March 24, 2011 // 3:26 am - Today Myce.com (linked above) interviewed PS3 hacker
KaKaRoToKS, who states that a
PS3 Firmware 3.60 solution is indeed coming after
reports and videos of a 3.60 JailBreak running code circulated last week.
Below is the the KaKaRoToKS interview in full, to quote:
What are your thoughts on the recent PS3 3.60 firmware cracking video that was uploaded and removed over the course of a day last week? Many dubbed it fake and said it was a debug PS3, but when we chatted with the guy who uploaded it he defended it as real and said it was a retail unit.
I’ve seen the videos, and I also talked to the people who did it. Whether it’s fake or not, I cannot tell as I have not been authorized by the authors to divulge what they did. All I can say is that they said they would never release it, so whether it’s fake or not has no importance, since in the end no one will have access to it.
However, as I’ve said to a few people on Twitter, the hack that was used on 3.55 and lower was unique and Sony fixed it. So, that’s finished and we can’t use that method anymore, but it doesn’t mean that there are no other methods to jailbreak. A solution for 3.60+ will be available soon, so no worries — people just need to be patient.
Most people associate “hacking” with “piracy.” You admit to taking steps to lock out piracy. Is that getting lost in the shuffle here? People assume “hacking” automatically means “pirating.” It seems like piracy is often a “necessary evil” that comes along with the process but then overtakes any other points.
There are four words that people keep confusing: “hacker,” “cracker,” “pirate” and “cheater.” But it’s not the same thing at all.
A hacker is basically someone who “innovates and finds solutions to a problem.” A cracker is someone who uses his skills to steal, scam or harm others. A pirate is someone who just steals copyrighted works without paying for it. And a cheater is someone who uses other’s skills in order to cheat in games and thinks he’s awesome for clicking on a button.
Yes, people unfortunately associate a hacker with a pirate, but it’s not the case at all. In my case for example, I’ve never pirated a PS3 game. I have bought over 150 games for my PS3 in the last 3 years, and I don’t think any of the hackers in the scene want piracy to happen. We all just want to find challenges and bring back the freedom that we are meant to have on our machines.
Piracy isn’t a “necessary evil.” It’s not necessary at all. The only reason piracy happened on the ps3 is because Sony were arrogant and they thought no one could get inside the PS3. But once you install a homebrew application, it has full access to everything. There is no protection inside the PS3 to prevent piracy. The only protection they have is to prevent you from installing a “non-authorized” application. If they secured the PS3 internally, piracy would probably never have happened because no one skilled enough to hack the PS3 would spend time on it!
We take steps to avoid piracy, but in the end, there’s always someone who will implement “backups support”, which is legitimate in many countries but unfortunately used for piracy too.
What has been the public’s reaction to your recent work on cracking the PS3’s firmware? Is it equal amounts scorn and appreciation? Are you getting hate mail from fanboys?
I do get/see hate mail, but it’s quite minimal. There was a huge reaction of appreciation and happiness. Recently though I’m seeing a lot of “stupidity” and “annoyance” : people asking everyday about a 3.60 CFW even though I’ve said 1,000 times that I’m not working on that.
Do you think GeoHot/FailOverflow’s PS3 jailbreaking will have an industry-wide impact come the next round of game consoles? If so, how? Any predictions on how Sony might try to block hacking in the future?
Yes, I think it will. For one, I think that the industry will try harder to make the consoles more secure. Sony will probably try to hire a real security expert, because as we’ve seen from Fail0verflow’s analysis the PS3 was not secure at all. It almost looks like they hired 5-year-olds to build their security! The Cell processor’s architecture is secure however, since IBM designed it, but in terms of implementation of security by Sony, they completely failed.
Honestly, the only reason the PS3 wasn’t hacked earlier is because it supported Linux from the start. Because of how arrogant Sony was – boasting about their unbreakable security – a lot of hackers abandoned it even before trying.
The one effect I’m looking forward to from the Geohot lawsuit is that I believe it will bring attention to the hacking community from the lawmakers in the U.S. and that jailbreaking a game console will be made legal — just like what happened with the iPhone.
Do you believe it’s futile at this point for Sony to combat the hacking?
Yes, it’s futile. Their code is full of bugs, and they can’t fix it fast enough. We have full access to the machines and we will keep creating solutions to whatever they come up with. However, it is understandable that they want to protect their investment and they will of course continue to fight.
I think the only solution for them to close this whole issue is if they bring back Linux support with full hardware access and add a new protection against piracy inside the PS3 so even if a homebrew application is installed it wouldn’t be allowed to do piracy. Then, they will have secured their system, because we’d have no more reason to try to hack it and all the hackers would simply stop.
Considering their reaction to the scene (suing geohot, grafchokolo and others, sending threats to every hacker and trying to enforce the message ‘if you touch your own property, we’ll make your life hell’
, they got a lot of people pissed at their scare tactics. I think some people will try to get revenge anyways, so maybe it’s too late for them.
We already saw one hacker who was offered a job by SCEA (Ed: Android hacker Koushik Dutta) and refused it because of their reaction to the community, and a lot of people are now boycotting Sony. They are already getting payback thanks to their poor community skills. Of course they’ll just blame the loss of sales on piracy, but they should really think of the fact that most of their losses will not be because of piracy but a reaction to their tactics.
How did you feel when your name was listed in a legal motion by Sony for a Twitter subpoena?
Well, I must say it wasn’t a happy feeling. I was quite pissed at Sony for trying to get information on me knowing quite well that they already know all there is to know.
All information about me – my name, email address, where I live and what my job is – are well known already, so I saw no point in them doing that. And considering that all my tweets are public, it makes no sense.
What pissed me off the most was about the Paypal subpoena, because that contains more personal information: credit card information, bank accounts, addresses, etc. But not for me; it was about getting that information from anyone I have had contact with through Paypal. I use Paypal for personal transactions, with friends and family, and having that kind of information sent to Sony simply because they want to screw with us is completely unacceptable. It violates my basic privacy rights as well as the rights of many unrelated people.
Seeing that got me a bit scared of course, but I’d say that mostly it got me very angry. I was thankful to see the judge quash their subpoena. I do not agree to my personal information, as well as the personal information of my friends, to be made available to a corporation like Sony.
Would the allure of hacking games consoles disappear if, as you predict, hacking them becomes legal under the DMCA? Or do you believe that would lead to more interest in hacking them?
I don’t think it would change anything. On the contrary, it might give the opportunity to those who are scared of Sony to actually step up and provide their help.
I don’t think anyone is hacking the games consoles because it’s supposedly illegal under the DMCA. It’s not about going against the system, or revolting. It’s more about freedom and about tinkering with our property– learning and gaining knowledge.
LOL? You can't be serious.
110$ for a game is freaking expensive. Here we pay them around 50-60$.
PS: HeyManHRU, Brazil is still considered as a third world country at the moment : en.wikipedia.org/wiki/Third_World
Obviously not the case. He means to explain why it's not so simple to have 4.00 OFW accept homebrew as he had promised earlier. Even then, there's always hope for an exploit that gets around it.
honored to see the front page
To quote: To popular demand, I have decided to try and explain how the ECDSA algorithm works. I've been struggling a bit to understand it properly and while I found a lot of documentation about it, I haven't really found any "ECDSA for newbies" anywhere.
So I thought it would be good to explain in simple terms how it works so others can learn from my research. I have found some websites that explain the basic principles but nowhere near enough to actually understand it, others that explains things without any basics, making it incomprehensible, and others that go way too deep into the the mathematics behind it.
ECDSA stands for "Elliptic Curve Digital Signature Algorithm", it's used to create a digital signature of data (a file for example) in order to allow you to verify its authenticity without compromising its security. Think of it like a real signature, you can recognize someone's signature, but you can't forge it without others knowing.
The ECDSA algorithm is basically all about mathematics.. so I think it's important to start by saying : "hey kids, don't slack off at school, listen to your teachers, that stuff might be useful for you some day!" But these maths are fairly complicated, so while I'll try to vulgarize it and make it understandable for non technical people, you will still probably need some knowledge in mathematics to understand it properly.
I will do this in two parts, one that is a sort of high level explanation about how it works, and another where I dig deeper into its inner workings to complete your understanding. Note however that I've just recently learned this stuff, so I'm definitely not an expert on the matter.
So the principle is simple, you have a mathematical equation which draws a curve on a graph, and you choose a random point on that curve and consider that your point of origin. Then you generate a random number, this is your private key, you do some magical mathematical equation using that random number and that "point of origin" and you get a second point on the curve, that's your public key. When you want to sign a file, you will use this private key (the random number) with a hash of the file (a unique number to represent the file) into a magical equation and that will give you your signature. The signature itself is divided into two parts, called R and S.
In order to verify that the signature is correct, you only need the public key (that point on the curve that was generated using the private key) and you put that into another magical equation with one part of the signature (S), and if it was signed correctly using the the private key, it will give you the other part of the signature (R). So to make it short, a signature consists of two numbers, R and S, and you use a private key to generate R and S, and if a mathematical equation using the public key and S gives you R, then the signature is valid. There is no way to know the private key or to create a signature using only the public key.
Alright, now for the more in depth understanding, I suggest you take an aspirin right now as this might hurt!
Let's start with the basics (which may be boring for people who know about it, but is mandatory for those who don't) : ECDSA uses only integer mathematics, there are no floating points (this means possible values are 1, 2, 3, etc.. but not 1.5..), also, the range of the numbers is bound by how many bits are used in the signature (more bits means higher numbers, means more security as it becomes harder to 'guess' the critical numbers used in the equation), as you should know, computers use 'bits' to represent data, a bit is a 'digit' in binary notation (0 and 1) and 8 bits represent one byte.
Every time you add one bit, the maximum number that can be represented doubles, with 4 bits you can represent values 0 to 15 (for a total of 16 possible values), with 5 bits, you can represent 32 values, with 6 bits, you can represent 64 values, etc.. one byte (8 bits) can represent 256 values, and 32 bits can represent 4294967296 values (4 Giga).. Usually ECDSA will use 160 bits total, so that makes well, a very huge number with 49 digits in it
ECDSA is used with a SHA1 cryptographic hash of the message to sign (the file). A hash is simply another mathematical equation that you apply on every byte of data which will give you a number that is unique to your data. Like for example, the sum of the values of all bytes may be considered a very dumb hash function.
So if anything changes in the message (the file) then the hash will be completely different. In the case of the SHA1 hash algorithm, it will always be 20 bytes (160 bits). It's very useful to validate that a file has not been modified or corrupted, you get the 20 bytes hash for a file of any size, and you can easily recalculate that hash to make sure it matches. What ECDSA signs is actually that hash, so if the data changes, the hash changes, and the signature isn't valid anymore.
Now, how does it work? Well Elliptic Curve cryptography is based on an equation of the form : y^2 = (x^3 + a * x + b) mod p
First thing you notice is that there is a modulo and that the 'y' is a square. This means that for any x coordinate, you will have two values of y and that the curve is symmetric on the X axis. The modulo is a prime number and makes sure that all the values are within our range of 160 bits and it allows the use of "modular square root" and "modular multiplicative inverse" mathematics which make calculating stuff easier (I think).
Since we have a modulo (p) , it means that the possible values of y^2 are between 0 and p-1, which gives us p total possible values. However, since we are dealing with integers, only a smaller subset of those values will be a "perfect square" (the square value of two integers), which gives us N possible points on the curve where N < p (N being the number of perfect squares between 0 and p). Since each x will yield two points (positive and negative values of the square-root of y^2), this means that there are N/2 possible 'x' coordinates that are valid and that give a point on the curve.
So this elliptic curve has a finite number of points on it, and it's all because of the integer calculations and the modulus. Another thing you need to know about Elliptic curves, is the notion of "point addition". It is defined as adding one point P to another point Q will lead to a point S such that if you draw a line from P to Q, it will intersect the curve on a third point R which is the negative value of S (remember that the curve is symmetric on the X axis). In this case, we define R = -S to represent the symmetrical point of R on the X axis. This is easier to illustrate with an image :
So you can see a curve of the form y^2 = x^3 + ax + b (where a = -4 and b = 0), which is symmetric on the X axis, and where P+Q is the symmetrical point through X of the point R which is the third intersection of a line going from P to Q. In the same manner, if you do P + P, it will be the symmetrical point of R which is the intersection of the line that is a tangent to the point P.. And P + P + P is the addition between the resulting point of P+P with the point P since P + P + P can be written as (P+P) + P.. This defines the "point multiplication" where k*P is the addition of the point P to itself k times here are two examples showing this :
Here, you can see two elliptic curves, and a point P from which you draw the tangent, it intersects the curve with a third point, and its symmetric point it 2P, then from there, you draw a line from 2P and P and it will intersect the curve, and the symmetrical point is 3P. etc you can keep doing that for the point multiplication. You can also already guess why you need to take the symmetric point of R when doing the addition, otherwise, multiple additions of the same point will always give the same line and the same three intersections.
One particularity of this point multiplication is that if you have a point R = k*P, where you know R and you know P, there is no way to find out what the value of 'k' is. Since there is no point subtraction or point division, you cannot just resolve k = R/P. Also, since you could be doing millions of point additions, you will just end up on another point on the curve, and you'd have no way of knowing "how" you got there. You can't reverse this operation, and you can't find the value 'k' which was multiplied with your point P to give you the resulting point R.
This thing where you can't find the multiplicand even when you know the original and destination points is the whole basis of the security behind the ECDSA algorithm, and the principle is called a "trap door function".
Now that we've handled the "basics", let's talk about the actual ECDSA signature algorithm. For ECDSA, you first need to know your curve parameters, those are a, b, p, N and G. You already know that 'a' and 'b' are the parameters of the curve function (y^2 = x^3 + ax + b), that 'p' is the prime modulus, and that 'N' is the number of points of the curve, but there is also 'G' that is needed for ECDSA, and it represents a 'reference point' or a point of origin if you prefer.
Those curve parameters are important and without knowing them, you obviously can't sign or verify a signature. Yes, verifying a signature isn't just about knowing the public key, you also need to know the curve parameters for which this public key is derived from.
So first of all, you will have a private and a public key.. the private key is a random number (of 20 bytes) that is generated, and the public key is a point on the curve generated from the point multiplication of G with the private key. We set 'dA' as the private key (random number) and 'Qa' as the public key (a point), so we have : Qa = dA * G (where G is the point of reference in the curve parameters).
So how do you sign a file/message ? First, you need to know that the signature is 40 bytes and is represented by two values of 20 bytes each, the first one is called R and the second one is called S.. so the pair (R, S) together is your ECDSA signature.. now here's how you can create those two values in order to sign a file.. first you must generate a random value 'k' (of 20 byes), and use point multiplication to calculate the point P=k*G. That point's x value will represent 'R'. Since the point on the curve P is represented by its (x, y) coordinates (each being 20 bytes long), you only need the 'x' value (20 bytes) for the signature, and that value will be called 'R'. Now all you need is the 'S' value.
To calculate S, you must make a SHA1 hash of the message, this gives you a 20 bytes value that you will consider as a very huge integer number and we'll call it 'z'. Now you can calculate S using the equation : S = k^-1 (z + dA * R) mod p
Note here the k^-1 which is the 'modular multiplicative inverse' of k it's basically the inverse of k, but since we are dealing with integer numbers, then that's not possible, so it's a number such that (k^-1 * k ) mod p is equal to 1. And again, I remind you that k is the random number used to generate R, z is the hash of the message to sign, dA is the private key and R is the x coordinate of k*G (where G is the point of origin of the curve parameters).
Now that you have your signature, you want to verify it, it's also quite simple, and you only need the public key (and curve parameters of course) to do that. You use this equation to calculate a point P : P= S^-1*z*G + S^-1 * R * Qa
If the x coordinate of the point P is equal to R, that means that the signature is valid, otherwise it's not.
Pretty simple, huh? now let's see why and how and this is going to require some mathematics to verify : We have :
P = S^-1*z*G + S^-1 * R *Qa
but Qa = dA*G, so:
P = S^-1*z*G + S^-1 * R * dA*G = S^-1 (z + dA* R) * G
But the x coordinate of P must match R and R is the x coordinate of k * G, which means that :
k*G = S^-1 (z + dA * R) *G
we can simplify by removing G which gives us :
k = S^-1(z + dA * R)
by inverting k and S, we get :
S = k^-1 (z + dA *R)
and that is the equation used to generate the signature.. so it matches, and that is the reason why you can verify the signature with it.
You can note that you need both 'k' (random number) and 'dA' (the private key) in order to calculate S, but you only need R and Qa (public key) to validate the signature. And since R=k*G and Qa = dA*G and because of the trap door function in the ECDSA point multiplication (explained above), we cannot calculate dA or k from knowing Qa and R, this makes the ECDSA algorithm secure, there is no way of finding the private keys, and there is no way of faking a signature without knowing the private key.
The ECDSA algorithm is used everywhere and has not been cracked and it is a vital part of most of today's security.
Now I'll discuss on how and why the ECDSA signatures that Sony used in the PS3 were faulty and how it allowed us to gain access to their private key.
So you remember the equations needed to generate a signature.. R = k*G and S= k^-1(z + dA*R) mod p.. well this equation's strength is in the fact that you have one equation with two unknowns (k and dA) so there is no way to determine either one of those.
However, the security of the algorithm is based on its implementation and it's important to make sure that 'k' is randomly generated and that there is no way that someone can guess, calculate, or use a timing attack or any other type of attack in order to find the random value 'k'. But Sony made a huge mistake in their implementation, they used the same value for 'k' everywhere, which means that if you have two signatures, both with the same k, then they will both have the same R value, and it means that you can calculate k using two S signatures of two files with hashes z and z' and signatures S and S' respectively :
S - S' = k^-1 (z + dA*R) - k^-1 (z' + da*R) = k^-1 (z + da*R - z' -dA*R) = k^-1 (z - z')
So : k = (z - z') / (S - S')
Once you know k, then the equation for S because one equation with one unknown and is then easily resolved for dA :
dA = (S*k - z) / R
Once you know the private key dA, you can now sign your files and the PS3 will recognize it as an authentic file signed by Sony. This is why it's important to make sure that the random number used for generating the signature is actually "cryptographically random". This is also the reason why it is impossible to have a custom firmware above 3.56, simply because since the 3.56 version, Sony have fixed their ECDSA algorithm implementation and used new keys for which it is impossible to find the private key.. if there was a way to find that key, then the security of every computer, website, system may be compromised since a lot of systems are relying on ECDSA for their security, and it is impossible to crack.
Finally! I hope this makes the whole algorithm clearer to many of you.. I know that this is still very complicated and hard to understand. I usually try to make things easy to understand for non technical people, but this algorithm is too complex to be able to explain in any simpler terms. After all that's why I prefer to call it the MFET algorithm (Mathematics For Extra Terrestrials)
But if you are a developer or a mathematician or someone interested in learning about this because you want to help or simple gain knowledge, then I'm sure that this contains enough information for you to get started or to at least understand the concept behind this unknown beast called "ECDSA".
That being said, I'd like to thank a few people who helped me understand all of this, one particularly who wishes to remain anonymous, as well as the many wikipedia pages I linked to throughout this article, and Avi Kak thanks to his paper explaining the mathematics behind ECDSA, and from which I have taken those graph images aboves.
P.s: In this article, I used '20 bytes' in my text to talk about the ECDSA signature because that's what is usually used as it matches the SHA1 hash size of 20 bytes and that's what the PS3 security uses, but the algorithm itself can be used with any size of numbers. There may be other inaccuracies in this article, but like I said, I'm not an expert, I just barely learned all of this in the past week.
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SanctumSlayer: I forgive you. No hard feelings.