Ramanujan graphs in cryptography

In this paper we study the security of a proposal for Post-Quantum Cryptography from both a number theoretic and cryptographic perspective. Charles-Goren-Lauter in 2006 [CGL06] proposed two hash functions based on the hardness of finding paths in Ramanujan graphs. One is based on Lubotzky-Phillips-Sarnak (LPS) graphs and the other one is based on Supersingular Isogeny Graphs. A 2008 paper by Petit-Lauter-Quisquater breaks the hash function based on LPS graphs. On the Supersingular Isogeny Graphs proposal, recent work has continued to build cryptographic applications on the hardness of finding isogenies between supersingular elliptic curves. A 2011 paper by De Feo-Jao-Pl\^{u}t proposed a cryptographic system based on Supersingular Isogeny Diffie-Hellman as well as a set of five hard problems. In this paper we show that the security of the SIDH proposal relies on the hardness of the SIG path-finding problem introduced in [CGL06]. In addition, similarities between the number theoretic ingredients in the LPS and Pizer constructions suggest that the hardness of the path-finding problem in the two graphs may be linked. By viewing both graphs from a number theoretic perspective, we identify the similarities and differences between the Pizer and LPS graphs.Comment: 33 page

KALwEN: a new practical and interoperable key management scheme for body sensor networks

Key management is the pillar of a security architecture. Body sensor networks (BSNs) pose several challenges–some inherited from wireless sensor networks (WSNs), some unique to themselves–that require a new key management scheme to be tailor-made. The challenge is taken on, and the result is KALwEN, a new parameterized key management scheme that combines the best-suited cryptographic techniques in a seamless framework. KALwEN is user-friendly in the sense that it requires no expert knowledge of a user, and instead only requires a user to follow a simple set of instructions when bootstrapping or extending a network. One of KALwEN's key features is that it allows sensor devices from different manufacturers, which expectedly do not have any pre-shared secret, to establish secure communications with each other. KALwEN is decentralized, such that it does not rely on the availability of a local processing unit (LPU). KALwEN supports secure global broadcast, local broadcast, and local (neighbor-to-neighbor) unicast, while preserving past key secrecy and future key secrecy (FKS). The fact that the cryptographic protocols of KALwEN have been formally verified also makes a convincing case. With both formal verification and experimental evaluation, our results should appeal to theorists and practitioners alike

Agent-Based Simulations of Blockchain protocols illustrated via Kadena's Chainweb

While many distributed consensus protocols provide robust liveness and consistency guarantees under the presence of malicious actors, quantitative estimates of how economic incentives affect security are few and far between. In this paper, we describe a system for simulating how adversarial agents, both economically rational and Byzantine, interact with a blockchain protocol. This system provides statistical estimates for the economic difficulty of an attack and how the presence of certain actors influences protocol-level statistics, such as the expected time to regain liveness. This simulation system is influenced by the design of algorithmic trading and reinforcement learning systems that use explicit modeling of an agent's reward mechanism to evaluate and optimize a fully autonomous agent. We implement and apply this simulation framework to Kadena's Chainweb, a parallelized Proof-of-Work system, that contains complexity in how miner incentive compliance affects security and censorship resistance. We provide the first formal description of Chainweb that is in the literature and use this formal description to motivate our simulation design. Our simulation results include a phase transition in block height growth rate as a function of shard connectivity and empirical evidence that censorship in Chainweb is too costly for rational miners to engage in. We conclude with an outlook on how simulation can guide and optimize protocol development in a variety of contexts, including Proof-of-Stake parameter optimization and peer-to-peer networking design.Comment: 10 pages, 7 figures, accepted to the IEEE S&B 2019 conferenc

Broadcast Authentication for Wireless Sensor Networks Using Nested Hashing and the Chinese Remainder Theorem

Secure broadcasting is an essential feature for critical operations in wireless sensor network (WSNs). However, due to the limited resources of sensor networks, verifying the authenticity for broadcasted messages is a very difficult issue. μTESLA is a broadcast authentication protocol, which uses network-wide loose time synchronization with one-way hashed keys to provide the authenticity verification. However, it suffers from several flaws considering the delay tolerance, and the chain length restriction. In this paper, we propose a protocol which provides broadcast authentication for wireless sensor networks. This protocol uses a nested hash chain of two different hash functions and the Chinese Remainder Theorem (CRT). The two different nested hash functions are employed for the seed updating and the key generation. Each sensor node is challenged independently with a common broadcasting message using the CRT. Our algorithm provides forward and non-restricted key generation, and in addition, no time synchronization is required. Furthermore, receivers can instantly authenticate packets in real time. Moreover, the comprehensive analysis shows that this scheme is efficient and practical, and can achieve better performance than the μTESLA system

KALwEN: A New Practical and Interoperable Key Management Scheme for Body Sensor Networks

Key management is the pillar of a security architecture. Body sensor networks(BSNs) pose several challenges -- some inherited from wireless sensor networks(WSNs), some unique to themselves -- that require a new key management scheme to be tailor-made. The challenge is taken on, and the result is KALwEN, a new lightweight scheme that combines the best-suited cryptographic techniques in a seamless framework. KALwEN is user-friendly in the sense that it requires no expert knowledge of a user, and instead only requires a user to follow a simple set of instructions when bootstrapping or extending a network. One of KALwEN's key features is that it allows sensor devices from different manufacturers, which expectedly do not have any pre-shared secret, to establish secure communications with each other. KALwEN is decentralized, such that it does not rely on the availability of a local processing unit (LPU). KALwEN supports global broadcast, local broadcast and neighbor-to-neighbor unicast, while preserving past key secrecry and future key secrecy. The fact that the cryptographic protocols of KALwEN have been formally verified also makes a convincing case

Statistically-secure ORAM with O~(log⁡2n)\tilde{O}(\log^2 n) Overhead

We demonstrate a simple, statistically secure, ORAM with computational overhead $\tilde{O}(\log^2 n)$; previous ORAM protocols achieve only computational security (under computational assumptions) or require $\tilde{\Omega}(\log^3 n)$ overheard. An additional benefit of our ORAM is its conceptual simplicity, which makes it easy to implement in both software and (commercially available) hardware. Our construction is based on recent ORAM constructions due to Shi, Chan, Stefanov, and Li (Asiacrypt 2011) and Stefanov and Shi (ArXiv 2012), but with some crucial modifications in the algorithm that simplifies the ORAM and enable our analysis. A central component in our analysis is reducing the analysis of our algorithm to a "supermarket" problem; of independent interest (and of importance to our analysis,) we provide an upper bound on the rate of "upset" customers in the "supermarket" problem