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In many blockchains, e.g., Ethereum, Binance Smart Chain (BSC), the primary representation used for wallet addresses is a hardly memorable 40-digit hexadecimal string. As a result, users often select addresses from their recent transaction…
In this paper we provide a survey of various libraries for homomorphic encryption. We describe key features and trade-offs that should be considered while choosing the right approach for secure computation. We then present a comparison of…
Motivated by the recent 10 million dollar AIMO challenge, this paper targets the problem of finding all functions conforming to a given specification. This is a popular problem at mathematical competitions and it brings about a number of…
Given a set $S$ of $n$ keys, a perfect hash function for $S$ maps the keys in $S$ to the first $m \geq n$ integers without collisions. It may return an arbitrary result for any key not in $S$ and is called minimal if $m = n$. The most…
All the current modern encryption algorithms utilize fixed symbols for plaintext and cyphertext. What I mean by fixed is that there is a set and limited number of symbols to represent the characters, numbers, and punctuations. In addition,…
Bitcoin is the first and undoubtedly most successful cryptocurrecny to date with a market capitalization of more than 100 billion dollars. Today, Bitcoin has more than 100,000 supporting merchants and more than 3 million active users.…
We study the problem of providing blockchain applications with \emph{economically viable randomness} (EVR), namely, randomness that has significant economic consequences. Applications of EVR include blockchain-based lotteries and gambling.…
The bit-wise unequal error protection problem, for the case when the number of groups of bits $\ell$ is fixed, is considered for variable length block codes with feedback. An encoding scheme based on fixed length block codes with erasures…
Alice seeks an information-theoretically secure source of private random data. Unfortunately, she lacks a personal source and must use remote sources controlled by other parties. Alice wants to simulate a coin flip of specified bias…
Bitcoin and Ethereum, whose miners arguably collectively comprise the most powerful computational resource in the history of mankind, offer no more power for processing and verifying transactions than a typical smart phone. The system…
Fully homomorphic encryption is a kind of encryption scheme, which enables arbitrary computation on encrypted data without accessing the data. We present the quantum version of fully homomorphic encryption scheme, which is constructed based…
Let $p$ be a prime. We define $S(p)$ the smallest number $k$ such that every positive integer is a sum of at most $k$ squares of integers that are not divisible by $p$. In this article, we prove that $S(2)=10$, $S(3)=6$, $S(5)=5$, and…
Blockchain systems often employ proof-of-work consensus protocols to validate and add transactions into hashchains. These protocols stimulate competition among miners in solving cryptopuzzles (e.g. SHA-256 hash computation in Bitcoin) in…
Bit-commitment is a fundamental cryptographic task, in which Alice commits a bit to Bob such that she cannot later change the value of the bit, while, simultaneously, the bit is hidden from Bob. It is known that ideal bit-commitment is…
A system is described for exchanging encrypted short messages between computers which remain permanently isolated from any network accessible to the attacker. The main advantage is effective protection of these computers from malware which…
The digital currency Bitcoin has had remarkable growth since it was first proposed in 2008. Its distributed nature allows currency transactions without a central authority by using cryptographic methods and a data structure called the…
Cryptographic hash functions for calculating the message digest of a message has been in practical use as an effective measure to maintain message integrity since a few decades. This message digest is unique, irreversible and avoids all…
We investigate a family of bugs in blockchain-based smart contracts, which we call event-ordering (or EO) bugs. These bugs are intimately related to the dynamic ordering of contract events, i.e., calls of its functions on the blockchain,…
In this paper, we characterize graphs with circular chromatic number less than 3 in terms of certain balancing labellings studied in the context of signed graphs. In fact, we construct a signed graph which is universal for all such…
The Discrete Logarithm Problem is well-known among cryptographers, for its computational hardness that grants security to some of the most commonly used cryptosystems these days. Still, many of these are limited to a small number of…