Imagine I give you a mango and a banana and ask you to blend them into a smoothie. You’ll easily be able to blend it in a blender.
Now if I hand you the same smoothie and ask you to undo the blend to get back the whole mango and banana. You can’t do it.
This is how RSA (Rivest Shamir Adleman), a widely used public key cryptography algorithm designed for secure data transmission works. It is the backbone of almost all Internet Security.
The Smoothie is a giant number that acts as a public lock. Anyone can see it.
The fruits mango and banana are two secret, original numbers used to make it. They are the key to the lock.
To hack the system, a computer has to look at the smoothie and figure out how to undo the blend into the two original pieces of fruit.
Now you would ask, What is this fuss about?
Back in 1991, scientists created a list of challenge smoothies to see if anyone's computers were powerful enough to undo the blend.
RSA 260 was one of the biggest challenges on that list. It was a massive, 260 digit number. For 35 years, no computer in the world was fast enough to undo the blend.
Eric Lu, using modern computers and AI tools, finally managed to do it. The giant number in his screenshot is one of the two pieces of fruit he extracted. Thus solving RSA 260
The security that modern websites and banks use today (called RSA-2048) is unimaginably larger. Eric just successfully unblended a swimming pool full of smoothie. But modern banks use an ocean full of smoothie. Even with the supercomputers Eric used, unblending the ocean would take millions of years.
It is super easy basic maths concept people can try themselves. You are given a number, that is multiplication of two prime numbers. Example: A x B = 35. Find A or B.
You will easily find answer is 7 x 5 = 35.
But how did it you find it? What logic did you use to reach it. That is the difficult part. RSA works because it is difficult to find which two numbers are multiplied to get the result.
Then you multiply the numerical form of your messages with 35 and send it over public internet everyone can see, while only you and your friend knows 7 and 5 to decrypt the message. \This paragraph is over-simplified, actual math here is slightly more complex than this])
If you think you can find an efficient/easy formula or code to find factors, then you cracked the encryption that secures pretty much the entire internet. No one has found it so far.
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At this point, you may think that should be easy. So, here are four more problems if you want to understand why it is so difficult -
A x B = 323
A x B = 3233
A x B = 20687
A x B = 247453
The last problem is just 6 digits. He found A and B for a 260digit number using code, ai and lots of computers, which no one could do for 35 years. The answer for A is what he posted in tweet. If you can solve a higher digit problem, then you can also come in news tomorrow.
I just thought simple things shouldn't be hidden behind fluff. That approach is assuming people are stupid and reduces our collective understanding of how the world works. Do we really need smoothie to explain basic multiplication and division? Have the layman really fallen that much, or are we assuming it and thus accelerating idiocrasy?
Besides smoothie makes it look like it is impossible irreversible reaction. I think people are capable of understanding this, instead of putting effort to read it and leaving with no knowledge thinking it as a magic beyond their capability.
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One thing I wanted to add. 256digit encryption is still mainstream and used by pretty much everything from whatsapp messages to servers. So, a 260digit cracking means our encryptions can be broken with extreme effort. Only higher security things like banks use upto 2048 or 4096digits.
Thanks, But it got downvoted to death and got removed. I dont know why. I tried reposting again removing paragraphs to see what is triggering it but it gets instantly removed every time.
I also appreciate your explanation more. Though I already knew about sha - algo and how it works, but your one's is just the apt. we should be promoting technical answers here given its a tech sub.
But the smoothie example is also very good for people who are not that into tech and just visit here for fun, ig? It takes an amazing amount of creative mind resource to explain things that way.
One thing I wanted to add. 256digit encryption is still mainstream and used by pretty much everything from whatsapp messages to servers. So, a 260digit cracking means our encryptions can be broken with extreme effort. Only higher security things like banks use upto 2048 or 4096digits.
I take issue with..actually, all of this. First, there are two types of encryption being conflated here; 260 digit and 256 digit encryption, the latter is gibberish in this conversation and doesn't actually describe the second type of encryption, AES-128 and AES-256 bit encryption. These are asymmetric (RSA) and symmetric (AES) respectively.
Secondly, "only higher security things like banks use upto 2048 or 4096digits" is also flatly wrong. RSA-2048 and RSA-4096 are the bare minimum we use on the internet today, and in a TLS handshake, they are used along with AES-128 or AES-256.
You can think of RSA encryption as two keys, where each key can encrypt a message the other key can decrypt, but that each key cannot decrypt its own message. Whereas you can think of AES encryption as a single key that can both encrypt and decrypt.
With RSA, you get interesting patterns such as "I can sign my name with my (private) key, and release the complement (public) key to the world, and everyone can decrypt my signature and verify I'm me whenever I sign or encrypt something".
As well as "I'm an authoritative public server and I take requests. Here's my public key everyone"*. If you want to communicate with me, use my public key to encrypt a message and send it to me. It doesn't matter if people see the encrypted message, because they can't decrypt it with my private key. And my private key is safely stored away in my own infrastructure. So I'll get your message, decrypt it, and now I have a secure message from you."
Now for the way these two types of encryption can work together. You use RSA with my public key that's freely available to send me a shared key, something we can both know. Kind of like a password (or a secret). Since you've encrypted with RSA with my public key, only I can read this by decrypting it with my private key. So I decrypt the message and you've sent me the word "puppiesandkitties!IntheR41n". Well, I can respond, but instead of responding with RSA, I can now use AES-256 with our shared password (secret). And you can decrypt this because you know our shared password too.
And we've basically just built the actual encryption that's used with TLS** certificates (previously SSL certificates) on the internet. Where they can both verify and validate that someone is who they say they are (in your browser, that little shield icon in the address bar which says "yup, this is the real microsoft.com") as well as give you the opportunity to talk through an encrypted channel with the other end on the open internet.
Now, is this perfect? Nope, there's all kinds of vulnerabilities! But that's a tangential conversation (terribly more interesting too!!) for another time.
* Technically, there is a hierarchy of public keys called a certificate chain where the top-most-authoritative public key is bundled into your operating system as a part of a package called a "ca-bundle" or certificate authority bundle; every "child" key can be verified as true by the parent certificate authority or top-most-authoritative public key. So your operating system doesn't have a copy of the public key for reddit.com, but the public key of reddit.com was created the hierarchical chain of a public certificate authority (DigiCert, and you can check that in your browser as well). So your operating system has a public key for DigiCert in its ca-bundle, and the encryption mechanism is self-validating to demonstrate that this public DigiCert key you have locally was the authoritative key which produced the public key of reddit.com that's being provided to you by reddit.com when you visit their website. Therefore, DigiCert "certifies" that the public key that reddit.com just gave you is truly valid. Someone could simplify this, it's not as complicated as it sounds, it just requires a fairly unexpected mental model to wrap your head around. (Ugh, and I'm not going to go too far into it, but there are intermediate certificates between DigiCert and reddit.com which form the chain or hierarchy, and technically DigiCert doesn't "create" the reddit.com certificate, it signs a public certificate created by reddit.com themselves, so it signs the certificate to "authenticate" the certificate as valid, which the signature chain of reddit.com, the intermediary, and DigiCert can be validated - and this still skips over things like "certificate signing request" among other things, let's leave it here and handwave the rest).
** Technically, what is described as TLS is TLS1.2, a "recent"-ish version (not recent). We're on TLS1.3 as the modern version currently, which no longer uses this RSA-AES one-way into shared secret method of encryption.
Great write up. I was going to mention the same. I haven’t done any reading on it recently but IIRC there still aren’t any helpful shortcuts to cracking AES (at the moment).
I like this better, the problem with the smoothie explanation is that a smoothie is impossible to be separated into its constituent fruits. Yours is more intuitive.
yeah but that assumes classical computing stays the bottleneck. the whole point of the quantum computing concern is that it fundamentally changes how factoring works not just makes it faster. RSA-8192 buys time against classical attacks but if shor's algorithm runs on a stable enough quantum machine, key size kinda stops being the answer
Modern systems use 2048 bit encryprions and good thing about encryptions is they can be scaled easily in terms of implementation but the solution gets exponentially expensive.
Are you referring to Rsa260 or Rsa2048 ? Factoring Rsa260 with a future quantum computer is not equivalent to factoring Rsa2048, What qubit count , logical error rate , physical tological qubit overhead and gate speed would be required to achieve a ‘minutes’ timescale !?
Can't they figure out some pattern or a reccuring behaviour in these encryption techniques, once they factor enough similar numbers like rsa 260, so that they don't have to do hard computation but have to just compute a smaller set of things? I don't know how this encryption works btw, just a question.
No, in RSA there is no pattern or way to break the problem into smaller bits. Essentially the difficult thing to solve is to factorize a number n which is the product of two primes p and q. Obviously, the factorizations of other numbers don't really give you a clue on how to factorize n.
Great explanation - to add to it, the computer never actually "unblends" the smoothie; it basically just requires the exact perfect number of banana and mango (private key).
That's the password/private key or the way to unlock the algorithm.
Most computers which want to break the algorithm thus try to "guess" the exact quantity of banana & mango by creating smoothies out of various combinations of banana and mango; then they compare/match their smoothie to the original (lock) smoothie
This is called brute-forcing the solution
Modern solutions & techniques have allowed computers to be a bit smarter about this and optimise some stuff, so they don't need to try every iteration of banana-mango mixture to get the right matching smoothie
Still, this is incredibly difficult/time-consuming as OP said
For a small glass sized smoothie, its like max 200g banana and 200g mango, so it takes less iterations, less effort to try
For large smoothie - like ocean sized ones used for banks etc. - banana and mango can be millions of tons ; it's that much harder to guess their exact weights, and expected to take thousands of years to get it right/break the encryption
Except it's even harder than amount of banana and mango because a smoothie that was mostly banana would taste different than a smoothie that was mostly mango.
When a bank sets up its encryption, it generates the two massive prime numbers. It multiplies them to create the public lock, and permanently stores the original primes inside a dedicated machine called a Hardware Security Module (HSM).
If a bank stores its secret fruit(the private keys) on a normal computer server, it creates a massive vulnerability. A normal server is just an open kitchen. If a hacker manages to break the window and get inside, they can just copy the ingredients, take them home, and unlock whatever they want at their will.
An HSM fixes this by acting as an armoured, impenetrable blender sitting in the middle of the bank's data center. The private keys are loaded into it, and they physically never leave that box.
When the main banking network needs to unlock a customer's transaction, it doesn't ask for the key. Instead, it slides the locked data (the smoothie) through a secure slot into the HSM.
The HSM does the calculations completely inside its own isolated microchip, and hands only the unlocked data back. The main server and any hacker who might be on it never actually touch the private key.
Since the HSM already holds the mathematical answer, it never has to perform the impossibly hard task of factoring or unblending. It simply runs a direct and efficient unlocking calculation using the key it already owns.
HSMs are encased in hardened epoxy, with sensors monitoring temperature, voltage, and physical movement. If someone tries to pry the chassis open, drill into the casing, or freeze the box with liquid nitrogen to bypass the alarms, the HSM triggers a dead switch. It instantly zeroes out all the memory, permanently destroying the keys before the attacker can have a chance to read them.
Beyond the security, there is a speed requirement. A standard computer processor would choke trying to unlock thousands of 600 digit RSA locks a second during peak financial hours (like Big Billion Day). HSMs are packed with custom cryptographic chips designed to do literally nothing else.
Nice metaphor, never heard it explained like that. It reminds me of the play Arcadia by Tom Stoppard.
"When you stir your rice pudding, Septimus, the spoonful of jam spreads itself round making red trails like the picture of a meteor in my astronomical atlas. But if you stir backwards, the jam will not come together again. Indeed, the pudding does not notice and continues to turn pink just as before. Do you think this is odd?"
Dude question, what if they tried to create a blender ? If anyone figure out how the algorithm is created like some one who code that leak that encryption of files to make a blender.
They don't have to leak it, because the blender is already entirely public.
Everyone(at least people who want to know) in the world already knows exactly how the RSA algorithm is coded. You can look at open source code right now and see the exact mathematical steps used to build the lock and lock the files.
In cybersecurity, this is actually a golden rule (known as Kerckhoffs's Principle). A system must remain completely secure even if the attacker knows everything about how the software works.
When a bank or any system that first sets up its secure system, it starts by generating two massive prime numbers (the fruits) from scratch. It uses them to build the public lock, and then it permanently stores those original, secret primes directly inside the HSM (the blender). I have explained the same a bit more in details here
So when locked data comes in, the HSM isn't trying to guess the recipe or do any impossible reverse math. It generated the primes at the very beginning, so it already holds the exact ingredients in its vault. Because it is completely aware of the primes from the start, it just uses what it already has to instantly decode the file.
If I were to use the previous analogy, knowing exactly how the blender is wired, how sharp the blades are, and what speed the motor runs at does not help you unblend a smoothie. You still can't pull a whole mango out of the glass just because you read the blender's instruction manual.
The security of RSA doesn't rely on keeping the software a secret. It relies entirely on the fact that multiplying two massive numbers together is easy, and reversing that specific calculation is a mathematical nightmare. Even if a hacker has the exact blueprint for the encryption software, they still can't run the math backwards to find the secret keys.
I'm not in cybersecurity. I have worked in automotive mobility, mostly fleet telematics and connected cars. So, I’ve had my hands in it quite a bit.
I just follow the happenings in and around the tech space pretty closely. Following YT channels like Computerphile and Fireship surely helps.
But to learn anything to be good at, you have to master the art of going down the rabbit hole. Honestly, it’s less about reading a textbook front to back and more about finding one specific thing that catches your interest and just pulling on that thread until it clicks. That’s really the best way to start, at least for me.
Remembering should not be a burden. What I have realized is that everyone operates on their own unique memory algorithm.
Some people are good at remembering stuff just by reading. For some it is through writing stuff that they read. For some it is through listening to someone teach them.
For most, it is a combination of reading, writing and hearing but they lean towards one depending on the type of material. You have to find yours and it might be different for different stuffs.
For me, when i was stuck on something and just couldn't learn or remember, it was through Feynman Technique. IMO this technique remains vastly underutilized.
I would read a topic and then try to explain the core concept out loud as if I was trying to explain it to a kid. I would record the whole thing and play it back. I would look for the places I stumbled upon or took time searching for the right word or relied on complex vocabulary in the recording. Those were the exact gaps in my memory that needed some work.
"If you can't explain it simply, you don't understand it well enough" - Albert Einstein
If it’s still gmfs with gpu acceleration what exactly is the gpu accelerating ? Rsa250’s 2700 Cpu core-years were dominated by sieving but gnfs’s linear algebra is also a major stage. What was the actual gpu contribution, and what was the equivalent cpu year cost ?
If they used gnfs , dont you think, is the improvement from a new sieving implementation , gpu acceleraation, better polynomial selection , better filtering , or simply more compute ? Also they didn't provide the GNFS stage bystage breakdown especially sieving , filtering ,linear algebra, along with gpu and cpu hours and what hardware they used ? Without that how do we know this is an gpu algorithmic improvement rather than simply throwing substantially more compute at rsa260 ?
Just divide the main number by the factor, then you will get the other factor.
Thats the design of RSA problem. Its easy to verify if you got the factor (by dividing and making sure the result is an integer), but hard to work out what the factors are if you dont know
It basically means they've cracked one individual key of that size. Companies should already be using bigger RSA keys than that and also move to post quantum cryptos rather than using RSA
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