863 research outputs found
On High-Rate Cryptographic Compression Functions
The security of iterated hash functions relies on the properties of underlying compression functions. We study highly efficient compression functions based on block ciphers. We propose a model for high-rate compression functions, and give an upper bound for the rate of any collision resistant compression function in our model. In addition, we show that natural generalizations of constructions by Preneel, Govaerts, and Vandewalle to the case of rate-2 compression functions are not collision resistant
Compression functions of uniform embeddings of groups into Hilbert and Banach spaces
We construct finitely generated groups with arbitrary prescribed Hilbert
space compression \alpha from the interval [0,1]. For a large class of Banach
spaces E (including all uniformly convex Banach spaces), the E-compression of
these groups coincides with their Hilbert space compression. Moreover, the
groups that we construct have asymptotic dimension at most 3, hence they are
exact. In particular, the first examples of groups that are uniformly
embeddable into a Hilbert space (respectively, exact, of finite asymptotic
dimension) with Hilbert space compression 0 are given. These groups are also
the first examples of groups with uniformly convex Banach space compression 0.Comment: 21 pages; version 3: The final version, accepted by Crelle; version
2: corrected misprints, added references, the group has asdim at most 2, not
at most 3 as in the first version (thanks to A. Dranishnikov); version 3:
took into account referee remarks, added references. the paper is accepted in
Crell
A quasi-isometric embedding theorem for groups
We show that every group of at most exponential growth with respect to
some left invariant metric admits a bi-Lipschitz embedding into a finitely
generated group such that is amenable (respectively, solvable,
satisfies a non-trivial identity, elementary amenable, of finite decomposition
complexity, etc.) whenever is. We also discuss some applications to
compression functions of Lipschitz embeddings into uniformly convex Banach
spaces, F{\o}lner functions, and elementary classes of amenable groups
The universality of iterated hashing over variable-length strings
Iterated hash functions process strings recursively, one character at a time.
At each iteration, they compute a new hash value from the preceding hash value
and the next character. We prove that iterated hashing can be pairwise
independent, but never 3-wise independent. We show that it can be almost
universal over strings much longer than the number of hash values; we bound the
maximal string length given the collision probability
On Compression Functions over Small Groups with Applications to Cryptography
In the area of cryptography, fully homomorphic encryption (FHE) enables any
entity to perform arbitrary computation on encrypted data without decrypting
the ciphertexts. An ongoing group-theoretic approach to construct FHE schemes
uses a certain "compression" function implemented by group operators on
a given finite group (i.e., it is given by a sequence of elements of
and variable ), which satisfies that and where is some element of order three. The previous
work gave an example of such over by just a heuristic approach.
In this paper, we systematically study the possibilities of such . We
construct a shortest possible over smaller group , and prove that
no such exists over other groups of order up to .Comment: 10 page
A New Hybrid Method of IPv6 Addressing in the Internet of Things
Humans have always been seeking greater control over their surrounding
objects. Today, with the help of Internet of Things (IoT), we can fulfill this
goal. In order for objects to be connected to the internet, they should have an
address, so that they can be detected and tracked. Since the number of these
objects are very large and never stop growing, addressing space should be used,
which can respond to this number of objects. In this regard, the best option is
IPv6. Addressing has different methods, the most important of which are
introduced in this paper. The method presented in this paper is a hybrid
addressing method which uses EPC and ONS IP. The method proposed in this paper
provides a unique and hierarchical IPv6 address for each object. This method is
simple and does not require additional hardware for implantation. Further, the
addressing time of this method is short while its scalability is high, and is
compatible with different EPC standards
Compression functions of uniform embeddings of groups into Hilbert and Banach spaces
We construct finitely generated groups with arbitrary prescribed Hilbert space compression α ∈ [0, 1]. This answers a question of E. Guentner and G. Niblo. For a large class of Banach spaces ℰ (including all uniformly convex Banach spaces), the ℰ-compression of these groups coincides with their Hilbert space compression. Moreover, the groups that we construct have asymptotic dimension at most 2, hence they are exact. In particular, the first examples of groups that are uniformly embeddable into a Hilbert space (moreover, of finite asymptotic dimension and exact) with Hilbert space compression 0 are given. These groups are also the first examples of groups with uniformly convex Banach space compression
Preimage resistance beyond the birthday bound: Double-length hashing revisited
Security proofs are an essential part of modern cryptography. Often the challenge is not to come up with appropriate schemes but rather to technically prove that these satisfy the desired security properties.
We provide for the first time techniques for proving asymptotically optimal preimage resistance bounds for block cipher based double length, double call hash functions. More precisely, we consider for some \keylength>\blocklength compression functions H:\{0,1\}^{\keylength+\blocklength} \rightarrow \{0,1\}^{2\blocklength} using two calls to an ideal block cipher with an \blocklength-bit block size. Optimally, an adversary trying to find a preimage for should require \Omega(2^{2\blocklength}) queries to the underlying block cipher. As a matter of fact there have been several attempts to prove the preimage resistance of such compression functions, but no proof did go beyond the \Omega(2^{\blocklength}) barrier, therefore leaving a huge gap when compared to the optimal bound.
In this paper, we introduce two new techniques on how to lift this bound to \Omega(2^{2\blocklength}). We demonstrate our new techniques for a simple and natural design of , being the concatenation of two instances of the well-known Davies-Meyer compression function
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