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The underlying fundaments of blockchain are cryptography and cryptographic concepts that provide reliable and secure decentralized solutions. Although many recent papers study the use-cases of blockchain in different industrial areas, such as finance, health care, legal relations, IoT, information security, and consensus building systems, only few studies scrutinize the cryptographic concepts used in blockchain. To the best of our knowledge, there is no Systematization of Knowledge (SoK) that gives a complete picture of the existing cryptographic concepts which have been deployed or have the potential to be deployed in blockchain. In this paper, we thoroughly review and systematize all cryptographic concepts which are already used in blockchain. Additionally, we give a list of cryptographic concepts which have not yet been applied but have big potentials to improve the current blockchain solutions. We also include possible instantiations of these cryptographic concepts in the blockchain domain. Last but not least, we explicitly postulate 21 challenging problems that cryptographers interested in blockchain can work on.

Abstract-Minimum-Storage Regenerating (MSR) codes have emerged as a viable alternative to Reed-Solomon (RS) codes as they minimize the repair bandwidth while they are still optimal in terms of reliability and storage overhead. Although several MSR constructions exist, so far they have not been practically implemented mainly due to the big number of I/O operations. In this paper, we analyze high-rate MDS codes that are simultaneously optimized in terms of storage, reliability, I/O operations, and repair-bandwidth for single and multiple failures of the systematic nodes. The codes were recently introduced in [1] without any specific name. Due to the resemblance between the hashtag sign # and the procedure of the code construction, we call them in this paper HashTag Erasure Codes (HTECs). HTECs provide the lowest data-read and data-transfer, and thus the lowest repair time for an arbitrary sub-packetization level α, where α ≤ r k/r , among all existing MDS codes for distributed storage including MSR codes. The repair process is linear and highly parallel. Additionally, we show that HTECs are the first high-rate MDS codes that reduce the repair bandwidth for more than one failure. Practical implementations of HTECs in Hadoop release 3.0.0-alpha2 demonstrate their great potentials.

Abstract-This paper presents a novel construction of (n, k, d = n − 1) access-optimal regenerating codes for an arbitrary sub-packetization level α for exact repair of any systematic node. We refer to these codes as general sub-packetized because we provide an algorithm for constructing codes for any α less than or equal to r is not necessarily an integer. This leads to a flexible construction of codes for different code rates compared to existing approaches. We derive the lower and the upper bound of the repair bandwidth. The repair bandwidth depends on the code parameters and α. The repair process of a failed systematic node is linear and highly parallelized, which means that a set of ⌈ α r ⌉ symbols is independently repaired first and used along with the accessed data from other nodes to recover the remaining symbols.

In a multihop wireless network, it is crucial but challenging to schedule transmissions in an efficient and fair manner. In this paper, a novel distributed node scheduling algorithm, called Local Voting, is proposed. This algorithm tries to semi-equalize the load (defined as the ratio of the queue length over the number of allocated slots) through slot reallocation based on local information exchange. The algorithm stems from the finding that the shortest delivery time or delay is obtained when the load is semiequalized throughout the network. In addition, we prove that, with Local Voting, the network system converges asymptotically towards the optimal scheduling. Moreover, through extensive simulations, the performance of Local Voting is further investigated in comparison with several representative scheduling algorithms from the literature. Simulation results show that the proposed algorithm achieves better performance than the other distributed algorithms in terms of average delay, maximum delay, and fairness. Despite being distributed, the performance of Local Voting is also found to be very close to a centralized algorithm that is deemed to have the optimal performance. Index TermsMultihop wireless networks, Node scheduling algorithm, Wireless mesh networks, Load balancing. D. J. Vergados is with the