Deposits of clastic carbonate-dominated (calciclastic) sedimentary slope systems in the rock record have been identified mostly as linearly-consistent carbonate apron deposits, even though most ancient clastic carbonate slope deposits fit the submarine fan systems better. Calciclastic submarine fans are consequently rarely described and are poorly understood. Subsequently, very little is known especially in mud-dominated calciclastic submarine fan systems. Presented in this study are a sedimentological core and petrographic characterisation of samples from eleven boreholes from the Lower Carboniferous of Bowland Basin (Northwest England) that reveals a >250 m thick calciturbidite complex deposited in a calciclastic submarine fan setting. Seven facies are recognised from core and thin section characterisation and are grouped into three carbonate turbidite sequences. They include: 1) Calciturbidites, comprising mostly of highto low-density, wavy-laminated bioclast-rich facies; 2) low-density densite mudstones which are characterised by planar laminated and unlaminated muddominated facies; and 3) Calcidebrites which are muddy or hyper-concentrated debrisflow deposits occurring as poorly-sorted, chaotic, mud-supported floatstones. These

Phd by thesis

We have obtained two results since leaving Chapter 3 which make this return to βℕ possible. The first of these was Corollary 4.30 in which we found, under the assumption of the Continuum Hypothesis, that ℕ* contains a dense subset of 2C P-points. The second was Corollary 6.30 in which we saw that no point of ℕ* has its own type as a relative type with respect to any copy of ℕ contained in ℕ*. Here we will make use of these two properties of ℕ* to continue the investigation of βℕ and especially of ℕ*.

β ℕ Revisited

We propose a relaxation of zero-knowledge, by allowing the simulator to run in quasi-polynomial time. We show that protocols satisfying this notion can be constructed in settings where the standard definition is too restrictive. Specifically, we construct constant-round straight-line concurrent quasi-polynomial time simulatable arguments and show that such arguments can be used in advanced composition operations without any set-up assumptions. Our protocols rely on slightly strong, but standard type assumptions (namely the existence of one-to-one one-way functions secure against subexponential circuits).

Simulation in quasi-polynomial time, and its application to protocol composition

Functional encryption (FE) is an extremely powerful cryptographic mechanism that lets an authorized entity compute on encrypted data, and learn the results in the clear. However, all current cryptographic instantiations for general FE are too impractical to be implemented. We construct IRON, a provably secure, and practical FE system using Intel's recent Software Guard Extensions (SGX). We show that IRON can be applied to complex functionalities, and even for simple functions, outperforms the best known cryptographic schemes. We argue security by modeling FE in the context of hardware elements, and prove that IRON satisfies the security model.

IRON: Functional Encryption using Intel SGX

We present new constructions of round-efficient, or even round-optimal, Multi-Party Computation (MPC) protocols from Oblivious Transfer (OT) protocols. Our constructions establish a tight connection between MPC and OT: In the setting of semi-honest security, for any $k \ge 2$, k-round semi-honest OT is necessary and complete for k-round semi-honest MPC. In the round-optimal case of $k = 2$, we obtain 2-round semi-honest MPC from 2-round semi-honest OT, resolving the round complexity of semi-honest MPC assuming weak and necessary assumption. In comparison, previous 2-round constructions rely on either the heavy machinery of indistinguishability obfuscation or witness encryption, or the algebraic structure of bilinear pairing groups. More generally, for an arbitrary number of rounds k, all previous constructions of k-round semi-honest MPC require at least OT with $k'$ rounds for $k' \le \lfloor k/2 \rfloor $.

/pdf/k-round-multiparty-computation-from-k-round-oblivious-n73tej47fz.pdf

k -Round Multiparty Computation from k -Round Oblivious Transfer via Garbled Interactive Circuits

We develop a general approach to adding a threshold functionality to a large class of (non-threshold) cryptographic schemes. A threshold functionality enables a secret key to be split into a number of shares, so that only a threshold of parties can use the key, without reconstructing the key. We begin by constructing a threshold fully-homomorphic encryption scheme (ThFHE) from the learning with errors (LWE) problem. We next introduce a new concept, called a universal thresholdizer, from which many threshold systems are possible. We show how to construct a universal thresholdizer from our ThFHE. A universal thresholdizer can be used to add threshold functionality to many systems, such as CCA-secure public-key encryption (PKE), signature schemes, pseudorandom functions, and others primitives. In particular, by applying this paradigm to a (non-threshold) lattice signature system, we obtain the first single-round threshold signature scheme from LWE.

/pdf/threshold-cryptosystems-from-threshold-fully-homomorphic-41d7xoq7t3.pdf

Threshold Cryptosystems From Threshold Fully Homomorphic Encryption.

Threshold Cryptosystems from Threshold Fully Homomorphic Encryption

In this work, we show how to construct indistinguishability obfuscation from subexponential hardness of four well-founded assumptions. We prove: 
Let $\tau \in (0,\infty), \delta \in (0,1), \epsilon \in (0,1)$ be arbitrary constants. Assume sub-exponential security of the following assumptions, where $\lambda$ is a security parameter, and the parameters $\ell,k,n$ below are large enough polynomials in $\lambda$: 
- The SXDH assumption on asymmetric bilinear groups of a prime order $p = O(2^\lambda)$, 
- The LWE assumption over $\mathbb{Z}_{p}$ with subexponential modulus-to-noise ratio $2^{k^\epsilon}$, where $k$ is the dimension of the LWE secret, 
- The LPN assumption over $\mathbb{Z}_p$ with polynomially many LPN samples and error rate $1/\ell^\delta$, where $\ell$ is the dimension of the LPN secret, 
- The existence of a Boolean PRG in $\mathsf{NC}^0$ with stretch $n^{1+\tau}$, 
Then, (subexponentially secure) indistinguishability obfuscation for all polynomial-size circuits exists.

Indistinguishability Obfuscation from Well-Founded Assumptions

The existence of secure indistinguishability obfuscators ($i\mathcal {O}$) has far-reaching implications, significantly expanding the scope of problems amenable to cryptographic study. All known approaches to constructing $i\mathcal {O}$ rely on d-linear maps. While secure bilinear maps are well established in cryptographic literature, the security of candidates for $d>2$ is poorly understood.

Indistinguishability Obfuscation Without Multilinear Maps: New Paradigms via Low Degree Weak Pseudorandomness and Security Amplification

Indistinguishability obfuscation, introduced by [Barak et. al. Crypto 2001], aims to compile programs into unintelligible ones while preserving functionality. It is a fascinating and powerful object that has been shown to enable a host of new cryptographic goals and beyond. However, constructions of indistinguishability obfuscation have remained elusive, with all other proposals relying on heuristics or newly conjectured hardness assumptions. In this work, we show how to construct indistinguishability obfuscation from subexponential hardness of four well-founded assumptions. We prove: Informal Theorem: Let τ ∈ (0,∞), δ ∈ (0,1), ∈ (0,1) be arbitrary constants. Assume sub-exponential security of the following assumptions: - the Learning With Errors (LWE) assumption with subexponential modulus-to-noise ratio 2kє and noises of magnitude polynomial in k, where k is the dimension of the LWE secret, - the Learning Parity with Noise (LPN) assumption over general prime fields ℤp with polynomially many LPN samples and error rate 1/lδ, where l is the dimension of the LPN secret, - the existence of a Boolean Pseudo-Random Generator (PRG) in NC0 with stretch n1+τ, where n is the length of the PRG seed, - the Decision Linear (DLIN) assumption on symmetric bilinear groups of prime order. Then, (subexponentially secure) indistinguishability obfuscation for all polynomial-size circuits exists. Further, assuming only polynomial security of the aforementioned assumptions, there exists collusion resistant public-key functional encryption for all polynomial-size circuits.

Aayush Jain

Papers

Threshold Cryptosystems From Threshold Fully Homomorphic Encryption.

Threshold Cryptosystems from Threshold Fully Homomorphic Encryption

Indistinguishability Obfuscation from Well-Founded Assumptions

Indistinguishability Obfuscation Without Multilinear Maps: New Paradigms via Low Degree Weak Pseudorandomness and Security Amplification

Indistinguishability obfuscation from well-founded assumptions