Hey Guys today let us talk about the mysterious cryptography!!!
As a graduate student at the Massachusetts Institute of Technology in 1996, Amit Sahai was fascinated by the strange notion of a “zero-knowledge” proof, a type of mathematical protocol for convincing someone that something is true without revealing any details of why it is true. As Sahai mulled over this counterintuitive concept, it led him to consider an even more daring notion: What if it were possible to mask the inner workings not just of a proof, but of a computer program, so that people could use the program without being able to figure out how it worked?
The idea of “obfuscating” a program had been around for decades, but no one had ever developed a rigorous mathematical framework for the concept, let alone created an unassailable obfuscation scheme. Over the years, commercial software companies have engineered various techniques for garbling a computer program so that it will be harder to understand while still performing the same function. But hackers have defeated every attempt. At best, these commercial obfuscators offer a “speed bump,” said Sahai, now a computer science professor at the University of California, Los Angeles. “An attacker might need a few days to unlock the secrets hidden in your software, instead of a few minutes.”
Secure program obfuscation would be useful for many applications, such as protecting software patches, obscuring the workings of the chips that read encrypted DVDs, or encrypting the software controlling military drones. More futuristically, it would allow people to create autonomous virtual agents that they could send out into the computing “cloud” to act on their behalf. If, for example, you were heading to a remote cabin in the woods for a vacation, you could create and then obfuscate a computer program that would inform your boss about emails you received from an important client, or alert your sister if your bank balance dropped too low. Your passwords and other secrets inside the program would be safe.
“You could send that agent into the computing wild, including onto untrusted computers,” Sahai said. “It could be captured by the enemy, interrogated, and disassembled, but it couldn’t be forced to reveal your secrets.”
As Sahai pondered program obfuscation, however, he and several colleagues quickly realized that its potential far surpassed any specific applications. If a program obfuscator could be created, it could solve many of the problems that have driven cryptography for the past 40 years — problems about how to conduct secure interactions with people at, say, the other end of an Internet connection, whom you may not know or trust.
“A program obfuscator would be a powerful tool for finding plausible constructions for just about any cryptographic task you could conceive of,” said
Yuval Ishai, of the Technion in Haifa, Israel.
Precisely because of obfuscation’s power, many computer scientists, including Sahai and his colleagues, thought it was impossible. “We were convinced it was too powerful to exist,” he said. Their earliest research findings seemed to confirm this, showing that the most natural form of obfuscation is indeed impossible to achieve for all programs.
Then, on July 20, 2013, Sahai and five co-authors
posted a paper on the Cryptology ePrint Archive demonstrating a candidate protocol for a kind of obfuscation known as “indistinguishability obfuscation.” Two days later, Sahai and one of his co-authors,
Brent Waters, of the University of Texas, Austin,
posted a second paper that suggested, together with the first paper, that this somewhat arcane form of obfuscation may possess much of the power cryptographers have dreamed of.
“This is the first serious positive result” when it comes to trying to find a universal obfuscator, said
Boaz Barak, of Microsoft Research in Cambridge, Mass. “The cryptography community is very excited.” In the six months since the original paper was posted, more papers have appeared on the ePrint archive with “obfuscation” in the title than in the previous 17 years.
However, the new obfuscation scheme is far from ready for commercial applications. The technique turns short, simple programs into giant, unwieldy albatrosses. And the scheme’s security rests on a new mathematical approach that has not yet been thoroughly vetted by the cryptography community. It has, however, already withstood the first attempts to break it.
Researchers are hailing the new work as a watershed moment for cryptography. For many cryptographers, the conversation has shifted from whether obfuscation is possible to how to achieve it.
“Six or seven years ago, you could have looked at this question and wondered if we’ll ever know the answer,” said
Leonard Schulman, of the California Institute of Technology in Pasadena. “The fact that there’s now a plausible construction is huge.”
Too Powerful to Exist
When Sahai started thinking about obfuscation 17 years ago, the first task was simply to define it. After all, users can always learn something about a garbled version of a program simply by feeding it inputs and seeing what comes out.
The most natural, and also the strongest, definition was the idea of a “black box” obfuscator, which would jumble a program so thoroughly that a person with the best available computational resources could figure out nothing at all about it, except for what might be gleaned from inputs and outputs. You could not figure out the value of a password hidden inside the software, unless that password was one of the program’s outputs, nor could you reassemble parts of the program to compute anything meaningful other than what the program was originally designed to compute.
A black box obfuscator, if it existed, would be immensely powerful, providing instant solutions to many cryptography problems that took decades to figure out or in some cases remain unsolved. Take, for example, public key encryption, whose development in the 1970s paved the way for Internet commerce. Prior to its creation, two people who wanted to communicate secretly had to meet in advance to choose an encryption scheme and share a secret key for encoding and decoding messages. Public key encryption allows you to announce a key to the entire world that permits people you’ve never met to send you messages that only you can decrypt. The innovation so revolutionized cryptography that its early developers have been recognized with one award after another.
) generating the 
th term of the sequence. Some special classes of 
, 2, and 4. It is not known how to solve a general recurrence equation to produce an explicit form for the terms of the recursive sequence, although computers can often be used to calculate large numbers of terms through brute force (combined with more sophisticated techniques such as caching, etc.).
