A common strategy for constructing multivariate encryption schemes is to use a central map that is easy to invert over an extension field, along with a small number of modifications to thwart ...potential attacks. In this work, we study the effectiveness of these modifications, by deriving estimates for the number of degree fall polynomials. After developing the necessary tools, we focus on encryption schemes using the
C
∗
and Dobbertin central maps, with the internal perturbation (
ip
), and
Q
+
modifications. For these constructions, we are able to accurately predict the number of degree fall polynomials produced in a Gröbner basis attack, up to and including degree 5 for the Dob encryption scheme and four for
C
∗
. The predictions remain accurate even when fixing variables. Based on this new theory, we design a novel attack on Dob, which completely recovers the secret key for the parameters suggested by its designers. Due to the generality of the presented techniques, we also believe that they are of interest to the analysis of other big-field schemes.
Fully homomorphic encryption (FHE) is a powerful tool in cryptography that allows one to perform arbitrary computations on encrypted material without having to decrypt it first. There are numerous ...FHE schemes, all of which are expanded from somewhat homomorphic encryption (SHE) schemes, and some of which are considered viable in practice. However, while these FHE schemes are semantically (IND-CPA) secure, the question of their IND-CCA1 security is much less studied, and we therefore provide an overview of the IND-CCA1 security of all acknowledged FHE schemes in this paper. To give this overview, we grouped the SHE schemes into broad categories based on their similarities and underlying hardness problems. For each category, we show that the SHE schemes are susceptible to either known adaptive key recovery attacks, a natural extension of known attacks, or our proposed attacks. Finally, we discuss the known techniques to achieve IND-CCA1-secure FHE and SHE schemes. We concluded that none of the proposed schemes were IND-CCA1-secure and that the known general constructions all had their shortcomings.
We show how to build a binary matrix from the MRHS representation of a symmetric-key cipher. The matrix contains the cipher represented as an equation system and can be used to assess a cipher’s ...resistance against algebraic attacks. We give an algorithm for solving the system and compute its complexity. The complexity is normally close to exhaustive search on the variables representing the user-selected key. Finally, we show that for some variants of LowMC, the joined MRHS matrix representation can be used to speed up regular encryption in addition to exhaustive key search.
Annexin A2 (AnxA2) is a multi-functional and -compartmental protein whose subcellular localisation and functions are tightly regulated by its post-translational modifications. AnxA2 and its ...Tyr23-phosphorylated form (pTyr23AnxA2) are involved in malignant cell transformation, metastasis and angiogenesis. Here, we show that H2O2 exerts rapid, simultaneous and opposite effects on the Tyr23 phosphorylation status of AnxA2 in two distinct compartments of rat pheochromocytoma (PC12) cells. Reactive oxygen species induce dephosphorylation of pTyr23AnxA2 located in the PML bodies of the nucleus, whereas AnxA2 associated with F-actin at the cell cortex is Tyr23 phosphorylated. The H2O2-induced responses in both compartments are transient and the pTyr23AnxA2 accumulating at the cell cortex is subsequently incorporated into vesicles and then released to the extracellular space. Blocking nuclear export by leptomycin B does not affect the nuclear pool of pTyr23AnxA2, but increases the amount of total AnxA2 in this compartment, indicating that the protein might have several functions in the nucleus. These results suggest that Tyr23 phosphorylation can regulate the function of AnxA2 at distinct subcellular sites.
We address the factorization problem in this paper: Given an integer
N
=
pq
, find two factors
p
and
q
of
N
such that
p
and
q
are of same bit-size. When we say integer multiplication of
N
, we mean ...expressing
N
as a product of two factors
p
and
q
such that
p
and
q
are of
same bit-size
. We work on this problem in the light of Binary Decision Diagrams (BDD). A Binary Decision Diagram is an acyclic graph which can be used to represent Boolean functions. We represent integer multiplication of
N
as product of factors
p
and
q
using a BDD. Using various operations on the BDD we present an algorithm for factoring
N
. All calculations are done over
GF
(
2
)
. We show that the number of nodes in the constructed BDD is
O
(
n
3
)
where
n
is the number of bits in
p
or
q
. We do factoring experiments for the case when
p
and
q
are primes as in the case of RSA modulus
N
, and report on the observed complexity. The multiplication of large RSA numbers (that cannot be factored fast in practice) can still be easily represented as a BDD.
In this paper we study Boolean equation systems, and how to eliminate variables from them while bounding the degree of polynomials produced. A procedure for variable elimination is introduced, and we ...relate the techniques to Gröbner bases and XL methods. We prove that by increasing the degree of the polynomials in the system by one for each variable eliminated, we preserve the solution space, provided that the system satisfies a particular condition. We then estimate how many variables we need to eliminate in order to solve the resulting system by re-linearization, and show that we get complexities lower than the trivial brute-force
O
(
2
n
)
when the system is overdetermined.
Annexin A2 (AnxA2) is a widely expressed multifunctional protein found in different cellular compartments. In spite of lacking a hydrophobic signal peptide, AnxA2 is found at the cell surface of ...endothelial cells, indicative of a role in angiogenesis. Increased extracellular levels of AnxA2 in tumours correlate with neoangiogenesis, metastasis and poor prognosis. We hypothesised that extracellular AnxA2 may contribute to angiogenesis by affecting endothelial cell-cell interactions and motility. To address this question, we studied the effect of heterotetrameric and monomeric forms of AnxA2, as well as its two soluble domains on the formation and maintenance of capillary-like structures by using an in vitro co-culture system consisting of endothelial and smooth muscle cells. In particular, addition of purified domains I and IV of AnxA2 potently inhibited the vascular endothelial growth factor (VEGF)-dependent formation of the capillary-like networks in a dose-dependent manner. In addition, these AnxA2 domains disrupted endothelial cell-cell contacts in preformed capillary-like networks, resulting in the internalisation of vascular endothelial (VE)-cadherin and the formation of VE-cadherin-containing filopodia-like structures between the endothelial cells, suggesting increased cell motility. Addition of monoclonal AnxA2 antibodies, in particular against Tyr23 phosphorylated AnxA2, also strongly inhibited network formation in the co-culture system. These results suggest that extracellular AnxA2, most likely in its Tyr phosphorylated form, plays a pivotal role in angiogenesis. The exogenously added AnxA2 domains most likely mediate their effects by competing with endogenous AnxA2 for extracellular factors necessary for the initiation and maintenance of angiogenesis, such as those involved in the formation/integrity of cell-cell contacts.
Increasing evidence points to the participation of the multifunctional protein Annexin A2 (AnxA2) in mRNA localisation as well as the translation of certain mRNAs on cytoskeleton-bound polysomes, and ...thereby in the regulation of the biosynthesis of specific proteins, such as c-Myc and AnxA2 itself, which are linked to cellular transformation. AnxA2 is most likely activated by signalling pathways, which result in its post-translational modifications and modulate its binding to various ligands, including specific mRNAs. Positive and polar residues in helices C-D in domain IV of AnxA2 bind to cis-acting elements in the 3'-UTRs of its cognate, c-myc, collagen prolyl 4-hydroxylase-α(I) and N-methyl-D-aspartate R1 mRNAs, thus contributing to post-transcriptional regulation of the expression of specific genes. The cis-acting elements appear to constitute a higher order structure, frequently containing the consensus sequence 5'-AA(C/G)(A/U)G; however, non-canonical AnxA2 binding sites may also be involved. In the case of c-myc mRNA, the association with AnxA2 appears to regulate its localisation and translation. In addition, the binding of AnxA2 to a pseudoknot structure present in infectious bronchitis viral RNA results in reduced efficiency of -1 ribosomal frameshifting, indicating its recruitment as a host protein during viral infection. Finally, the association of AnxA2 with endosomes and exosomes suggests a role in co-ordinated transport of mRNA and vesicles, i.e. processes that respond to extracellular signals and are expected to employ multifunctional proteins.
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