Largest Prime Number

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yogi
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Largest Prime Number

Post by yogi » 14 Jan 2017, 15:08

The largest known prime number is 2^74,207,281-1 and was discovered by Dr Curtis Cooper at the University of Central Missouri. That's more than 22 million digits long.
:thud:

http://www.bbc.com/news/technology-35361090

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Kellemora
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Re: Largest Prime Number

Post by Kellemora » 15 Jan 2017, 14:04

Say what?

From the article definition:
"Prime numbers - such as two, three, five and seven - are divisible only by themselves and one."

Can you give me an example of a number that is not divisible by itself or one?

Any number divided by itself will produce the answer of 1.
Any number divided by 1 will produce the original number.

I think they left out part of the definition. Composite numbers can be divided by other numbers besides themselves and one.

OK, maybe I misunderstood the word "ONLY" in the original definition, doh, hi hi...

The way I think, it seems a prime number would be easier to crack than a random number sequence. If you know it is a prime number, that eliminates one heck of a lot of possible combinations.

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yogi
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Re: Largest Prime Number

Post by yogi » 16 Jan 2017, 06:00

Prime numbers are important in the process of data encryption. I could not explain to you why that is the case, but this latest discovery has 22 million digits. It's not a useful number because technology isn't good enough these days to be able to fit that many digits into any known math processing unit we have. That will change when quantum computing is wide spread, all of which is why it is an important discovery.

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Kellemora
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Re: Largest Prime Number

Post by Kellemora » 16 Jan 2017, 13:58

Many years ago, I used to dabble in cryptology as a hobby.

I figured out the codes used to generate the Missouri Drivers License number.
Had a lot of phun knowing that one, as I could tell folks the first four and last four digits of their driver license.

I realize encryption is a whole lot different than cryptography.

Many things put into code are not as secure as folks think they are.
Even when using layered codes of two or three levels, most of the time it is self-defeating, because it can still be broken using only a single layer to do so. In most cases it is simple letter substitution, so no matter how many times you duplicate the process to create layers, it is still simple substitution.
The hardest ones to figure out are those that use a phrase of random length words associated with a number then back to a letter again. Although hard, they were still solvable, if you wanted to spend the time to do it. This was back before computers of course.

We can push a button to encrypt our hard drives, even the NAS has this option.
But what happens when the computer breaks and you move the drive to a new computer?
Can the data be recovered? I don't know and don't take that chance, hi hi...

Just food for thought here. How many people are involved in the development an encryption technology?
Would not any of those people be a weak link in the security of the code they developed?
After all, they would know the formula to both encrypt and decrypt whatever their program encrypted.

Have a great day Yogi!

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yogi
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Re: Largest Prime Number

Post by yogi » 16 Jan 2017, 15:11

You all know about encryption keys, right? That key is used in an algorithm to scramble the data. Thus, if you move the encrypted hard drive to another computer, you will need two things: the key and the correct algorithm. Windows has something called Bit Locker which takes the unique id of the memory device into account in it's encryption scheme. That's why it's considered easier than most to figure out. Everybody knows how to do it. If you take that Bit Locker device to a Linux machine, the UUID will be different (I'm only 90% certain there) and of course you will not be able to read the data.

Somebody, or a group of somebodies at Microsoft came up with the Bit Locker algorithm. It's not a big secret outside of Microsoft, but of course they are not going to spread it around willingly. In any case, people who know how Bit Locker works don't have any more of an advantage than you or I would when it comes to breaking the code. The UUID, your key, and I'm betting some prime number, are all unknowns that are part of the scheme. Also, it's not a simple letter swap. We are talking about scrambling the order of the individual bits that compose the ASCII characters. Good luck with trying to substitute that kind of scramble.

There are standards out there for encryption. The FBI, CIA, NAS, and everyone else knows what those standards are. Again, they may be much more complicated than Microsoft's Bit Locker, but there are a lot of missing parts and variables to take into account. Obviously some people can do it, and have. The latest trend is to only store part of the code on a given server. The other parts are stored on other servers, maybe a dozen altogether. Each segment has it's own key so that you would need to know a dozen keys to get at the data. But, you better do it quick because the segments are continually being swapped among the server group members. Trying to keep track of that kind of hodge podge isn't easy for your average hacker. Some Chinese or Russion military dudes may have it down pat, but It's hard to believe anyone else would.

Encryption isn't as simple as it used to be and what you read about in the papers these days are break ins due to human stupidity not military intelligence. It's called social engineering.

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Re: Largest Prime Number

Post by Kellemora » 17 Jan 2017, 12:24

I can see the importance of encryption for many things, like banking, finance, and some personal data.
What I don't understand is why bother with any type of encryption of public data intended for everyone to see anyhow.
Unless this is to protect the users account data from being pulled off the transmissions to like a website.
But is the data encrypted before it gets to the website?
Like I log into Farcebook and post a public message. Hopefully they would have my log-in info secure. But I could care less about the message I'm posting to the public. Everyone can read it anyhow.

As far as the data on my hard drives here at home, my most sensitive data, such as accounting and client records are stored and backed up on a machine that has no connection to the Internet. Only recently did I start trusting my own machine to machine LAN, blocked from accessing the Internet on two other use specific machines.

I know you think I'm paranoid about my data. Perhaps I am, but my redundancy has saved my tail more than once, hi hi...

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Re: Largest Prime Number

Post by yogi » 18 Jan 2017, 08:24

Why bother? Encryption makes life more difficult for the identity thieves of the world. Encryption validates the data to be genuine and from the expected source. Encryption protects sensitive data from being casually observed in transit. The fact that data is transmitted over a public network does not automatically make it public domain. At the moment the Internet is a utility similar to telephone wires. Does use of that public utility mean your phone calls should not be protected? Yes, all those things can be defeated and intercepted. Nothing is perfect.

My greatest concern is not over hackers and data thieves. I'm very concerned about the people and organizations we trust with all the public information we give them regarding our private lives. When they use that information to their financial benefit without my permission, then I'm thinking there are some issues of ethics that need to be addressed. We can't expect Facebook to keep the photographs of our young daughters posted therein out of the hands of perverted stalkers. But why do they feel they have a right to use that picture as a means to generate advertising revenue? Telling me that it's part of their TOS doesn't make it any better.

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Kellemora
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Re: Largest Prime Number

Post by Kellemora » 18 Jan 2017, 13:22

I hear ya Yogi!

I've been on the radio since I was 10, got my first Ham license when I was only 12.
I understood fully that anything I said over the air could be intercepted and used by anyone.
After all, they are the public air waves and travel through space, houses, and your bodies for that matter.

I've been just as cautious when using a landline telephone, because anyone could tap into the lines.
And I view the Internet the same way. If you put it out over the Internet, it is out there forever.

The key word here is forever...

What encryption schemes they came up with over the years to make using the Internet safer, becomes old hat in a very short time. The schemes get broken, and all that once secure data is now easily accessible.

They keep building better mousetraps, but all the old data is still out there, using old encryption techniques that a child can pick up a program and access it all.
How many things did you order on-line with a credit or debit card in the 1990s?
Have you changed banking account and credit card numbers since let's say 1999?
When did newer encryption come out? Is your personal data from a decade ago still out there? Of course it is! How is it protected?

My point here is, no matter how good the latest and greatest methods of data protection are, it only applies to today.
And to the best of my knowledge, almost all early forms of encryption have already been hacked, or the method to crack them solved and made public.

Remember when 5-1/4 floppies were protected using a Spiral technique. That lasted all of about 6 months before we had programs to defeat the spiral so we could copy the data from the disks.
A lot of books come with DRM locks. Now, simple to crack!

All I'm saying is, if they build a better mousetrap, it will become obsolete as soon as the hackers figure it out.
Then all the data protected by that technique will be available.
In other words, there is no true protection for any of us...

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yogi
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Re: Largest Prime Number

Post by yogi » 18 Jan 2017, 14:59

Your observations are only partially true. The air waves are indeed free and anybody with the proper receiving equipment can intercept any of the messages out there. While it's true that you can listen in to cell phone conversations, it is illegal to take action on what you hear. You are free to copy down my credit card information, for example, but it is against the law for you to use that information to purchase merchandise.

It's also true that there is no known perfect encryption system, yet. I don't know that they have all been cracked, but the encryption theory is all out there in the public domain for anybody to learn. Again, using decryption for nefarious purposes is not legal. Being illegal will not stop a hacker, I admit. However there are many schemes out there where it would not be worth the time it takes to crack the code. Some schemes require equipment that has not been invented yet to break.

The best data security is only as good as it's weakest link. Those banks and financial institutions to which I gave my personal information thirty or more years ago probably still have it. Their security systems, however, are not thirty years old. I can guarantee that. The unfortunate reality is that not all banks have modern protection. There is no protection at all on IoT devices, which is why the Internet was shut down a couple months ago. It's not like the data out there cannot be made safe. People we trust with our data may not be doing everything they can to catch up with reality.

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Re: Largest Prime Number

Post by Kellemora » 19 Jan 2017, 11:37

I would think most banks try to keep their customers accounts, and their own data, as secure as possible.

Anything to do with encryption is so far over my head, most of what I think about it is probably all hog wash anyhow.

Like anything else though, locks only keep the honest people out!

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