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How To Put Your Business In Front of Millions of Viewers on TV
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Re: RE: Two ideas for random number generation
- Original Message - From: Bill Stewart [EMAIL PROTECTED] I've been thinking about a somewhat different but related problem lately, which is encrypted disk drives. You could encrypt each block of the disk with a block cypher using the same key (presumably in CBC or some similar mode), but that just feels weak. Why does it feel weak? CBC is provably as secure as the block cipher (when used properly), and a disk drive is really no different from many others. Of course you have to perform various gyrations to synchronise everything correctly, but it's doable. So you need some kind of generator of pretty-random-looking keys so that each block of the disk gets a different key, or at the very least a different IV for each block of the disk, so in some sense that's a PRNG. (You definitely need a different key for each block if you're using RC4, but that's only usable for Write-Once media, i.e. boring.) Obviously you need repeatability, so you can't use a real random number generator. Well it's not all the complicated. That that same key, and encrypt the disk block number, or address or anything else. This becomes completely redoable (or if you're willing to sacrifice a small portion of each block you can even explicitly stor ethe IV. I've been thinking that Counter Mode AES sounds good, since it's easy to find the key for a specific block. Would it be good enough just to use Hash( (Hash(Key, block# )) or some similar function instead of a more conventional crypto function? Not really you'd have to change the key every time you write to disk, not exactly a good idea, it makes key distribution a nightmare, stick with CBC for disk encryption. Joe
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disk encryption modes (Re: RE: Two ideas for random number generation)
On Fri, Apr 26, 2002 at 11:48:11AM -0700, Joseph Ashwood wrote: From: Bill Stewart [EMAIL PROTECTED] I've been thinking about a somewhat different but related problem lately, which is encrypted disk drives. You could encrypt each block of the disk with a block cypher using the same key (presumably in CBC or some similar mode), but that just feels weak. Why does it feel weak? CBC is provably as secure as the block cipher (when used properly), and a disk drive is really no different from many others. Of course you have to perform various gyrations to synchronise everything correctly, but it's doable. The weakness is not catastrophic, but depending on your threat model the attacker may see the ciphertexts from multiple versions of the plaintext in the edit, save cycle. This could happen for example the attacker has read access to your disk, or if the attacker gained temporary physical access to the machine but didn't have enough resources to install software trojan, or if good disk checksumming is in place, didn't have enough resources to install hardware trojan. So you need some kind of generator of pretty-random-looking keys so that each block of the disk gets a different key, or at the very least a different IV for each block of the disk, so in some sense that's a PRNG. (You definitely need a different key for each block if you're using RC4, but that's only usable for Write-Once media, i.e. boring.) Obviously you need repeatability, so you can't use a real random number generator. Well it's not all the complicated. That same key, and encrypt the disk block number, or address or anything else. Performance is often at a premium in disk driver software -- everything moving to-and-from the disk goes through these drivers. Encrypt could be slow, encrypt for IV is probably overkill. IV doesn't have to be unique, just different, or relatively random depending on the mode. The performance hit for computing IV depends on the driver type. Where the driver is encrypting disk block at a time, then say 512KB divided (standard smallest disk block size) into AES block sized chunks 16 bytes each is 32 encrypts per IV geenration. So if IV generation is done with a block encrypt itself that'll slow the system down by 3.125% right there. If the driver is higher level using file-system APIs etc it may have to encrypt 1 cipher block size at a time each with a different IV, use encrypt to derive IVs in this scenario, and it'll be a 100% slowdown (encryption will take twice as long). This becomes completely redoable (or if you're willing to sacrifice a small portion of each block you can even explicitly stor ethe IV. That's typically not practical, not possible, or anyway very undesirable for performance (two disk hits instead of one), reliability (write one without the other and you lose data). I've been thinking that Counter Mode AES sounds good, since it's easy to find the key for a specific block. Would it be good enough just to use Hash( (Hash(Key, block# )) or some similar function instead of a more conventional crypto function? Not really you'd have to change the key every time you write to disk, not exactly a good idea, it makes key distribution a nightmare, stick with CBC for disk encryption. CBC isn't ideal as described above. Output feedback modes like OFB and CTR are even worse as you can't reuse the IV or the attacker who is able to see previous disk image gets XOR of two plaintext versions. You could encrypt twice (CBC in each direction or something), but that will again slow you down by a factor of 2. Note in the file system level scenario an additional problem is file system journaling, and on-the-fly disk defragmentation -- this can result in the file system intentionally leaving copies of previous or the same plaintexts encrypted with the same key and logical position within a file. So it's easy if performance is not an issue. Another approach was Paul Crowley's Mercy cipher which has a 4Kbit block size (= 512KB = sector sized). But it's a new cipher and I think already had some problems, though performance is much better than eg AES with double CBC, and it means you can use ECB mode per block and key derived with a key-derivation function salted by the block-number (the cipher includes such a concept directly in it's key-schedule), or CBC mode with an IV derived from the block number and only one block, so you don't get the low-tide mark of edits you get with CBC. But Mercy as a set of design criteria is very interesting for this application. Adam -- http://www.cypherspace.org/adam/
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Block key generation algorithms
which is encrypted disk drives. You could encrypt each block of the disk with a block cypher using the same key (presumably in CBC or some similar mode), but that just feels weak. So you need some kind of generator of pretty-random-looking keys so that each block of the disk gets a different key, What I employ in rubberhose is a hardened version of this: Take two encryption functions (or one encryption and one decryption function), e_1, and e_2, and some salt. For each lsb in the block number: block_key = block_key xor salt_n if (lsb == 0) block_key = e_1(master_key, block_key) else block_key = e_2(master_key2, block_key) This provides a n^2 tree of keys such that even if you break one of the leaves traveling up the branches to other leaves remains very difficult. It also protects against yet to be discovered related key, related plain-text attacks. If you have blind faith in your ciphers: block_key = e(master_key, block_num) Or: block_key = hash(master_key || block_num) Is just fine. -- Julian Assange|If you want to build a ship, don't drum up people |together to collect wood or assign them tasks and [EMAIL PROTECTED] |work, but rather teach them to long for the endless [EMAIL PROTECTED] |immensity of the sea. -- Antoine de Saint Exupery
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Re: Two ideas for random number generation
At 10:18 AM 4/25/02 -0700, Tim May wrote: On Thursday, April 25, 2002, at 07:45 AM, Major Variola (ret) wrote: Predictability gets much worse if one of the walls of a pool-table is curved, then the uncertainty in a perfectly-round ball's momentum is magnified after reflection, compared to a pool-table of 3 or more flat walls. Yes, of course. There are many sources of divergence, and curved walls certainly add divergence. But, as you acknowledge, the curvature of the spherical balls is a source. In fact, the radius of curvature of a ball is much smaller than that of curved side walls, so of course they are huge sources of divergence. Yep. I misremembered the model. The importance of curved walls is only in abstract-billiards with point-balls. Otherwise, analytically, you get into fixed sequences with flat walls. Pong-like games can demonstrate this. Its all about, as you said, the effect of divergence on initial uncertainty. And it's important for people not to think that the curved walls or curved balls are important to the phenomenon: if all surfaces were nominally flat (say, to a sixteenth wavelength, about the best a telescope mirror is ground to), the divergences would _still_ occur. Tiny alternations in temperature would affect dimensions, friction, speeds, and hence would alter arrival times. At some point, objects in one history would bounce and in another history would miss...the changes at this point are _huge_. These are unavoidable *empirical* sources of uncertainty; the above gedankenbilliards divergence addresses *analytic* magnification of uncertainty. (I actually did a project at Intel which exploited this. I devised a scheme whereby known good microprocessors would be imaged by an electron microcope, state by state (using beam blanking to only illuminate the chip during a specific state), and then would be digitally subtracted or otherwise compared to the internal states of chips having some speed problem, or some voltage problem, or just plain failing. By examining the time evolution of divergent states, especially by running the history backwards, we could pinpoint the first divergence, the first state where voltage levels differed noticeably. This was usually a place where a design needed to be tweaked, or where a marginality was present, or a flaw, etc. This machine, the Dynamic Fault Imager, was used to get speeds up on the 80286 and later processors.) Much more finesse than your 'cutting the crap out of packaging materials' trick... BTW, someone was speculating about history healing itself (this is my term for it, a familiar trope in SF). A look at the billiard ball model will show how this cannot conceivably happen: as soon as one ball misses another, all of the later trajectories are radically different. If this is not immediately clear, spend several minutes drawing pictures. Time-machine inventor reports that his stepping on a butterfly in Brazil averted a Chinese cyclone... If the writer was talking about conserved quantities (I think he mentioned vapors in an elevator, for example), this is not at all what we are talking about. Yes, the total energy of the billiard balls will remain roughly the same in both histories, though divergences will occur even in total energy, just more slowly. Yes, the earth's overall climate is not dramatically affected by butterflies. To track one (odor) molecule's position into the future, you'd need exponentially more information (about the other molecules it interacts with) the farther you want to predict in time. ... Jim Bell was just doing physics-of-computation experiments in IRS offices..
