Wikipedia:Reference desk/Archives/Mathematics/2006 December 17

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[edit] December 17

[edit] Surjectivity of hash functions

  • Hi guys, could you please recommend a good quality paper/web site covering surjectivity of hash functions? For the record, the issue came up while writing a simple cryptographic library in C++: so far a digest object can only be constructed by asking the corresponding hasher (a simple state machine which implements a chosen hash algorithm); in at least a couple of cases, though, it would be handy to construct a digest from a given byte-sequence (e.g. when testing :-)) and I feel it to be a conceptual abuse to allow construction from an arbitrary such sequence if it can't possibly be the result of the corresponding hash function (there are different types, in the type system sense, of digests: you must declare if the digest is, say, an MD5 digest, a SHA-1 digest or whatever). Of course I imagine the property to be desirable but didn't found any mathematical discussion of it. —Gennaro Prota•Talk 14:06, 17 December 2006 (UTC)
Take a look at the Handbook of Applied Cryptography. Specifically, chapter 9, which covers hash functions. Other chapters might have information that you might be interested in too. If you have any questions, let me know. I'm familiar with this stuff. :) --Brad Beattie (talk) 01:25, 20 December 2006 (UTC)
Thanks Brad, I actually consulted chapter 9 before posting my question. But I don't see an answer there. Perhaps other chapters give a hint or a bibliographic reference, I don't know. In practice I have other (and overall preferable) solutions for the library but I'm still curious about the theoretical issue. —Gennaro Prota•Talk 21:27, 20 December 2006 (UTC)

[edit] maths project

iave to do a math project on the applications of mathematics in everyday life so could you give me a way to satrt and give me a few ideas.

thanxMi2n15 15:42, 17 December 2006 (UTC)

Pretty much everything you see in everyday life required math to design, construct, deliver, price, etc. Why don't you pick just one item, like a bike, say, and talk about all the math that goes into designing it (gear ratios, torque, center of gravity calcs, weight calcs, etc.), setting the price (per unit costs, fixed costs, profit margin, retailer markup-up, etc.), shipping it (size restrictions on boxes used to transport unassembled units, etc.). StuRat 15:57, 17 December 2006 (UTC)

thanks a lot that was one approach that i hadnt thought about Mi2n15 17:28, 17 December 2006 (UTC)

You're welcome. StuRat 01:20, 18 December 2006 (UTC)

[edit] Plurisubharmonic functions

I have a problem with plurisubharmonic functions. How can i show, that the function g: C^n->R, g:=log|f| ,with f holomorph function, is plurisubharmonic? I need this for the proof of convexity of ronkin function. Ronkin function is

N_f(x,y)=\int_{\log^{-1}(x,y)} \log|f(z1,z2)| \frac{dz_1}{2\pi i} \frac{dz_2}{2\pi i}

for example. I have to show, that the ronkin function is convex. First i have to show, that the function g:=log|f| is plurisubharmonic, after that i have to show, that the ronkin function is plurisubharmonic too. Than i can say that the ronkin function is convex, because all plurisubharmonic functions are pseudoconvex. It would be great if somebody can help me with the proof. Katharina Jung 62.104.142.15 18:28, 17 December 2006 (UTC)
PS:I need this for my diplom. I'm writing about projections of complex algebraic curves: amoebas and coamoebas (algas).

I know next to nothing of the topic, but just following the definition of plurisubharmonic function and reading the section on subharmonic functions in the complex plane, it would appear that for the first part it suffices to prove that for any pair of points a, b \in {\mathbb{C}}^n the function h defined by
h(z) = f(a + bz), z \in \mathbb{C}
is also a holomorphic function, which, if I'm not mistaken, is obvious, as h is the functional composition of two holomorphic functions.  --LambiamTalk 20:31, 17 December 2006 (UTC)