In a previous post I described mathematicians’ ongoing search for key properties of prime numbers. That effort may seem to belong entirely within the realm of pure mathematics; but surprisingly, the importance of primes goes far beyond the abstruse obsessions of ivory-tower mathematicians. In fact, the use of prime numbers underlies some of the most dramatic events in the news these past weeks: the story behind Edward Snowden’s revelations that the National Security Agency (NSA) is snooping on the communications of both American citizens and European diplomats.
While the Europeans have protested about their internal communications being intercepted by the NSA—ironically—the tools that one can use for protection from spying by anyone are readily accessible online, in the professional literature, and in publicly-available manuals and textbooks. These methods all rely on clever uses of prime numbers.
The essentials of these techniques are far from new. The foundations of a program to create codes so powerful that they could not be broken even if an eavesdropper were to use the entire available worldwide computing power were laid more than 35 years ago. The year 1976 saw the development of theDiffie-Hellman key exchange method (named after Whitfield Diffie and Martin Hellman; the names Ralph Merkle, James Ellis, Clifford Cocks, and Malcolm Williamson are often also associated with it); and the following, 1977, witnessed the appearance of the RSA algorithm. Both methods have advanced over the past three and a half decades, but information about their extensions is also readily available to anyone.
How do these techniques work? I will explain both methods here—necessarily in a simplified way. (Those interested in learning more can read some of the articles in the links that appear throughout this post.)
Alice sends Bob a secret message
The Diffie-Hellman key exchange idea has been described in a clear and concise way using an analogy by Terence Tao, whose work on prime numbers I mentioned in my previous post. The idea is as follows. Alice wants to send Bob a secret message (cryptographers prefer to use “from Alice to Bob” instead of the mundane “from A to B”) and she wants to prevent Eve (the “eavesdropper”) from reading it. So Alice places the message in a box, puts a good lock on it, keeps the key, and sends the package to Bob. (If Alice were to separately send Bob the key, there would be a chance that Eve could intercept both the package and the key.)
Bob has no key to Alice’s lock. So what he does instead is to put his ownlock on the box. And he now sends the package back to Alice, locked twice: using both her lock and his. Alice gets the package, removes her own lock using her key, and then sends the box, still safe because it bears Bob’s lock, back to Bob. Now Bob uses his key, opens the box, and gets the message! Each person here used his or her own lock and key—and yet a message was passed perfectly safely from Alice to Bob.
This idea is implemented digitally in the Diffie-Hellman key exchange. The message to be sent from Alice to Bob is a secret number, call it n. Alice’s “key” is an exponent, a, which she chooses, and then uses it to raise n to. So the “locked box with the message” that Alice sends Bob is na. Bob has his own “key,” which is a number of his own choosing, b, that he uses as an exponent. He doesn’t know n or a, but he has na, which he got from Alice, so he raises this number to the power b. He thus sends Alice the “box with the two locks”: nab. Alice’s using her own key to open her own lock means her taking the ath root of nab, which, from the simple math of exponents, we know gives her nb, which she now sends back to Bob. Using his “key,” his exponent b, Bob takes the bth root of nb, and he thus obtains the secret number n that Alice wanted to convey to him.
It is possible to send a secret number from Alice to Bob as I just described, and if the numbers are large enough, one would have a reasonable probability that the number might not be deduced by Eve. In actuality, however, modern implementations of the Diffie-Hellman key exchange use more sophisticated elements to make it more difficult to break the code. And the secret number is not sent from Alice to Bob, but rather deduced by both of them using the formula nab (which, of course, is also equal to nba).
Alice and Bob choose a prime number, which they assume can be known to Eve, or to anyone in the world. Let’s say that this number is 11. They then do all calculations using the mathematical multiplicative group of integers modulo 11 (like a clock going around to 12 and then starting from 1, this group starts to count again after reaching 11). They also choose a base, and let’s suppose it is the number 5. Alice then chooses her secret number, say 3. Independently, Bob chooses his secret number, 4.
Alice raises the commonly-agreed-on base of 5 to the power of her secret number 3, and does the calculation modulo 11. She gets: 53 = 125, but 125 modulo 11 is 4 (it’s the remainder of dividing 125 by 11, which gives 11 and a remainder of 4—it acts like 16 hours in a clock, but this clock is based on 11 rather than 12). She sends Bob the answer, the number 4. Recall that Bob had chosen a secret number of 4, so he raises the 4 he got from Alice to the 4th power, modulo 11, and this gives him 44 = 256, but 256 modulo 11 is 3 (because 11×23 = 253, leaving the remainder 3), which is his final answer.
Alice gets from Bob the original 5 they had both agreed on, but now raised to the power of his secret number, 4, modulo 11, which is 625 modulo 11, which is 9 (as 11×56 = 616, leaving a remainder of 9). She then raises this number to the power of her secret number of 3, again doing this calculation modulo 11. She gets the same number that Bob got, 3 (because 93 = 729, but modulo 11 it is 3, since 11×66 = 726, which leaves a remainder of 3).
Using this complicated modular arithmetic based on a prime number, but essentially raising a number to hidden powers as in the previous section, Alice and Bob establish a common secret number, in this example, 3. Modular arithmetic using prime numbers helps make the algorithm much more difficult to decipher by an eavesdropper.* In reality, the prime number is large, and so are the other numbers. When Alice and Bob use secret numbers 100 digits long, the common number jointly deduced by Alice and Bob cannot be learned by Eve even if she has access to all the world’s available computing power.
Once Alice and Bob have established a common secret number, they can use it as a key to encrypt messages from one to the other and should have a high probability that their communication will not be deciphered by an outsider.
The year after the Diffie-Hellman algorithm was published, three academics then working at MIT—Ron Rivest, Adi Shamir, and Leonard Adelman—came up with a brilliant idea for encrypting messages. What they tried to do was to avoid the stage in which Alice and Bob must create a common secret number, since this stage slows down the communication between them.
The three MIT scientists developed the notion of a pair of keys: a public key and a private key, which are then jointly used for communicating secret messages. The public key can be published and known to all. Its use saves time. The private key is a secret that Bob keeps, allowing him to decipher coded messages from Alice (or from anyone who knows his public key). Bob publishes his public key, which is a large number. This number is obtained when he multiplies together two very large prime numbers, known only to him (they constitute his private key). When Alice wants to send Bob a secret message, she encrypts it using his known public key. But in order to decrypt the message, one would need to know Bob’s private key, which is the two prime numbers he had used to create his publicly-known key. Supposedly, only Bob can do this.
Encrypting and decrypting messages using the RSA algorithm is a complicated mathematical procedure that relies on modular arithmetic and prime numbers similarly to the way they are used in the description of the Diffie-Hellman system above. But it is more sophisticated so that it can allow deciphering using only the private key. The public key alone is useless for deciphering the RSA code.
The essential element of RSA is the fact that the public key is composed of the product of two very large unknown prime numbers. It so happens thatfactoring a number into its prime components is very difficult when the primes are large. (35 = 7×5, a product of two primes, is easy; but 46,324,637 = 5,881 × 7,877 is harder, and primes used in RSA encryption are much larger still.) It is this fact alone that keeps Eve in the dark. She knows the product of the two prime numbers—but she can’t easily (and hopefully not at all) deduce what the two primes are!
Right after the RSA system was invented, Martin Gardner published in Scientific American an encrypted message and a large RSA number, with 129 digits, that was the product of two primes. He challenged his readers to break the code, offering a $100 prize. It took 17 years for the number to be factored and the message deciphered. This was a relatively short period of time—many had expected that it would take an exceedingly long time, and Rivest, Shamir, and Adelman had jested that it could take several “quadrillion years.” The complex operation was achieved using distributed computing with thousands of computers around the world performing parts of the general calculation—thus demonstrating the power of such an approach.
RSA Security, founded by the academics, has since published several similar numbers, and for a time there was a cash prize offered for their factoring into pairs of primes, which the company subsequently withdrew. By now, some of these challenges have been met by mathematicians using distributed computing. Here is one problem that is still outstanding, an RSA number with 210 digits, that has never yet been factored into two primes:
RSA-210 = 245246644900278211976517663573088018467026787678332759743414451715061600830038587216952208399332071549103626827191679864079776723243005600592035631246561218465817904100131859299619933817012149335034875870551067
Obviously, the larger the number to be factored, the longer the time needed to break it into a pair of primes. Beyond a certain length (in decimal digits), the RSA code becomes impregnable and therefore any message based on it undecipherable (in a reasonably finite length of time) by an eavesdropper. The RSA algorithm is widely used today in Internet security.
NSA’s uses and abuses of encryption
In adopting standards for encryption in the United States, and for exporting encryption products, the NSA has pushed for, and succeeded in implementing, legal limits on the size of the numbers used in RSA coding, so that—with its supercomputers—it would be able to decipher any message based on it. Presumably, the Europeans are not bound by these restrictions, and their cryptanalysts should have been able to easily devise an unbreakable RSA code (by choosing primes that are large enough) for use in routine European diplomatic communications as well as protecting their computers from hacking.
And as history has shown, supercomputers are less effective than wide-ranging worldwide distributed computing for breaking advanced codes—but by its very nature, the NSA could never employ the latter. On the other hand, the most recent revelations seem to indicate that one of the purposes of NSA searches is in fact to identify people or entities that use encryption in their communications. If so, all the more reason for the European governments to use established, Western, advanced codes, so as to set themselves apart from terrorist entities, whose codes would necessarily look different. This would actually help the NSA concentrate on identifying real threats rather than wasting resources on intercepting Brussels messages such as: “Pierre, Italian or Chinese for lunch today? Yours, Hans.”
Thus we find ourselves where we do now, in an arms race of encryption and decryption, a world in which pure mathematics plays the key role in helping invent better and better codes. As the codes become more sophisticated, so do the code-breakers, and the cycle perpetuates itself. What is so amazing is that codes that were considered absolutely unbreakable a few decades ago do become breached as the technology improves—but then again, those designing new encryption methods, on all sides, use ever more complicated math to keep a step ahead of their pursuers.
*There are two good reasons for using modular arithmetic. The first is that it acts as a many-to-one function, in the sense that many numbers, when divided by a prime, will give the same remainder—thus making Eve’s life much more complicated (she can’t uniquely reconstruct Alice and Bob’s secret numbers). Using the clock example, if she should overhear that a meeting is to take place at 1 o’clock, she couldn’t tell if it’s a.m. or p.m., or which day. The second reason is that it puts a cap on the size of numbers involved when using exponentials, since (by definition!) without modular arithmetic these numbers grow “exponentially,” and could make computations intractable.
The much-anticipated private solar-powered plane Solar Impulse took off from California this morning on a flight across America that is expected to last approximately two months. From Mountain View the plane will fly to New York without using a drop of fuel, making stops along the way in Phoenix, Dallas, St. Louis, AND Washington, D.C.
The plane sports 12,000 solar cells built into the wings and smaller tail fins. The cells charge four lithium batteries, attached to the bottom of the wings, that
power the plane during the nighttime. The longest nonstop trip the plane has made thus far is 26 hours. The plane could theoretically fly continuously but stops are necessary for the health of the pilot—the plane’s extreme sensitivity to turbulence means piloting it requires intense mental concentration. Swiss co-founders of the project Bertrand Piccard and Andre Borschberg will alternate turns in the cockpit.
Solar cells account for most of the plane’s slight weight, which is equivalent to that of a small car, while its wingspan matches that of a jumbo jet. Unlike a jet, however, Solar Impulse flies relatively slowly—an average pace of just 43 miles per hour—as can be seen in the below clip of its transit over the Golden Gate Bridge.
The current journey to Phoenix is expected to take 19 hours. You could drive that distance in two-thirds the time, but speed is not the point of the flight—rather, it’s meant to bring attention to clean-energy technologies, according to the Solar Impulse company.
And though a feat in its own right, the cross-country flight is primarily a test run for a future flying machine the company plans to build to circumnavigate the world in 2015.
Introversion, it seems, is the Internet’s current meme du jour. Articles on introverts are nothing new, of course—The Atlantic’s 2003 classic “Caring for Your Introvert” still gets passed around Facebook on a regular basis—but the topic has gained some sort of strange critical mass in the past few weeks, and has been popping up everywhere from Gawker to Forbes.
This latest swarm of articles ranges from glorified personality quizzes (31 Unmistakable Signs That You’re An Introvert”) to history lessons (“16 Outrageously Successful Introverts”) to business essays (“Why Introverts Can Make Excellent Executives”) to silly, self-aware send-ups of the trend itself (“15 Unmistakable, Outrageously Secret Signs You’re an Extrovert”). The vast majority of them also come packaged with the assumption the reader understands the basic concept of introversion, and already has a pretty clear idea of whether he or she is an introvert or an extrovert.
Scroll through the comments sections, though, and you’ll find that quite a few readers—even introverted ones—don’t appreciate being put in a labeled box. For every grateful response from a self-professed introvert, you’ll find several responses along the lines of, “No one is always extroverted and no one is always introverted,” and, “I consider myself an extrovert but a lot of these introvert traits apply to me.”
What does neuroscience have to say about all this? Do the brains of introverted people really look and behave differently from those of extroverts? And if so, what might those differences mean?
Introvert v. Extrovert
Before we go any further, it’s important to point out a significant distinction. When Carl Jung coined the terms “extrovert” and “introvert” in the early twentieth century, he emphasized that introverts aren’t necessarily shy or insecure—nor are extroverts necessarily empathic or loving. The distinction between the two, Jung wrote, lies mainly in the fact that introverts get exhausted by social interaction, while extroverts get anxious when left alone. Introverts need solitude in order to recharge, while extroverts draw energy from socializing.
Modern psychologists have added a third category, the ambivert, a personality that combines both introverted and extroverted traits—for example, a ruthless lawyer or CEO who loves to lead but doesn’t crave peer approval. And the Russian psychologist Mihaly Csikszentmihalyi reports that his most artistic patients tended to drift between introversion and extroversion throughout their lives. “[They’re] usually one or the other,” he wrote, “either preferring to be in the thick of crowds or sitting on the sidelines and observing the passing show.”
And there’s evidence that artists and execs aren’t alone in this mutability. Psychologists today generally think of introversion and extroversion as labels for areas of a continuous personality spectrum, just as words like “red” and yellow” are labels for certain areas of the light spectrum. We all draw energy from others at times, just as we all need to recharge with some alone time every now and then. Still, says Jason Castro, an assistant professor of neuroscience at Bates College in Maine, “We know there are a few structural features in the brain that correlate with whether a person is relatively introverted, versus extroverted.”
For one thing, a 2012 study by Harvard psychologist Randy Buckner found that people who identify as introverts tend to have larger and thicker gray matter in certain areas of the prefrontal cortex, a highly complex brain region associated with abstract thought and decision-making. People who identify as strongly extroverted, on the other hand, tend to have thinner gray matter in those same prefrontal areas—which hints that introverts tend to devote more neural resources to abstract pondering, while extroverts tend to live in the moment.
A 2013 study by Cornell University scientists Richard A. Depue and Yu Fu supports this idea. This team of investigators gathered a mixed sample of introverts and extroverts, then randomly split these volunteers into two groups. The first group took the stimulant Ritalin, while the second group took a placebo. The researchers then showed the participants a series of videos such as random landscape shots and forest scenes.
After three days of video-watching, the researchers took away the drugs and showed the films again, and then measured the subjects’ alertness and demeanor. Extroverts who’d taken Ritalin were excited by the films even in the absence of the drug; extroverts who hadn’t showed no change in their reaction to the films. These people had instinctively associated exciting feelings, if they had them, with the videos they’d watched.
But introverts weren’t happier or more alert post-video, regardless of whether they’d taken Ritalin or not. The Cornell researchers think this finding is rooted in a crucial difference between the ways introverts and extroverts process feelings of excitement. Extroverts, the researchers believe, tend to associate feelings of reward with their immediate environment, whereas introverts tend to associate them with their inner thoughts—or perhaps interpret them as anxiety rather than excitement.
Other studies have found that the right-hemisphere amygdala tends to be larger in extroverts than in introverts, as does the anterior cingulate cortex—except in female extroverts, whose anterior cingulate cortices are apparently smaller than those of female introverts. Since other studies have implicated the anterior cingulate in social error detection, this may point to some underlying (but still incompletely understood) differences in the ways introverts and extroverts process social missteps.
Personality differences may have physical effects. Though no one’s been able to measure a difference in reaction time between extroverts and introverts, researchers have found that an introvert’s premotor cortex tends to process stimuli more quickly than that of an introvert.
Still other studies have found that cortical neurons of introverts and extroverts may respond differently to the neurotransmitter chemicals gamma-aminobutyric acid (GABA) and N-methyl D-aspartate (NMDA)—an intriguing finding since both GABA and NMDA have both been implicated in anxiety disorders
In short, although the science of personality is still in the relative Dark Ages, researchers have begun to draw links between what these structural and functional brain differences between personality types might mean in terms of their respective peccadilloes.
But brain differences that correlate with introversion or extroversion don’t necessarily show which of these differences—if any—causeintroversion or extroversion. “We don’t have experiments that really address whether those brain differences play a causal role,” Castro says. “We’re still pretty far from having … a scientific description of personality differences at the level of cells and synapses.”
And it’s important to keep in mind that our brain structures vary from person to person along all sorts of axes that inform our personalities—not just introversion and extroversion. As the science of brain mapping develops, maybe we’ll have a myriad of new spectrums we can use to describe our personalities in terms of our gray matter.
In a first, researchers in Japan have captured the brain activity of a living animal as it pursues its prey.
“Seeing is believing,” says Koichi Kawakami, a molecular and developmental biologist at Japan’s National Institute of Genetics. In the past, he says, researchers have had to infer brain processes indirectly, by watching behavior and surmising what the brain must be doing. That makes his feat a big improvement. “Nothing is better than direct observation,” he says.
For years, researchers have regarded the ability to watch an organism’s neurons fire — at high resolution, as the animal behaves naturally — as the pinnacle of brain observation. In humans, neuroimaging techniques show brain activity, but the methods aren’t fast or fine-grained enough to give a clear picture, Kawakami says. Attempts on mice and rats have been challenging: Their brains must be opened, which is invasive and makes it difficult to capture brain activity in natural conditions.
In most animals, including humans and rodents, the biggest problem is that skulls and brains are opaque. Kawakami and his team cleared that hurdle by choosing the zebrafish as their model. Zebrafish embryos and larvae are transparent, and their genetics are well-known.
The researchers tinkered with the fish’s DNA so that a protein present only in neurons would fluoresce when the neurons were firing. They then watched the neuronal activity of the developing fish at high resolution as it moved about its natural environment, eyeing and attacking its prey.
“The fundamental brain functions are conserved between fish and human,” says Kawakami.
“We hope that we can understand the processes at cellular and molecular levels by studying the fish brain,” he adds.
The New York Times website has gone offline for the second time this month after what the company described as a "malicious external attack".
On its Facebook page, the Times said it was working to fix the problem, which appears to have started at 15:00 local time (19:00 GMT) on Tuesday.
A technical problem knocked NYTimes.com offline on 14 August.
Analysts said evidence showed a group supporting Syrian president Bashar al-Assad was behind Tuesday's attack.
The website was partially back online three hours later, although some users still reported difficulties. During the suspension the New York Times published new articles on its Facebook page as well as a mirror site.
Mark Frons, the company's chief information officer, warned New York Times employees the attack was perpetrated by the Syrian Electronic Army, which backs Mr Assad, "or someone trying very hard to be them".
He cautioned staff to "be careful when sending e-mail communications until this situation is resolved".
Security experts said there was enough evidence to link the hacking group to the problems.
"The NYTimes.com domain is pointing at SyrianElectronicArmy.com which maps to an IP address in Russia, so it's clearly a malicious attack," Ken Westin, a security researcher for Tripwire, an online security company, told the BBC.
In a separate posting on Tuesday, the group also claimed responsibility for hacking Twitter's administrative contact information.
Recently, the Washington Post, CNN and Time magazine websites were targeted in attacks attributed to supporters of the group.
"Media attacks seem to be escalating and moving away from annoying, simple denial of service attacks and toward full domain compromise which, if successful, puts millions of NYT website users at risk," said Mr Westin.
As it did after the first New York Times suspension, competitor Wall Street Journal took down its pay wall and offered its content free to all visitors.
In January, the New York Times said hackers had accessed its website and stolen the passwords of 53 employees after it published a report on the wealth of China Premier Wen Jiabao's family.
Michael Fey, chief technology officer at cybersecurity firm McAfee, said that as long as media organisations play a crucial role in reporting news and influencing debate, they will continue to be targets of cyber-attacks.
"Regardless of technology or tactics deployed, we should expect to see more of these attacks,'' he said.
Google Inc's Android, the dominant mobile operating system, is by far the primary target for malware attacks, mostly because many users are still using older versions of the software, according to a study by the Department of Homeland Security and the Federal Bureau of Investigation.
Android was a target for 79 percent of all malware threats to mobile operating systems in 2012 with text messages representing about half of the malicious applications, according to the study from the government agencies, which was published by Public Intelligence website.
Google did not respond to a request for comment. DHS declined to comment.
By comparison, about 19 percent of malware attacks were targeted at Nokia's Symbian system and less than 1 percent each at Apple Inc's iOS software, Microsoft Corp's Windows and BlackBerry Ltd.
Android continues to be a "primary target for malware attacks due to its market share and open source architecture," said the study, which was addressed to police, fire, emergency medical and security personnel.
(Reporting By Poornima Gupta. Editing by Andre Grenon)
In Peru, home to the spectacular Inca city of Machu Picchu and thousands of ancient ruins, archaeologists are turning to drones to speed up sluggish survey work and protect sites from squatters, builders and miners.
Remote-controlled aircraft were developed for military purposes and are a controversial tool in U.S. anti-terrorism campaigns, but the technology's falling price means it is increasingly used for civilian and commercial projects around the world.
Small drones have been helping a growing number of researchers produce three-dimensional models of Peruvian sites instead of the usual flat maps - and in days and weeks instead of months and years.
Speed is an important ally to archaeologists here. Peru's economy has grown at an average annual clip of 6.5 percent over the past decade, and development pressures have surpassed looting as the main threat to the country's cultural treasures, according to the government.
Researchers are still picking up the pieces after a pyramid near Lima, believed to have been built some 5,000 years ago by a fire-revering coastal society, was razed in July by construction firms. That same month, residents of a town near the pre-Incan ruins of Yanamarca reported that informal miners were damaging the three-story stone structures as they dug for quartz.
And squatters and farmers repeatedly try to seize land near important sites like Chan Chan on the northern coast, considered the biggest adobe city in the world.
Archaeologists say drones can help set boundaries to protect sites, watch over them and monitor threats, and create a digital repository of ruins that can help build awareness and aid in the reconstruction of any damage done.
"We see them as a vital tool for conservation," said Ana Maria Hoyle, an archaeologist with the Culture Ministry.
Hoyle said the government plans to buy several drones to use at different sites, and that the technology will help the ministry comply with a new, business-friendly law that has tightened the deadline for determining whether land slated for development might contain cultural artifacts.
Commercial drones made by the Swiss company senseFly and the U.S. firms Aurora Flight Sciences and Helicopter World have all flown Peruvian skies.
Drones are already saving archaeologists time in mapping sites - a crucial but often slow first step before major excavation work can begin. Mapping typically involves tedious ground-level observations with theodolites or pen and paper.
"With this technology, I was able to do in a few days what had taken me years to do," said Luis Jaime Castillo, a Peruvian archaeologist with Lima's Catholic University and an incoming deputy culture minister who plans to use drones to help safeguard Peru's archaeological heritage.
Castillo started using a drone two years ago to explore the San Jose de Moro site, an ancient burial ground encompassing 150 hectares (0.58 square miles) in northwestern Peru, where the discovery of several tombs of priestesses suggests women ruled the coastal Moche civilization.
"We have always wanted to have a bird's-eye view of where we are working," said Castillo.
In the past, researchers have rented crop dusters and strapped cameras to kites and helium-filled balloons, but those methods can be expensive and clumsy. Now they can build drones small enough to hold with two hands for as little as $1,000.
"It's like having a scalpel instead of a club, you can control it to a very fine degree," said Jeffrey Quilter, an archaeologist with Harvard University who has worked at San Jose de Moro and other sites in Peru. "You can go up three meters and photograph a room, 300 meters and photograph a site, or you can go up 3,000 meters and photograph the entire valley."
Drones, also known as unmanned aerial vehicles or UAVs, have flown over at least six different archaeological sites in Peru in the past year, including the colonial Andean town Machu Llacta some 4,000 meters (13,123 feet) above sea level.
Peru is well known for its stunning 15th century Machu Picchu ruins, likely a getaway for Incan royalty that the Spanish were unaware of during their conquest, and the Nazca Lines in southern Peru, which are best seen from above and were mysteriously etched into the desert more than 1,500 years ago.
But archaeologists are just as excited about other chapters of Peru's pre-Hispanic past, like coastal societies that used irrigation in arid valleys, the Wari empire that conquered the Andes long before the Incas, and ancient farmers who appear to have been domesticating crops as early as 10,000 years ago.
With an archaeology budget of around $5 million, the Culture Ministry often struggles to protect Peru's more than 13,000 sites. Only around 2,500 of them have been properly marked off, according to the ministry.
"And when a site is not properly demarcated, it is illegally occupied, destroyed, wiped from the map," said Blanca Alva, an official with the ministry charged with oversight.
Steve Wernke, an archaeologist with Vanderbilt University exploring the shift from Incan to Spanish rule in the Andes, started looking into drones more than two years ago.
He tried out a drone package from a U.S. company that cost around $40,000. But after the small plane had problems flying in the thin air of the Andes, Wernke and his colleague, engineer Julie Adams, teamed up and built two drones for less than $2,000.
The drones continue to have altitude problems in the Andes, and Wernke and Adams now plan to make a drone blimp.
"There is an enormous democratization of the technology happening now," Wernke said, adding that do-it-yourself websites like DIYdrones.com have helped enthusiasts share information.
"The software that these things are run on is all open-source. None of it is locked behind company patents," he said.
There are some drawbacks to using drones in archaeology. Batteries are big and short-lived, it can take time to learn to work with the sophisticated software and most drones struggle to fly in higher altitudes.
In the United States, broader use of drones has raised privacy and safety concerns that have slowed regulatory approvals. Several states have drafted legislation to restrict their use, and one town has even considered offering rewards to anyone who shoots a drone down.
But in Peru, archaeologists say it is only a matter of time before drones replace decades-old tools still used in their field, and that the technology can and should be used for less destructive uses.
"So much of the technology we use every day comes from warfare," said Hoyle. "It is natural this is happening."
Some of the first aerial images taken of Peru's archaeological sites also have their roots in combat.
The Shippee-Johnson expedition in 1931 was one of several geographic surveys led by U.S. military pilots that emerged from the boom in aerial photography during World War I. It produced reams of images still used by archaeologists today.
After seeing one of those pictures at a museum in New York some 10 years ago, Wernke decided he would study a town designed to impose Spanish culture on the indigenous population in the 1570s. He describes it as "one of the largest forced resettlement programs in history."
"I went up the following year to see it and found the site, and I said, 'OK, that's going to be a great project once I can afford to map it," said Wernke. He said drones have mapped nearly half of his work site. "So it all started with aerial images in the '30s, and now we want to go further with UAVs."
(Editing by Kieran Murray and Douglas Royalty)