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censorship circumvention call for methods to represent uniformly random
points on elliptic curves as uniformly random bit strings, so that, for
example, ECC network traffic can masquerade as random traffic.
At ACM CCS 2013, Bernstein et al. proposed an efficient approach,
called ``Elligator,\'\' to solving this problem for arbitrary elliptic
curve-based cryptographic protocols, based on the use of efficiently
invertible maps to elliptic curves. Unfortunately, such invertible maps
are only known to exist for certain classes of curves, excluding in
particular curves of prime order and curves over binary fields. A variant
of this approach, ``Elligator Squared,\'\' was later proposed by Tibouchi
(FC 2014) supporting not necessarily injective encodings to elliptic
curves (and hence a much larger class of curves), but, although some
rough efficiency estimates were provided, it was not clear how an actual
implementation of that approach would perform in practice.
In this paper, we show that Elligator Squared can indeed be implemented
very efficiently with a suitable choice of curve encodings. More
precisely, we consider the binary curve setting (which was not discussed
in Tibouchi\'s paper), and implement the Elligator Squared bit string
representation algorithm based on a suitably optimized version of the
Shallue--van de Woestijne characteristic 2 encoding, which we show can
be computed using only multiplications, trace and half-trace
computations, and a few inversions.
On the fast binary curve of Oliveira et al. (CHES 2013), our
implementation runs in an average of only 22850 Haswell cycles, making
uniform bit string representations possible for a very reasonable
overhead---much smaller even than Elligator on Edwards curves.
As a side contribution, we also compare implementations of Elligator and
Elligator Squared on a curve supported by Elligator, namely
Curve25519. We find that generating a random point and its uniform
bitstring representation is around 35-40% faster with Elligator for
protocols using a fixed base point (such as static ECDH), but 30-35%
faster with Elligator Squared in the case of a variable base point
(such as ElGamal encryption). Both are significantly slower
than our binary curve implementation.
drowning step of re-randomization, in which we apply the
Rényi divergence instead of the conventional statistical distance as a measure of distance between distributions. Our second improvement is to reduce the number of randomizers needed from $\\Omega(n \\log n)$ to $2$, where $n$ is the dimension of the underlying ideal lattices. These two contributions allow us to decrease the bit size of the public parameters from $O(\\lambda^5 \\log \\lambda)$ for the
GGH scheme to $O(\\lambda \\log^2 \\lambda)$ in GGHLite, with respect to the security parameter $\\lambda$ (for a constant multilinearity parameter $\\kappa$).
CloudFlare is looking for a talented software engineer to join our security team. We are working on a number of ambitious projects to secure the web and protect our customers from threats of all sorts. The role of security engineer at CloudFlare is more that of a builder than a breaker. You will have to approach problems with creativity and flexibility and be able to identify and use the best tools for the job or build better ones from scratch. At CloudFlare, we are serious about protecting our customers and advancing the state of the art in computer security.
We are looking for experienced engineers (5+ years of experience preferred) with practical expertise in the areas of:
A block cipher is the foundation stone of symmetric-key cryptography. Due to its simplicity and high performance, it is often the workhorse for providing confidentiality - one of the primary goals of cryptography. Hence the security of a block cipher is of fundamental importance in the entire infrastructure of cryptography, and therefore block ciphers shall be analyzed and evaluated. This practice is called block cipher cryptanalysis. In this thesis, we analyze a few block ciphers in the classic meet-in-the-middle model and in the recently proposed multidimensional linear cryptanalysis model.
Besides for encryption, block ciphers are also one of the most versatile building blocks used for constructing many other cryptographic primitives. One such example is the compression function of cryptographic hash functions, and there is a close relation between the security analysis of block ciphers and hash functions. In addition, many dedicated cryptographic hash functions are designed with ideas used in block ciphers. Therefore, it is natural that many block cipher cryptanalysis techniques can be transferred to hash function analysis. In this thesis, we analyze hash functions with differential cryptanalysis and techniques inspired by differential cryptanalysis. On the other hand, recent advances in hash function cryptanalysis contribute to the analysis of block ciphers. We give one such example too.
In total we have four main topics on (or closely related to) the security analysis of block ciphers.