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Aug
21
comment Understanding the “cube-root math” behind an RSA signature forgery
The paper explains how it got this number immediately after the expression you are quoting. See equations (7) and (8) and the surrounding text (continuing onto the top of the next page).
Aug
20
comment Is there any research about cryptography on nondeterministic Turing machines?
"You appear to assume that if there is no such path, you don't get any usable output" - Yes, that's right. I agree: that's exactly the heart of it. See my comment on the question, where I asked for clarification about what the original poster (user8007) had in mind in this regard. I'm going based upon my best attempt at interpreting user8007's answer as well as my limited understanding of complexity theory. Do you know of any reference which suggests which is the right formulation? If so, can you share a reference where I can learn more? I'd love to learn more!
Aug
20
comment Is there any research about cryptography on nondeterministic Turing machines?
(cont.) It is easy to find a condition under which Bob accepts and outputs that $i=1$, but no amount of non-determinism is enough for Bob to accept and output that $i=0$. (There's no single guess that lets Bob verify that there is no solution to your equation. If Bob guesses one value of $M$ and find it isn't a solution to the equation, he has no idea whether some other value of $M$ might be a solution.) Encryption has the same problem. So, your example is not valid: neither encryption nor decryption can be computed using a non-deterministic algorithm.
Aug
20
comment Is there any research about cryptography on nondeterministic Turing machines?
Oops, forget everything I wrote earlier! I just figured out what I missed. Your example is no good because Bob cannot decrypt. Try writing out a non-deterministic algorithm Bob can use to decrypt. To see this, just try writing a non-det. algorithm Bob can use to compute a single biased bit $i$. Make sure you remember the rules of non-deterministic algorithms: you have to specify the criteria under which Bob accepts or rejects. What is the condition under which Bob accepts and outputs that $i=0$ (that there is no solution $M$)? Try to write it down -- you'll see you are stuck. (cont.)
Aug
19
comment Is there a security proof for the Triple-DES construction in the ideal cipher model?
@RickyDemer, I thought you were curious about whether 2-key 3DES is more secure than single DES (rather than whether it's more secure than double DES), and I believe the Aiello paper does demonstrate one sense in which it is. Anyway, it's not important -- if the Aiello paper isn't what you were looking for, I'm fine with that! The other papers should still be useful.
Aug
18
comment Textbook-RSA meet-in-the-middle attack against other RSA based schemes?
nlognfan, I see your comment that you are unable to edit your question or accept an answer. Make sure you are logged in as nlognfan. If you have lost access to that account, please try the account recovery process (or try clicking "click here to recover your account" on the sign-in page) and the StackExchange OpenID recovery page; if neither of those works for you, contact team@stackoverflow.com with as much information as you have to ask them to help you regain access.
Aug
16
comment Is there any research about cryptography on nondeterministic Turing machines?
It's not clear to me how you were expecting to use a non-deterministic Turing machine to encrypt. A non-deterministic Turing machine has many possible execution traces (and, typically, many possible outputs). How will you select which one to use as the ciphertext? For deciding/recognizing a language, we say that the input is treated as accepted if any of the possible execution traces accepts. What do you plan to do about this for encryption? The answer to the question might depend upon what you have in mind here.
Aug
12
comment Is it possible to subtract/multiply numbers using homomorphic encryption?
Have you read the Wikipedia article on homomorphic encryption? That'd be a good starting point. Also, search on this site. I think you'll find some answers....
Aug
11
comment Alice's forgetful banking
@NickODell, sorry, I mistyped -- I'll delete the erroneous comment. What I meant to ask was: You say that a barrier to having Alice send the bank a hash of her account number is that the hash will be brute-forceable. So why don't you just use a 40-digit account number? That won't be brute-forceable, and it seems to meet all your other requirements. (You said we could change the behavior on both ends, so this should be allowable.) So why did you reject the hash approach? Or is that a valid solution to your problem? I already asked about this once up in the 3rd comment from the top...
Aug
10
comment What is the fastest elliptic curve operation f(P) in affine coordinates such that f^n(P)=P only if n is large?
Richard, to enable us to help you more effectively, I think it's important for you to describe the problem in more detail publicly -- including your answers to the questions in the comment section. This site is intended to create archival-quality questions and answers that will be of utility not just to you but to others who might have the same question. (If you need help on a question where you cannot describe all the requirements publicly, you might be better off hiring a consultant.)
Aug
10
comment Efficient Incremental Updates to Large Merkle Tree
@bytemaster, if you like, the 4096-byte block can itself be structured as a Merkle tree. This is roughly equivalent to building a Merkle tree on all the records (each record = a leaf of the big Merkle tree) and only storing the top 20-21 levels of the Merkle tree in RAM, which is also a valid optimization. There are many possible optimizations -- hopefully my answer helps you identify some of the possibilities, so you can choose whichever one is most appropriate for your specific setting.
Aug
10
comment Alice's forgetful banking
If the account number is a capability that's all that's needed to withdraw all of the money from that account, then 8 digits isn't enough. If a bank has ten million customers, simple random guessing will succeed with probability 10%. So the problem as specified can't be quite right. Something smells like we don't have all the real requirements/constraints.... Can you try editing the question to tell us the real problem you have?
Aug
10
comment Alice's forgetful banking
I don't understand the constraints. What parts of the system can we modify? Can we modify both the client (the software Alice runs or the procedure Alice follows) and the server (the code that the banks run for authenticating Alice or that process they use to help Alice check about that account number)? If you can change both endpoints, why are you limited to just 8-digit account numbers: why can't you choose arbitrarily long account numbers? (Also, you later mention cryptographic keys. If we're talking about keys, those won't be 8 digits long and won't be brute-forceable, so which is it?)
Aug
9
comment why AKS is so slow in practice?
This question would be better suited to Computer Science Stack Exchange. The question is not about cryptography per se and so does not appear to be on-topic on this site.
Aug
9
comment Any problems with this secure time synchronization scheme?
@nightcracker, alas, I don't know of any literature on it. On first glance, it hardly seems possible (though maybe I shouldn't say that, maybe someone has some clever way that hasn't occurred to me). I wasn't aware that there was any issue with literature recommendations; my impression is that there's an issue with open-ended questions that solicit many answers ("what's the best book on cryptography?"), but not focused questions ("what's the state of the art on X?"), particularly if you done some searching on your own first.
Aug
8
comment Why is Merkle-Damgård construction insecure?
Possible dup: crypto.stackexchange.com/q/3978/351
Aug
7
comment Securing content and login with “same” password
I think the scheme in your last paragraph is better, given the requirement from the question that "the service should not be able to decode the information that it stores for the user". That scheme (from the last paragraph) seems like a good one to me!
Aug
7
comment Securing content and login with “same” password
@user12889, Regarding your first question, services should not be storing password hashes that are computed using a standard cryptographic hash function; this is standard advice. I recommend that you read standard material on password hashing. There's lots of good stuff on IT Security.Stack Exchange on password hashing, and on PAKE (see also Wikipedia): I encourage you to search there and read up on these topics before asking too many more follow-up questions.
Aug
7
comment Securing content and login with “same” password
@user12889, that's not enough. 1. If $H,H'$ is a standard hash functions, it'd be too easy for an attacker to recover $P$ from that, since standard hash functions are too fast. 2. The user still sends $H(P)$ to the server, so if the server is hacked, an attacker learns $H(P)$ and then may be able to recover $P$ (if $H$ is a fast hash). This is bad, because users often reuse the same password on other sites, and that means a successful security breach of your site may adversely affect the user's security on other sites. I suggest reading standard resources on password hashing.
Aug
7
comment Securing content and login with “same” password
@user12889, can you edit your question to indicate that fact? That wasn't clear from the question. We want questions to be self-contained (people shouldn't need to read comments to understand your intent), so I hope you can edit your question.