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bike locks and encryption
I figure there might be a few computer geeks here,
even though it's a bike sports board. Something occurred to me recently - bicycle locks as examples of one way functions, so useful in encryption. That is, easy to compute in one direction - for encryption - but hard the other way, lacking the key. Specifically, the combination type: 4 dials, numbered 0..9, the cylinder mates with the receptacle with the correct combination. . Like a good one way function, it's easy to 'encrypt' - even if you don't know the code - but hard to 'decrypt', i.e. unlock. Details left as an exercise. It seems kind of cute, if you're a mathematician. -- Rich |
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#2
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bike locks and encryption
On Tuesday, October 7, 2014 7:37:14 AM UTC+1, wrote:
I figure there might be a few computer geeks here, even though it's a bike sports board. Something occurred to me recently - bicycle locks as examples of one way functions, so useful in encryption. That is, easy to compute in one direction - for encryption - but hard the other way, lacking the key. Specifically, the combination type: 4 dials, numbered 0..9, the cylinder mates with the receptacle with the correct combination. . Like a good one way function, it's easy to 'encrypt' - even if you don't know the code - but hard to 'decrypt', i.e. unlock. Details left as an exercise. It seems kind of cute, if you're a mathematician. -- Rich Welcome to RBT, Rich. This isn't so much a "sports" bike forum as a bike tech forum. Some of the engineers here are pretty good thinkers and can also handle simple math; you want any electronics done, they'll be delighted to design really good stuff for you free of charge. Some of the others are idiots who try to make statistics lie for them and are routinely caught out; you'll catch on soon enough. The common four-tumbler 0-9 digital combination of a generic cable bike lock has a finite number of possibilities that you can see by eyeballing it and noting that it has sequential solutions from 0000 to 9999, thus 10,000 finite and determinable possibilities. A bicycle lock is therefore not a one way function as you claim. Adding more stops to each tumbler, or more tumblers, doesn't alter the fact that the solution is reversible by simple combination and permutation theory with a finite number of possible answers that a modern computer will find in a fraction of a second. There is no such thing as a truly unbreakable code. All codes are breakable by some means. The so-called "unbreakable codes" all depend on the fact that no computer is yet fast enough to break them by brute force, that is, by trying all possible solutions. But the NSA will break the common DES commercial code if they really have to. Note that even the very best code, RSA (1), can be broken by brute force, though if the primes with which you start are large enough, and correctly chosen, it could take all the computers in the world longer than the age of the universe before they stumble on the correct answer. RSA is a true one-way function code, which means that it cannot be broken by mathematical reverse engineering. You must have the key, or you must have enough computers and time to break it by brute force. Thus the protection of even a true one-way function is commercial, in that the cost of breaking it becomes too great: by the time you break it, the secret it hid will be very old and worthless. If any of your teachers told you different, they're not much chop. Of course, rather than an easilly breakable combination lock, I use a common key lock that disengages the steerer tube from the handlebars (much like a car steering lock) and makes the bike unrideable. (1) FOOTNOTE ONLY FOR MATHEMATICIANS Diffie, Hellman and Merkle laid out the philosophical ground rules for an asymmetric cipher that enabled the discovery of an irreversible formula (by using a one way function) by Ronald Rivest, Adi Shamir, and Leonard Adleman, who're the R, S and A. The big trick of RSA is that the encryption key can be published and is zero help in decoding an encrypted message. The decryption key d depends on the one-way modular function and the very large primes and the relationship between them: e * d = 1(mod (p-1) * (q-1)) in which p and q are very large primes. The owner of this code publishes an encryption key N (which is p * q) and another number e. ***He keeps p and q secret.*** Mathematically e and also p minus one and also q minus one should be relatively prime, but that's a technicality. N can't be bust back to the primes by any known formula; mathematicians have been searching for 2000 years... To get to C, the cipher text, plaintext X is first translated to binary form read as a decimal number M (let's call it ASCII), and then C = M^ e(mod N) To break the cipher C back to plaintext one uses the formula: M = C^(d mod N) and now you have a number M which you can look up in ASCII to get back to X.. The reason this exceptionally robust cipher is not used except by geeks and the truly desperate is that it is a veeeery slow in encoding even with a fast computer, so that it is basically a novelty suited only for short messages and files. An RSA message encrypted with a small N of only 10 to the order of 129 (that is, deliberately made unreasonably small to ensure a result within a human lifetime) took 17 years to break with six hundred mainframes and supercomputers linking up around the world. Andre Jute Polymath |
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bike locks and encryption
On October 6, RichD wrote:
bicycle locks as examples of one way function... Specifically, the combination type: 4 dials, numbered 0..9, the cylinder mates with the receptacle with the correct combination. To be precise, the cable type, with the ends that mate, not the U lock. -- Rich |
#4
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bike locks and encryption
On October 7, Andre Jute wrote:
bicycle locks as examples of one way functions, so useful in encryption. That is, easy to compute in one direction - for encryption - but hard the other way, lacking the key. Like a good one way function, it's easy to 'encrypt' - even if you don't know the code - but hard to 'decrypt', i.e. unlock. The common four-tumbler 0-9 digital combination of a generic cable bike lock has solutions from 0000 to 9999, thus 10,000 finite possibilities. A bicycle lock is therefore not a one way function as you claim. Think harder - the solution is reversible by simple permutation theory with a finite number of possible answers that a modern computer will find in a fraction of a second. In other words, you have to try every possible combination. That defines 'infeasible'. We're talking human fingers, not computers. The so-called "unbreakable codes" all depend on the fact that no computer is yet fast enough to break them by brute force, that is, by trying all possible solutions. Note that even the very best code, RSA (1), can be broken by brute force, RSA is a true one-way function code, which means that it cannot be broken by mathematical reverse engineering. You must have the key (1) FOOTNOTE ONLY FOR MATHEMATICIANS Diffie, Hellman and Merkle laid out the philosophical ground rules that enabled the discovery of an irreversible formula (by using a one way function) by Ronald Rivest, Adi Shamir, and Leonard Adleman. The big trick of RSA is that the encryption key can be published and is zero help in decoding an encrypted message. The decryption key d depends on the one-way modular function and the very large primes and the relationship between them: e * d = 1(mod (p-1) * (q-1)) For the listeners in Rio Linda: Given 54321 and 56789, it 's easy to multiply and get 3084835269, but given 3084835269, it's very difficult to discover 54321 and 56789. You missed the point completely. Assume you don't know the combination. Then, as noted, it's hard to open - 'decrypt' - a secured lock. But, with an open luck, after the dials have been twirled, inserting the cylinder - 'encryption' - is relatively easy. Think harder, Grasshopper! The one way function analogy came to me, after I faced exactly this situation recently. -- Rich |
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bike locks and encryption
On Wednesday, October 8, 2014 9:45:21 PM UTC+1, wrote:
We're talking human fingers, not computers. In that case I'll save my finger-time for useful work and leave the lockpicking, and in this case nitpicking, to the junior criminals. Ciao. Ande Jute |
#6
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bike locks and encryption
http://goo.gl/4Ozb3I http://goo.gl/Dgzrnn haven't had a cylinder lock I ages: hefty key lock with ditto chain. Here with organize crime mind readers hovering around ATM machine, as industrial spies....I was using storage down the street from the Porsche dealer. We think combo's in various other numbers NOT the used combo numbers. The local reader had a spy zombie at the Porsche shop...a race equippe....who or mentine to a higher up that Iwas using the fake number system...prompting an outburst from inside that YEAH WE DO THAT ALSO....... you wanna key in on that.... |
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