing that turns encrypted data into unencrypted data, is string of 256 1s or 0s. With each character having two possibilities (1 or 0), there are 2 256 possible combinations.
Typically, so only 2 255 need to be guessed. How long would it take to flip through each of the possible keys? When doing mundane, repetitive calculations (such as brute-forcing or bitcoin mining), the GPU is better suited than the CPU. A high-end GPU can typically do about 2 billion calculations per second (2 gigaflops). So, we'll use GPUs. Say you had a billion of these, all hooked together in a massively parallel computer system. Together, they could perform at 2e18 flops, or 2 000 000 000 000 000 000 keys per second (2 quintillion) 1 billion gpus @ 2 gigaflops each (2 billion flops) Since there are 31 556 952 seconds in a year, we can multiply by that to get the keys per year.31 556 952 =6.3113904e25 keys per year (10 septillion, 10 yottaflops) Now we divide 2 255 combinations by 6.3113904e25 keys per year: 2^255 / 6.3113904e25 =9.1732631e50 years The universe itself only existed for 14 billion (1.4e10) years.
It would take 6.7e40 times longer than the age of the universe to exhaust half of the keyspace of a AES-256 key. On top of this, there is an energy limitation. The is a theoretical limit of energy consumption of a computation. It holds that on a system that is logically irreversible (bits do not reset themselves back to 0 from 1), a change in the value of a bit requires an entropy increase according to kTln2, where k is the Boltzmann constant, T is the temperature of the circuit in kelvins and ln2 is the natural log(2). Lets try our experiment while considering power. Most high-end GPUs take around 150 watts of energy to power themselves at full load. This doesn't include cooling systems.
150 000 000 000 watts (150 gigawatts) 1 billion gpus @ 150 watts 1.5e11 watts This is enough power to power 50 million american households. The largest nuclear power reactors (Kashiwazaki-Kariwa) generate about 1 gigawatt of energy. 1.5e11 watts / 1 gigawatt = 150 Therefore, 1 billion GPUs would require 150 nuclear power plant reactors to constantly power them, and it would still take longer than the age of the universe to exhaust half of a AES-256 keyspace. 1 billion GPUs is kind of unrealistic.
How about a supercomputer? The Tianhe-2 Supercomputer is the world's fastest supercomputer located at Sun Yat-sen University, Guangzhou, China. It clocks in at around 34 petaflops.
Tianhe-2 Supercomputer @ 33.86 petaflops (quadrillion flops) =33 860 000 000 000 000 keys per second (33.86 quadrilion) 3.386e16. 31556952 seconds in a year 2 255 possible keys 2^255 / 1.0685184e24 =1.0685184e24 keys per year (1 septillion, 1 yottaflop) =5.4183479e52 years That's just for 1 machine. Reducing the time by just one power would require 10 more basketball court-sized supercomputers. To reduce the time by x power, we would require 10 x basketball court-sized supercomputers. It would take 10 38 Tianhe-2 Supercomputers running for the entirety of the existence of everything to exhaust half of the keyspace of a AES-256 key. Edit: corrections on my grade 12 math. That's called breaking the key-derivation function (the method used to convert a small password to a long key).
The password is usually short to be easily remembered, and the goal of a modern KDF is to take a very long time to make brute forcing harder (SHA is a bad example, because it's designed to be fast). AES, being a (symmetric) encryption standard, must be fast to minimise the impact of encryption - you don't want to wait half an hour to decrypt your porn with your dick in your hand. To make up for it, it has a long key that's almost impossible to brute-force. So a KDF is a slow algorithm that converts a short key to a long one that's used in a fast algorithm. Well, I have to correct myself here. Brute-forcing isn't really breaking anything more than the security. The KDF would only be considered broken in a cryptographic sense if an attack faster than brute-force existed (and even then it might not be practical - there's weaknesses in AES that effectively reduce key strength by several bits, but it's still well beyond current brute-forcing technology).
In any case, though, guessing passwords (a brute-force attack) is effectively an attack on the KDF - because once you've guessed the correct one, you've got the correct AES key. It's probably the weakest link, but is required if you don't want to enter a long key every time you need to decrypt it.
Oh, I'm not arguing that passwords are bad or anything. I don't want to slap in 256-bit codes every time I want to access my porn folder. Maybe some of the more masochistic folks would get off on that. Just want to point out that the password IS the weakest link.
With current dictionary and rule sets, you really need a fairly large, random password to keep a file secure if you lose control of it, because without that, they don't need a real brute force attack. Dictionaries and rule sets aren't exactly brute forcing.
Also, means your password won't be on a rainbow table if you're using it on a website and someone acquires their password hashes. Well, rainbow tables are worthless with a salt, if we ignore key collision - which we probably can here, since we don't know the desired hash, unlike trying to get passwords from a website's user database. With a good enough KDF, even trying dictionary attacks could take a remarkably long time - while MD5 and SHA hashrates can be measured in hundreds of millions per second, a good KDF could take a whole second or more per hash - remember, slower is better in this scenario (assuming local machine, otherwise you'd probably overload a server that has to spend 1 sec every time someone tries to log in).
Even if it were 1000/sec, it's still far better. And, yea, I agree. The main weaknesses now are probably short passwords, dictionary word (predictable) passwords and poor choice of KDF/password-hash algorithms - security-oriented programs like TrueCrypt tend to not have that particular problem.
As much as we try to make it harder, people still find ways to break in. I think the math is very good right up til the very last part. It would take 380 Tianhe-2 Supercomputers running for the entirety of the existence of everything to exhaust half of the keyspace of a AES-256 You're right that it would require a further 10 (well 9 actually but that's a minor point) of the computers to reduce the time by 1 power, but then it would require a further 100 to reduce it by 1 more power, then 1000 for the next power and so forth. So a further 380 computers would not reduce the time down to the length of the universe. You wouldnt even get down 4 powers. You'd need like 1e38 computers to get down to that level.
That's the problem with massive numbers like this. When they get past 1e10, we just can't fathom how big they are. If you want to be thorough, consider Figure out how long it would take a universe-sized supercomputer to do it.
Assume all matter in the universe is converted into computronium (a theoretical form of matter optimized for maximum computational power) - this would for example be performing computation using the colors of quarks as bits or even using strings if they exist. You'll need the for this calculation. Or you could go with the mass of the sun as comparison.
A universe-sized supercomputer isn't exactly practical given the time delay of propagating information through it. Also you'd need to convert a sizeable chunk of the universe's matter into energy to power the computation. A sun-sized supercomputer or 'jupiter brain' is still within the realm of theoretical stellar engineering. Your calculations have a slight mistake (wrong GPU speed, and ignores dedicated FGPA/ASIC hardware), but, yes, searching through a 256-bit keyspace would take an impossibly long time.
That's why algorithm weaknesses and side-channel attacks are a major focus nowadays, rather than brute-forcing. Brute-forcing is only really effective over a small search space, like a user password. A high-end GPU can typically do about 2 billion calculations per second (2 gigaflops) That's a several orders of magnitude too low.
Let's take a look at some numbers (they might be off by a bit). These are for single precision FLOPS (floating point operations per second): GPU/CPU FLOPS Raspberry Pi GPU Haswell CPU @ 3 GHz (single core) Haswell GPU (Intel HD 4xxx) Intel Iris Pro (Intel HD 5xxx) Nvidia GTX 760 Nvidia GTX 780 Ti Nvidia GTX TITAN AMD Radeon HD 8970 AMD Radeon HD 8990 Even the cheap RPi SoC GPU can beat your 'high-end GPU'! Look, a CPU does so!
Now, this isn't actually indicative of real-world or even encryption performance. Especially since this only addresses single-precision floating-point operations, where double-precision or integer performance may be worse. In fact, (SHA) hashing relies heavily on integer operations,. So integer operations, which don't always correspond to floating-point operations, would be more important. When doing mundane, repetitive calculations (such as brute-forcing or bitcoin mining), the GPU is better suited than the CPU.
That's, again, not quite correct, though the examples are. Whether a GPU is more suited or not depends on the nature of the calculation - whether it can be easily parallelised or not (broken into many parts to run at the same time) - many, most, common operations are strictly sequential and perform best on a CPU.It has nothing to do with 'mundane' or 'repetitive' - a computer has no concept of 'mundane', and everything is repetitive.
Also, keep in mind that a GPU is often limited by memory, and anything that necessarily use a large amount of memory (e.g. Scrypt) will be inefficient on a GPU. I'm not sure if 256-bit AES fits in this category or not.
Also, a lot of encryption-breaking is done by breaking the key-derivation function, which is usually used to convert a password (usually quite short) to the required key. This avoids the need to brute force such a massive keyspace entirely - which is also a reason most modern KDFs are specifically designed to be difficult for a GPU (e.g. Lots of memory, again) See Also, consider hardware-accelerated encryption (on CPUs nowadays) and even FPGAs or ASICs designed specifically to break encryption. Those are far more effective. Even then, they probably wouldn't search the whole keyspace in any reasonable time, but still.
Not only due to the recent rise in ransomware attacks is encryption an important issue. The history of the secrecy of information begins in the grey age where the first evidence is about 4,000 years old. At the time Egyptian scribes used special hieroglyphs to encode grail inscriptions. News – be it about war, important information or simple love letters – was written in such a way that an unintended reader could not grasp the meaning. One of the simplest methods was of moving characters in the ABC alphabet For the key “3”, the letter “D” replaces the value “A” – it moves up the scale of the alphabet by replacing it with a letter three positions forward. In this way “HELP” becomes “KHOS”. The recipient, who also has the key “3”, counts three digits backwards in the alphabet and decodes it into plain text.
Anyone thinking this is children’s games would be deceiving themselves. The Roman general Gaius Julius Caesar encrypted 2,000 years ago messages to the commanders of his troops using this very method. Encryption types In the First and Second World War the German military also strongly depended on the encryption of their orders. In addition to replacing one character with another character (substitution), the arrangement of the characters was also interchanged (transposition), for which a further key was required.
This procedure, which was customary in the First World War, was, however, quickly cracked, as the Allies had excellent cryptoanalysts, who were only concerned with converting encrypted information into legible text. As a result, mechanical processes were developed and rotor cipher machines were built, with different substitutions being possible for each letter. The best-known of these machines was the Enigma used in the Second World War, which was considered uncrackable. However, it did not take long for this encryption method to be cracked by the enemy. All previously mentioned methods use the same key for encryption and decryption, which is why these methods are called symmetric encryption. In the case of, which has existed for several decades, a completely different key (private key) is used for decryption than for encryption (public key). The secure network transmission paths “https” and “SSH” use these methods.
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How to crack encryption Even today, not only mathematicians and cryptologists but also hackers and criminals try to find new ways to “crack” encrypted documents. They often find weaknesses in the encryption algorithm, which enables them to generate the necessary private key mathematically to be able to read the information in plain text. The other way is, as in earlier times, the simple testing of all possible keys. This happens today, of course, with the help of computers, which can calculate hundreds of billions of keys per second – this method is called “”. With the encryption method of Julius Caesar, for example, a person can quickly determine which key was used by testing. The simple approach: the letter “E” is statistically most frequently used, at least in English and German texts, so the exchanged letter should also occur most frequently in the encrypted text.
For longer keys, which are used nowadays, the required time to decrypt naturally increases so that computers are used to test the various possibilities by means of the “Brute Force” method and calculation. What affects the possibility of decryption? In general, the longer the key the more difficult the decoding. The key length is measured in bits. The symmetric encryption algorithm, Data Encryption Standard (DES), which was considered not crackable until the end of the last millennium, used a 56-bit key, which means in order to crack with “Brute Force” 2 56 (= 7927936) keys must be tried.
In 1998 the “Deep Crack” computer, worth 250,000 US Dollars successfully cracked a 56 bit key for the first time in 56 hours. In 2006, the German universities of Bochum and Kiel combined efforts to build a computer that cost only 10,000 dollars, named COPACOBANA and was able to crack 56-bit keys in just 6 ½ days. The successor to the DES encryption method is the “” in versions AES-128, AES-192 and AES-256, whereas the numbers refer to the key length. AES-192 and AES-256 are approved in the US for state documents with the highest secrecy level and are currently not considered to be decryptable.
However, this will not always be the case. In all codes generated by computers, a mathematical decryption solution can be found – at least theoretically. And with the “Brute Force” method it is only a question of the computing speed of the computer(s) used until one finally succeeds. In the case of AES you need a supercomputer, which would cost several billon US dollars. The estimated time to build the machine would take several decades. There are, of course, a lot of other encryption methods currently used. But the methods used to crack the keys are the same: as long as there are no wanted or unintended backdoors or errors in the programming of the encryption and a mathematical solution has not yet been found, “violence” (brute force) must be used.
Can technology keep up with our decryption needs? The NSA (one of the United States secret services organisations) which is the world leader in deciphering, is handling this problem pragmatically: if there is no way to “decrypt” databases a supercomputer is used to try the “Brute Force” method. If, however, it is clear that this does not help the problem is put on standby and left until the technology develops that will make the decryption feasible within a reasonable financial and temporal framework. If, however, it is clear that even this will not be successful, the problem is put on hold and left until the technology is ready so that decryption is feasible both financially and timewise. The next step in decryption will be the quantum computer – then, with the available computing power and speed, the decryption of documents becomes child’s play.
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