Indistinguishability Obfuscation from Well-Founded Assumptions

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

Cryptography from tensor problems

We describe a new proposal for a trap-door one-way function. The new proposal belongs to the "multivariate quadratic" family but the trap-door is different from existing methods, and is simpler

Isogeny-based post-quantum key exchange protocols

The goal of this project is to understand and analyze the supersingular isogeny Diffie Hellman (SIDH), a post-quantum key exchange protocol which security lies on the isogeny-finding problem between supersingular elliptic curves. In order to do so, we first introduce the reader to cryptography focusing on key agreement protocols and motivate the rise of post-quantum cryptography as a necessity with the existence of the model of quantum computation. We review some of the known attacks on the SIDH and finally study some algorithmic aspects to understand how the protocol can be implemented

Quantum attacks on Bitcoin, and how to protect against them

The key cryptographic protocols used to secure the internet and financial transactions of today are all susceptible to attack by the development of a sufficiently large quantum computer. One particular area at risk are cryptocurrencies, a market currently worth over 150 billion USD. We investigate the risk of Bitcoin, and other cryptocurrencies, to attacks by quantum computers. We find that the proof-of-work used by Bitcoin is relatively resistant to substantial speedup by quantum computers in the next 10 years, mainly because specialized ASIC miners are extremely fast compared to the estimated clock speed of near-term quantum computers. On the other hand, the elliptic curve signature scheme used by Bitcoin is much more at risk, and could be completely broken by a quantum computer as early as 2027, by the most optimistic estimates. We analyze an alternative proof-of-work called Momentum, based on finding collisions in a hash function, that is even more resistant to speedup by a quantum computer. We also review the available post-quantum signature schemes to see which one would best meet the security and efficiency requirements of blockchain applications.Comment: 21 pages, 6 figures. For a rough update on the progress of Quantum devices and prognostications on time from now to break Digital signatures, see https://www.quantumcryptopocalypse.com/quantum-moores-law

A Survey of Layer-Two Blockchain Protocols

After the success of the Bitcoin blockchain, came several cryptocurrencies and blockchain solutions in the last decade. Nonetheless, Blockchain-based systems still suffer from low transaction rates and high transaction processing latencies, which hinder blockchains' scalability. An entire class of solutions, called Layer-1 scalability solutions, have attempted to incrementally improve such limitations by adding/modifying fundamental blockchain attributes. Recently, a completely different class of works, called Layer-2 protocols, have emerged to tackle the blockchain scalability issues using unconventional approaches. Layer-2 protocols improve transaction processing rates, periods, and fees by minimizing the use of underlying slow and costly blockchains. In fact, the main chain acts just as an instrument for trust establishment and dispute resolution among Layer-2 participants, where only a few transactions are dispatched to the main chain. Thus, Layer-2 blockchain protocols have the potential to transform the domain. However, rapid and discrete developments have resulted in diverse branches of Layer-2 protocols. In this work, we systematically create a broad taxonomy of such protocols and implementations. We discuss each Layer-2 protocol class in detail and also elucidate their respective approaches, salient features, requirements, etc. Moreover, we outline the issues related to these protocols along with a comparative discussion. Our thorough study will help further systematize the knowledge dispersed in the domain and help the readers to better understand the field of Layer-2 protocols.Comment: 21 pages, 15 figures, 2 table