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Topic: One way functions

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function mathematics

functional analysis

functional programming

trigonometric function

functional group

exponential function

probability density function

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graph of a function

Riemann zeta function

function domain

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	One-way function - Wikipedia, the free encyclopedia (Site not responding. Last check: 2007-11-07)
		A one-way function is a function that is easy to calculate but hard to invert — it is difficult to calculate the input to the function given its output.
		Thus, as far as the mere existence of one-way function goes, the notions of weak and strong one-way functions are equivalent.
		A trapdoor one-way function or trapdoor permutation is a special kind of one-way function.
	en.wikipedia.org /wiki/One_way_function (564 words)

	one way function (Site not responding. Last check: 2007-11-07)
		A one way function is a function which is "easy" to calculate but "hard" to invert — i.e, it is "hard" to calculate the input to the function given its output.
		A trapdoor one way function or trapdoor permutation is a special kind of one way function.
		A cryptographic hash function is like a one way function except that it is not required to be bijective and has more stringent requirements for hardness of inversion.
	www.yourencyclopedia.net /One_way_function.html (323 words)

	AspEncrypt.com - Crypto 101: One-way Hash Function
		A one-way hash function, also known as a message digest, fingerprint or compression function, is a mathematical function which takes a variable-length input string and converts it into a fixed-length binary sequence.
		Furthermore, a one-way hash function is designed in such a way that it is hard to reverse the process, that is, to find a string that hashes to a given value (hence the name one-way.) A good hash function also makes it hard to find two strings that would produce the same hash value.
		Although a one-way hash function is used mostly for generating digital signatures, it can have other practical applications as well, such as storing passwords in a user database securely or creating a file identification system.
	www.aspencrypt.com /crypto101_hash.html (307 words)

	Ideas, Concepts and Definitions (Site not responding. Last check: 2007-11-07)
		A one-way function is sometimes called a trap-door function.
		Like falling through a trap-door, a one-way function is a process that is easy to do, but very difficult or even impossible to undo.
		The Ice Cream Stands problem, or the problem of finding the minimum dominating set in a graph is an example of a one-way function.
	www.c3.lanl.gov /mega-math/gloss/compute/oneway.html (138 words)

	RSA Security - 2.3.2 What is a one-way function?
		A one-way function is a mathematical function that is significantly easier to compute in one direction (the forward direction) than in the opposite direction (the inverse direction).
		In almost all public-key systems, the size of the key corresponds to the size of the inputs to the one-way function; the larger the key, the greater the difference between the efforts necessary to compute the function in the forward and inverse directions (for someone lacking the trapdoor).
		For a digital signature to be secure for years, for example, it is necessary to use a trapdoor one-way function with inputs large enough that someone without the trapdoor would need many years to compute the inverse function (that is, to generate a legitimate signature).
	www.rsasecurity.com /rsalabs/node.asp?id=2188 (410 words)

	One way function (Site not responding. Last check: 2007-11-07)
		Multiplication of two large primes is one such: this is because integer factorization is thought to be a hard problem.Another is exponentiation in certain groups : this one relies on the presumed hardness of the computingthe discrete logarithm.
		A trapdoor one way function or trapdoorpermutation is a special kind of one way function.
		A cryptographic hash function is like aone way function except that it is not required to be bijective and has more stringent requirements for hardness ofinversion.
	www.therfcc.org /one-way-function-72565.html (278 words)

	Classics in the History of Psychology -- James (1890) Chapter 2
		In a similar way, the motor cortex might be sensitive as well as motor, and yet by this greater subtlety (or whatever the peculiarity may be) in the sensory currents, the sensibility might survive an amount of injury there by which the motility was destroyed.
		My conclusion then is this: that some of the restitution of function (especially where the cortical lesion is not too great) is probably due to genuinely vicarious function on the part of the centres that remain; whilst some of it is due to the passing off of inhibitions.
		This passage of functions forward to the ever-enlarging hemispheres would be itself one of the evolutive changes, to be explained like the development of the hemispheres themselves, either by fortunate variation or by inherited effects of use.
	psychclassics.yorku.ca /James/Principles/prin2.htm (17603 words)

	Imagination and creativity of the adolescent by Vygotsky (Site not responding. Last check: 2007-11-07)
		In exactly the same way, Kroh points out the fact that, along with the new variations which he associates with the development of thinking during school age, it is only in adolescence that the ability to handle logical concepts manifests itself.
		The observed phenomenon where higher psychological functions are not seen simply as a continuation of the basic functions and their automatic combination, but as an intrinsically new psychological creation whose development follows very special rules and which conforms to entirely different natural laws, has till now not succeeded in becoming part of child psychology.
		The only way of ever discovering the key to understanding the process of concept formation, is to study the functional use of words and their development and the varied forms of their usage, multifarious, quantitatively distinct at different ages, but genetically related to one another.
	www.marxists.org /archive/vygotsky/works/1931/adolescent/ch10.htm (15202 words)

	[No title]
		The function F is obtained by cascading a certain function f(x,y), where x is 32 bits and y is 48 bits.
		We remark that the trapdoor functions employed as public transformations in public-key systems are only a subclass of the class of one-way functions.
		The hash functions are pre-certified in the sense that their security can often be proven to be the same as that of the underlying conventional function.
	www.hackcanada.com /blackcrawl/encrypt/NIST-CRY.TXT (11163 words)

	Information Security Magazine (Site not responding. Last check: 2007-11-07)
		Public-key cryptosystems rely heavily on one-way functions, which involve mathematical functions that are considerably easier to perform in one direction (forward) than in the opposite direction (its inverse).
		Since the size of the key corresponds to the size of the inputs to the one-way function, the larger the key, the harder the problem is and the more effective the algorithm becomes.
		The forward direction of its one-way function is used for encryption and signature verification; the inverse direction for decryption and signature generation.
	infosecuritymag.techtarget.com /articles/1998/julycrypto.shtml (1985 words)

	[No title]
		The technology is ages old: You pass the initial password through a one way hash function, and store the garbled password in your database.
		I guess some of you don't know what hash functions are, so here's a short intro: Hash functions, or message digests, are one way functions that take a text as input, and produce a signature based on the text.
		Calling the function "one way" means that, given a signature, it is impossible to get back to the original text.
	shh.thathost.com /text/cleartext-passwords.txt (969 words)

	[No title]
		A one-way function is a mathematical function that is significantly easier to perform in one direction (the forward direction) than in the opposite direction (the inverse direction).
		A trap-door one-way function is a one-way function where the inverse direction is easy if you know a certain piece of information (the trap door), but difficult otherwise.
		Although hash functions in general have many uses in computer programs, in cryptography they are used to generate a small string (the message digest) that can represent securely a much larger string, such as a file or message.
	www.hackcanada.com /blackcrawl/encrypt/rsafaq.txt (21421 words)

	Citations: One-way Functions are Necessary and Sufficient for Secure Signatures - Rompel (ResearchIndex) (Site not responding. Last check: 2007-11-07)
		showed that the existence of one way functions can be used in order to design a signature scheme satisfying the very strong notion of security that was first defined by Goldwasser, Micali, and Rivest [10] With a secure signature scheme available, when the TSS receives the hash value, it appends.
		Rompel, One way functions are necessary and sufficient for secure digital signatures, Proceedings of the 22-nd Annual ACM Symposium on the Theory of Computing, pp.
		showed that one way functions are necessary and sufficient for digital signature schemes which are secure against chosen plaintext attack.
	citeseer.ist.psu.edu /cs?q=dbnum=1,GID=49868,DID=0,start=50,cluster=none,qtype=context: (1446 words)

	Q7: What is the Significance of One-Way Functions for Crytography? (Site not responding. Last check: 2007-11-07)
		In almost all public-key systems, the size of the key corresponds to the size of the inputs to the one-way function; the larger the key, the greater the difference between the efforts necessary to compute the function in the forward and inverse directions (for someone lacking the trap door).
		For a digital signature to be secure for years, for example, it is necessary to use a trap-door one-way function with inputs large enough that someone without the trap door would need many years to compute the inverse function.
		This means that it is theoretically possible that an algorithm will be discovered that can compute the inverse function easily without a trap door; this development would render any cryptosystem based on that one-way function insecure and useless.
	www.x5.net /faqs/crypto/q7.html (282 words)

	Using One-Way Functions to Protect Sensitive Information in SQL Server Databases
		One good tool is the one-way function , a mathematical mechanism that is easy to compute but close to impossible to invert.
		The best functions like MD5 (message digest 5) or the SHA (Secure Hash Algorithm), can reduce any array of bytes into a scrambled mixture of seemingly random pile of bits in such a way that it's practically impossible to reconstruct the original input.
		Some one-way functions are often called cryptographically secure hash functions because they are quite similar to the hash functions often used in some data structures.
	www.sql-server-performance.com /pw_sql_server_crypto.asp (707 words)

	Candidate One-Way Functions Based on Expander Graphs (Site not responding. Last check: 2007-11-07)
		We suggest a candidate one-way function using combinatorial constructs such as expander graphs.
		Thus, the function is extremely easy to evaluate: all that is needed is to take multiple projections of the input bits, and to use these as entries to a look-up table.
		Instead, we propose the study of the complexity of inverting this function as an interesting open problem, with the hope that further research will provide evidence to our belief that the inversion task is intractable.
	www.wisdom.weizmann.ac.il /~oded/ow-candid.html (222 words)

	One-Way Functions in Worst-Case Cryptography: Algebraic and Security Properties - Beygelzimer, Hemaspaandra, Homan, ... (Site not responding. Last check: 2007-11-07)
		According to [RS93], this line of research was initiated in 1984 by Rivest and Sherman who designed two-party secretkey agreement protocols that use strongly noninvertible, total, associative one-way functions as their key building blocks.
		6 An observation on associative one-way functions in complexit..
		4 Associative one-way functions: A new paradigm for secret-key..
	citeseer.ist.psu.edu /beygelzimer99oneway.html (520 words)

	Limits on the Provable Consequences of One-way Functions (Site not responding. Last check: 2007-11-07)
		We present strong evidence that the implication, "if one-way permutations exist, then secure secret key agreement is possible", is not provable by standard techniques.
		We also obtain, as a corollary, that there is an oracle relative to which the implication is false, i.e., there is a one-way permutation, yet secret-exchange is impossible.
		Furthermore, we show that if a certain combinatorial conjecture is true, then there is similar evidence to show that a one-way permutation can't be constructed from a one-way function.
	sunsite.berkeley.edu /TechRepPages/CSD-88-468 (371 words)

	Computation of Igusa's Local Zeta Functions, Trees, and One-Way Functions, by W. A. Zuniga-Galindo (Site not responding. Last check: 2007-11-07)
		Abstract: In this paper we present a polynomial time algorithm to compute the local zeta function $Z(s,f)$ attached to a polynomial \\ $f(x)\\in \\QTR\{Bbb\}\ {Z\}[x]$ (in one variable, with splitting field $\\QTR\{Bbb\}\{Q\}$) and a prime $p$.
		This reduction is accomplished by constructing a weighted tree from the $p-$adic expansion of th e roots of $f(x)$ modulo a certain power of $p$, and then associating a generating function to this tree.
		The genera\\-ting function constructed in this way coincides with the local zeta function of $f(x).$ We also propose a new class of candidates for one-way functions based on Igusa's zeta functions attached to polynomials in one variable.
	www.math.uiuc.edu /Algebraic-Number-Theory/0346 (154 words)

	Math Forum - Ask Dr. Math (Site not responding. Last check: 2007-11-07)
		Date: 06/01/99 at 12:07:03 From: Al Hewitt Subject: One-way function Hello, I am trying to figure out whether the following problem has a solution.
		To verify two functions are inverses of one another, you need to show that (f of g)(x) = x and that (g of f)(x) = x.
		I would like to know if there is a problem that exists that when composed, the two functions work one way, but not the other; i.e.: (f of g)(x) = x, but (g of f)(x) does not equal x.
	mathforum.org /library/drmath/view/54581.html (311 words)

	Computation of Igusa's Local Zeta Functions, Trees, and One-Way Functions, by W. A. Zuniga-Galindo (Site not responding. Last check: 2007-11-07)
		In this paper we present a polynomial time algorithm to compute the local zeta function Z(s,f) attached to a polynomial f(x) in Z[x] (in one variable, with splitting field Q) and a prime p.
		This reduction is accomplished by constructing a weighted tree from the p-adic expansion of the roots of f(x) modulo a certain power of p, and then associating a generating function to this tree.
		We also propose a new class of candidates for one-way functions based on Igusa's zeta functions attached to polynomials in one variable.
	front.math.ucdavis.edu /ANT/0346 (150 words)

	Cryptology ePrint Archive (Site not responding. Last check: 2007-11-07)
		These are one-way functions with the additional feature that there is a feasible way to approximate the number of preimages of a given output.
		A special case is regular one-way functions where each output has the same number of preimages.
		We construct such functions from approximable-preimage-size one-way functions using ``hashing techniques'' inspired by Hastad et al., SIAM Journal on Computing 1998.
	eprint.iacr.org /2004/335 (199 words)

	Cryptography, One-Way Functions, and Pseudorandom Generators
		This project studies one-way functions, pseudorandom generators, and cryptography.
		One-way functions in worst-case cryptography: Algebraic and security properties are on the house.
		One-way functions and the non-isomorphism of NP-complete sets.
	www.cs.rochester.edu /~lane/cryptography.html (341 words)

	Citations: Pseudo-random generation from one-way functions - Impagliazzo, Levin, Luby (ResearchIndex) (Site not responding. Last check: 2007-11-07)
		One-Way Functions, Hard on Average Problems, and - Statistical Zero-Knowledge..
		Impagliazzo, L. Levin and M. Luby: "Pseudo-random generation from one-way functions", Proceedings of the 21-th ACM Symposium on Theory of Computing, 1989, pp.12-24.
		Impagliazzo, L. Levin, and M. Luby, Pseudo-random generation from one-way functions, in Proceedings, 21st Annual ACM Symposium on the Theory of Computing, ACM, 1989," pp.
	citeseer.ist.psu.edu /context/24936/0 (574 words)

	Application of one-way functions to password security
		To make the password file slightly less useful to hackers, a one-way function is used.
		Now when a user tries to log in, supplying her name and password to the system, it applies the one-way function to the password, obtaining the image of the password under that function, and compares that result to the user's entry in the password file.
		The definition of a one-way function (namely the fact that it is computationally difficult to ``go backwards'') implies that the hacker cannot easily derive a user's password from the corresponding value stored in the password file.
	www.cs.brown.edu /courses/cs007/oneway/node4.html (467 words)

	Application of one-way functions to commitment
		A one-way function is a way to conceal without keys.
		A basic (and, as we will see, flawed) implementation of commitment using a one-way function f is as follows.
		Since f is a one-way function, knowing the value c does not enable you to determine s.
	www.cs.brown.edu /courses/cs007/oneway/node7.html (651 words)

	CIS Seminars and Talks
		Unlike in the study of secure function evaluation, in which privacy is preserved to the extent possible given a specific functionality goal, in the census problem privacy is paramount; intuitively, things that cannot be learned ``safely'' should not be learned at all.
		Next, we define a ``commit-prove-fair-open'' functionality and construct an efficient protocol that realizes it, using a new variant of a cryptographic primitive known as ``time-lines.'' With this functionality, we show that some of the existing secure MPC protocols can be easily transformed into fair protocols while preserving their security.
		We introduce a unifying framework for proving that predicate $P$ is hard-core for a one-way function $f$, and apply it to a broad family of functions and predicates, reproving old results in an entirely different way as well as showing new hard-core predicates for well known one-way function candidates.
	theory.lcs.mit.edu /%7Ecis/cis-talks.html (16659 words)

	ENS 2005 Memory Checking lecturer:Naor
		One-way functions are easy to compute one-way but given an image it is computationally hard to find a corresponding pre-image.
		Key results over the last twenty years have shown that the existence of one-way functions is equivalent to many other primitives such as pseudo-random generators.
		For this problem good schemes based on the existence of one-way functions are known.
	www.wisdom.weizmann.ac.il /~naor/COURSE/ens.html (290 words)

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