RSA-129 - Numberphile 

This man is "R" in "RSA"? Wow, thank you, numberphile!

$100 for 40 quadrillion years' work. Flipping heck, that's nowhere near a living wage.

It's worth mentioning that the RSA algorithm (under a different name) was known to the US/UK governments close to 10 years before RSA discovered it. Cliff Cocks was technically the "first" person to discover public key using prime numbers (though RSA discovered it independently as well).

oh my goodness this is the first time I've seen a live video from "the R" from "RSA"... every student or former student of computer science has run into RSA sooner or later. This is just great. Thank you!

When you learn about these guys in books and powerpoints in uni, which you pay a shitload for, and then get a lecture by the guy himself for free on the Internet. Praise kek

"$100 for that much computer time was really quite a coup" That gave me a good laugh haha

Thanks Brady for once again getting a great interview with yet another legend!

I grew up playing with this guy's RC4 algorithm. Neat to see him interviewed. Thank you Numberphile!

Who else imediately spotted the P = NP on the blackboard at 1:20?

1:19 The famous RSA trio had already proven P = NP on a classroom chalkboard decades before it became a millennium prize problem.

Typo at 5:24 - unless ScienTITific American is a real journal?

Back in the day in university learning about cryptography I would never have dreamed about one day seeing the 'R' in RSA talking in a youtube video about how they came up with those famous numbers. It feels like witnessing an important part of computing history. I'm so excited about this, thank you very much for doing this, I love your video 💙😭

Thanks for returning to Numberphile Ron! Please come back! We want to know more about the other mathematics you do!

Some years ago I wrote a novel based on the idea that in the 13th Century, Roger Bacon devised a method for quick factorization, and when this method was rediscovered in the present day, it threatened to break RSA. Couldn't sell it to a publisher though. Too much maths :(

Brady: How much prep do you do before interviewing people like Professor Ron Rivest? I enjoy how you ask "simple" questions to get things rolling, then dive in a bit deeper on the follow-up. Well done!

There also a sum who caracterise this number, rsa-129= a+2sqrt(ab+1)+b with ab+1 is a perfect square and 0

I believe there's already a number called "one twenty nine"! I can't remember which one though...

A. Lenstra is actually one of my professor

I'm watching this with spare time in my math class haha

Hi Numberphile, french fan here! I wondered if you guys would be interested in having someone to translate some of your subtitles in french (particularely this one, but others too). You have a lot of interesting videos I'd love to share with my high school students, unfortunately their english level isn't always enough to understand everything (or anything for some ^^). Thanks for reading me, I hope to hear from you soon. Bye!

I have seen this man in previous Numberphile videos but had no idea he was Ron Rivest from RSA! Amazing!

Hey random people reading comments, have a great day!

114381625757888867669235779976146612010218296721242362562561842935706935245733897830597123563958705058989075147599290026879543541st

Arjen Lenstra was my professor at EPFL, it was such an honour to attend his lectures!

This Channel is gold for CS and Math Students. Lots of love from India

Oh my goodness, an inventor of RSA, RC*, MD* and randomised partial checking? This man is a god!

I'm happy because for once I realized that I already knew something.

Watching this exactly a year after it was posted! Clicked on it out of pure interest!

Just read the description... You reckon it took 17 quadrillion years to solve? doubt it, Earth is only 6000 years old.

If you're reading this, have a Great day! 😄😄😄

11438(etc) : Number of tweets using the word "tremendous".

This guy is Ron Rivest. The R in RSA. Wow. This is such an honor.

I remember stumbling on an article by Helleman in the August 1979 issue of Scientific American called "The Mathematics of Public-Key Cryptography" as a young trainee programmer in the early 1980's. I used that article to implement a (fairly amateurish) public key encryption system in IBM Basic Assembler Language that ran (really slowly!) on an IBM 3031 mainframe. I still have the source code, but unfortunately it is on 9-track 6250 bpi round magnetic tape - and I have no way to read it to find out just how amateurish my effort was! Of course, at the time I had no idea how important public key cryptography would become, and so it is kind of annoying to not have proof that I once dabbled in leading edge technology

I'm studying at infosec faculty and I'm pretty sure we actually were told about this number and people and story behind it. Awesome.

I wonder how many viewers have never actually heard hardware making the modem sound that starts around 4:20 into the video. Ahh, the joys of dial-up connections. Those were the good-old days ... NOT!

what a great insight into the early development of a method almost everybody uses when connecting to the internet today! Do more on cryptography :)

You independently reinvented the algorithm. It was developed at GCHQ by Clifford Cocks. Deleting if mentioned later.

Second question: Can we use Dr. Tokieda's ruler-method to generate factor pairs? Find the square root of your large product of primes. Find the primes to either side, multiply. If too big, move the smaller one down the list of primes. If too small, move the larger up the list of primes...

Oh one of the RSA here !! Mr. Rivest ! :) I always was fascinated by his team's work ! very interesting topic ... then would such algorithm in the few coming years be substituted ?! technology actually advances in a way totally unexpected and unpredictable @_@

one of the better numberphile videos in recent history

Fermat's method of factorization generalizes to all figurate numbers.

i remember the part of the challenge that had integer partition generated numbers, hundreds of them i believe from 100 digits to 1000 digits. I was someone that even got published for factoring one of those, a really small number times a really large one.

Please more videos on cryptography! !!!!!! encryption, etc! Thanks. He puts the R in RSA.

I don't know what to think about the P = NP in the background at 1:18

In case anyone's curious, here's the message that RSA-129 encrypted: "The magic words are squeamish ossifrage." Also, Brady et al. -- have you ever touched on the seeming paradox of one to the power of infinity being undefined? Logically it should be 1, but...

It has been said that HP-50g is a computer as it can handle as large number as the memory can hold. But on the other hand it is a calculator as it is allowed to be used in school tests.

I am Brazil, factoring the prime number is taking the number multiplied by all the odds before it, from top to bottom, there will only be 1 that is prime and another is the rest that is a prime number.

What a humble genius!

what a warm and smiley cryptographer

I KNOW I KNEW THAT PHOTO WITH 3 GUYS AND "P = NP"! IT IS RSA!! How could I not have noticed? An absurdly large integer as the product of two huge primes together with a smaller number...

Intriguing way of attracting people's minds towards maths reality

for all primes numbers p above 1 and below RSA-129(r), if r/p is in primes: return (r,p)

Wow, this is one of the people who I can thank for RSA keys for my frequent SSH work! I knew the very basics of the RSA keys, but this is a great background. Thank you for this video. How long would it take to factor RSA129 with a modern top of the line single system? would AVX 2.0 make this far easier?

When he said “decimal digits,” I thought he meant decimal in the common meaning of the word for most people. I had to replay it twice to understand what he was saying.

I wrote a little prime factoring program back in the 90’s. You put in the number of your choice and it spits out a list of the prime factors. So in essence that is what is needed to find the factors of your number. The program couldn't digest that many digits though. Fun! I'm nowhere to being in your league though. Of course.

Without seeing the answer Id solve by using a computer to iteratively converge down to the solution, i.e. multiply large primes if the product is too small try larger ones, if the product is too large then try smaller, basically it would require some computer programming skills to write the correct program

The legends! Learnt these guys from my cryptography course!

I love how happy he is talking about this =P

f(x)=(x^2) +-2x +-[3-cos(x.pi)]/2 Any value for x (except 0 which gives 1)atleast 1of the 4 equation will generate a prime. Why this happens?

the question is there more then one answer. Well, if you look at the number and product. Solution should of been more apparent. 129 digit answer. 66 digit * 64 digit prime if I counted it right then its aprox. Take into account the rule of zero's a given answer, you can rule out swaths of numbers. Also useless combinations, relating to "end" and "start" product of the number. Such as How many numbers multiplied give 1. 1*1, 1*7, 3*7 9*9... etc of course all even combinaions are thrown out because its not a prime. that along eliminates the req considerable. working backwards one can narrow how 541 is created from a small number set simply be seeing the reverse operation. If product end is 541. Say if 9*9 was used, 81 1 is the result carry the eight want result is 4. We find that even less numbers exist to create it, and possibly a non combination later. So in doing chunks of the product backwards, with remainder carries, one could find the digits that comprise the p and q. Although one might not know the p and q. doing this method would eliminate many possibilities. What you have.. after sometime is end up with a few variants.. but like password it eliminates itself, because of its product and those multiplied are its prime. So 533 and 577. would appear as one of those variants of course one can verify and eliminate primes that are not part of the variants which intern isolate the and q further. Not sure a computer was needed for the solution... Since a list of primes exist. the law of zeros is that and since its primes multiplied. Its not 1 digit *129 digits, or 11 digits * 119 digits. the result was 66 digits*64 digits to give us the 129 digits needed. IN this case digits are added, but written out they would be multiples of 10's. 66+64 =130 digits.. now did I add wrong.. Who knows... anyways cool problems thats my thoughts.

Him: your calculator can't handle this easily Me: Uses BigInt in powershell to calculate it

Wonder why they chose their initials to be in that specific order, instead of alphabetical order...

Who else thinks Numberphile should make a video showing how they make their videos and how you can do the same and submit them to a specific website in which they can of videos on? Or at least to have a channel of your own like this one?

Can we create a candidate list of all likely primes (with a certain number of digits), and then just multiply the last few (3-ish) digits until a combination works to find the last few digits of the target number? Then once the candidate list is complete, double the number of digits that we care about, and rinse & repeat until there is only one possible combination? It seems like this would be much faster than trying to multiply out the whole prime values...

read the girl with the dragon tattoo!! They're 4 awesome books involving this

Nice Mighty Black Stump cameo

i got a loop running just picking random numbers and multiplying them to see if i can find it with blind luck.

Brady, you really need a mic on you, if you are to be heard when asking questions from behind the camera. Apart from that, another really interesting video.

What if you multiplied 100 prime numbers together. Then you randomly picked 2 factors of that number. The cracking of the code would become harder because not only would you have to factorise the number into it's primes, you'd also have to find the unique combination of the 100 primes. There are approximately 2^99 ways to split the number into two factors.

Why did they offer a $100 prize for the factorization? Seems kind of pointless.

Numberphile is poaching from computerphile now.

I have an alghorithm for factoring number as product of two primes with success of 50%.Pretty fast...

that must be the most satified 100$ ever recieved.

Wait, so i can just create a 300 digit P and Q number by adding 1 or other tests to find the closest prime number and then multiply the 2 and get a massive number that not even supercomputers can figure out the original numbers that generated that number?

this guy is a legend

u should touch on digital rooting and the vedic square. 9!!

But isn't the symbol for a random prime number capital pi?

Excellent video from the creator!

Why is it easy to determine that p and q are prime but difficult to find the factors of pq? Seems like you would need to find the factors of p and q individually to know whether they are prime... Is it just that pq is much bigger?

I have one of this guy's textbooks on my desk right now :)

3:11 If you were Brady, we would only need to break into his house, get to his computer desk and then find the notebook where he keeps this sort of stuff.

"...the cheapest purchase of lots and lots of computer time." Well played.

Can we try and do the most people solving the rubix cube at once ?

I was thinking that I could write code in an hour or so to solve this (but the time taken to execute said code would be a bit larger.)

This seems fairly easy to solve. Just take the list of all known prime numbers and start dividing them in.

I just learned about RSA in school and suddenly Numberphile comes along and has the guy who invented it! Creepy coincidence...

Is RSA-129 a method/postulation, by which 128BIT OS's can be used as a 'Virtual-129Bit-OS' on naturally-limited occasions, by creating '1-Virtual-Bite' from all other 128Bits, on uncompressing the data? To throw off all 128Bit-And-Less-Malware and All-128Bit-And-Less-Hacks?

Can someone solve this:How many rectangles are there in a 5x7 rectangular network?

see you created a critical table also known as the payment table where you restrict a one Pacific or large number then you'll end up going down the actual chart which indicates a permit wants it spread out these particular numbers in this chart have you tried a reverse technique of this chart by turning the chart upside down and working from a small number tours a big number multiplying or dividing or taking away

Ron Rivest is a genius.

great lecture!

I like how numberphile can make an interesting video out of algebraic math.

I'm pretty sure it wasn't cracked earlier due to the lack of incentive dollar wise.

I would love it if the answer was "we just put 129 random digits, and that's it".

This guy is a legend.

Was the cheque ever cashed? or kept for sentimental reasons?

129 decimal is less than 512 bits. 1024 was impressive last decade and now 2048 is considered minimal acceptable security.

Did i just notice the sneaky appearance of the mighty black stump in this video?

Awesome Video!!

Fantastic content thanks for sharing . What does he mean by 'rolling the dice' ? Obviously it's a metaphor but I'd like to understand what they did exactly .