All or Nothing at All

We continue a study of unconditionally secure all-or-nothing transforms (AONT) begun in \cite{St}. An AONT is a bijective mapping that constructs s outputs from s inputs. We consider the security of t inputs, when s-t outputs are known. Previous work concerned the case t=1; here we consider the problem for general t, focussing on the case t=2. We investigate constructions of binary matrices for which the desired properties hold with the maximum probability. Upper bounds on these probabilities are obtained via a quadratic programming approach, while lower bounds can be obtained from combinatorial constructions based on symmetric BIBDs and cyclotomy. We also report some results on exhaustive searches and random constructions for small values of s.Comment: 23 page

Generalizations of All-or-Nothing Transforms and their Application in Secure Distributed Storage

An all-or-nothing transform is an invertible function that maps s inputs to s outputs such that, in the calculation of the inverse, the absence of only one output makes it impossible for an adversary to obtain any information about any single input. In this thesis, we generalize this structure in several ways motivated by different applications, and for each generalization, we provide some constructions. For a particular generalization, where we consider the security of t input blocks in the absence of t output blocks, namely, t-all-or-nothing transforms, we provide two applications. We also define a closeness measure and study structures that are close to t-all-or-nothing transforms. Other generalizations consider the situations where: i) t covers a range of values and the structure maintains its t-all-or-nothingness property for all values of t in that range; ii) the transform provides security for a smaller, yet fixed, number of inputs than the number of absent outputs; iii) the missing output blocks are only from a fixed subset of the output blocks; and iv) the transform generates n outputs so that it can still reconstruct the inputs as long as s outputs are available. In the last case, the absence of n-s+t outputs can protect the security of any t inputs. For each of these transforms, various existence and non-existence results, as well as bounds and equivalence results are presented. We finish with proposing an application of generalization (iv) in secure distributed storage

A Scalable Post-quantum Hash-Based Group Signature

Abstract. We present a construction for hash-based one-time group signature schemes, and develop a traceable post-quantum multi-time group signature upon it. A group signature scheme allows group members to anonymously sign a message on behalf of the whole group. The signatures are unforgeable and the scheme enables authorized openers to trace the signature back to the original signer when needed. Our construction utilizes three nested layers to build the group signature scheme. The first layer is key management; it deploys a transversal design to assign keys to the group members and the openers, providing the construction with traceability. The second layer utilizes hash pools to build the group public verification key, to connect group members together, and to provide anonymity. The final layer is a post-quantum hash-based signature scheme, that adds unforgeability to our construction. We extend our scheme to multi-time signatures by using Merkle trees, and show that this process keeps the scalability property of Merkle-based signatures, while it supports the group members signing any number of messages. Keywords: Post Quantum Signatures, Hash-based Signatures, Group Signatures, Transversal Designs, Multi-opener Signature

Rectangular, Range, and Restricted AONTs: Three Generalizations of All-or-Nothing Transforms

All-or-nothing transforms (AONTs) were originally defined by Rivest as bijections from $s$ input blocks to $s$ output blocks such that no information can be obtained about any input block in the absence of any output block. Numerous generalizations and extensions of all-or-nothing transforms have been discussed in recent years, many of which are motivated by diverse applications in cryptography, information security, secure distributed storage, etc. In particular, $t$-AONTs, in which no information can be obtained about any $t$ input blocks in the absence of any $t$ output blocks, have received considerable study. In this paper, we study three generalizations of AONTs that are motivated by applications due to Pham et al. and Oliveira et al. We term these generalizations rectangular, range, and restricted AONTs. Briefly, in a rectangular AONT, the number of outputs is greater than the number of inputs. A range AONT satisfies the $t$-AONT property for a range of consecutive values of $t$. Finally, in a restricted AONT, the unknown outputs are assumed to occur within a specified set of secure output blocks. We study existence and non-existence and provide examples and constructions for these generalizations. We also demonstrate interesting connections with combinatorial structures such as orthogonal arrays, split orthogonal arrays, MDS codes and difference matrices

Constructions and bounds for codes with restricted overlaps

Non-overlapping codes have been studied for almost 60 years. In such a code, no proper, non-empty prefix of any codeword is a suffix of any codeword. In this paper, we study codes in which overlaps of certain specified sizes are forbidden. We prove some general bounds and we give several constructions in the case of binary codes. Our techniques also allow us to provide an alternative, elementary proof of a lower bound on non-overlapping codes due to Levenshtein in 1964.Comment: 25 pages. Extra citations, typos corrected and explanations expande

Assisted Oocyte Activation following Intracytoplasmic Sperm Injection: A Sensible Option for Infertile Couples with Severe Teratozoospermia

The intracytoplasmic sperm injection (ICSI) has significantly improved male factor infertility treatment; however, complete fertilization failure still occurs in 1-5% of ICSI treatment cycles mainly due to oocyte activation failure. It is estimated that around 40-70% of oocyte activation failure is associated with sperm factors after ICSI. Assisted oocyte activation (AOA) as an effective approach to avoid total fertilization failure (TFF) has been proposed following ICSI. In the literature, several procedures have been described to overcome failed oocyte activation. These include mechanical, electrical, or chemical stimuli initiating artificial Ca2+ rises in the cytoplasm of oocytes. AOA in couples with previous failed fertilization and those with globozoospermia has resulted in varying degrees of success. The aim of this review is to examine the available literature on AOA in teratozoospermic men undergoing ICSI-AOA and determine whether the ICSI-AOA should be considered as an adjunct fertility procedure for these patients

PPARγ/Pgc-1α-Fndc5 pathway up-regulation in gastrocnemius and heart muscle of exercised, branched chain amino acid diet fed mice

BACKGROUND: Previous studies have revealed the inductive effect of branched-chain amino acids (BCAAs) catabolism on fatty acid oxidation and metabolism, especially in muscle cells. In the present investigation, we have attempted to address whether a combination of BCAAs supplement consumption with aerobic exercise could elaborate the expression of PPARγ, Pgc-1α and Fndc5 genes in gastrocnemius muscle and heart tissue of male C57BL/6 mice. METHODS: Thirty-six young male mice with an average weight of 18 ± 2 g were selected. Mice were randomly assigned to 6 groups: 20 mg/mL of BCAAs consumption with simultaneous exercise-training, 60 mg/mL of BCAAs consumption with simultaneous exercise-training, exercise-trained with no BCAAs consumption group, 20 mg/mL BCAAs without exercise-training, 60 mg/mL BCAAs without exercise-training, and untrained mice without BCAAs consumption. RESULTS: The findings showed a combination of 20 mg/mL BCAAs with aerobic exercise significantly increased Fndc5, PPARγ, Pgc-1α gene expression in skeletal muscles although, circulating Irisin levels remained unchanged (p < 0.05). Interestingly, plasma urea and lactate levels were significantly increased in 60 mg/mL BCAAs administrated mice which performed exercised (p < 0.05). Two-way analysis of variance (ANOVA) was used to examine significant difference between groups and sedentary group. CONCLUSIONS: Results showed inductive effect of 20 mg/mL BCAAs on expression levels of Fndc5, PPARγ, Pgc-1α in gastrocnemius muscle similar with counterparts in heart tissue. Of note, higher serum irisin levels were detected after 20 mg/mL BCAAs supplementation coincided with the exercise. GRAPHICAL ABSTRACT: An Overview on supplemantaion of branched chain amoinoacids on metablism of skeletal muscle and heart: https://media.springernature.com/lw685/springer-static/image/art%3A10.1186%2Fs12986-018-0298-3/MediaObjects/12986_2018_298_Figa_HTML.png?as=web