Cyril Grunspan’s research while affiliated with Pôle Universitaire Léonard de Vinci and other places

For a mining strategy we define “profit lag” as the minimum time it takes to be profitable after that moment. We compute closed forms for the profit lag and the revenue ratio for the strategies “selfish mining” and “intermittent selfish mining”. This corroborates prior numerical simulations and provides further elucidation regarding the issue of profitability as discussed in the existing literature. We also study mining pairs of PoW cryptocurrencies, often coming from a fork, with the same mining algorithm. This represents a vector of attack that can be exploited using the “alternate network mining” strategy that we define. We compute closed forms for the profit lag and the revenue ratio for this strategy that is more profitable than selfish mining and intermittent selfish mining. It is also harder to counter since it does not rely on a flaw in the difficulty adjustment formula that is the reason for profitability of the other strategies.

E-cash was invented in 1982 by David Chaum as an anonymous cryptographic electronic cash system based on blind signatures. It is not a decentralized form of money as Bitcoin. It requires trust on the server or Mint issuing the e-cash tokens and validating the transactions for preventing double spends. Moreover, the users also need to trust the Mint to not debase the value of e-cash tokens by Minting an uncontrolled number. In particular, this is critical for e-cash tokens representing a note of another asset as a currency, or bitcoin, or another cryptocurrency. Thus it would be suitable to implement a public auditing system providing a proof of reserves that ensures that the Mint is not engaging into a fractional reserve system. In this article we describe how to implement a proof of reserves system for Chaumian Mints. The protocol also provides a proof of non-double spends.

We present the new mining protocol Proof-of-Reputation (PoR) for decentralized Proof-of-Work (PoW) blockchains, in particular for Bitcoin. PoR combines the classical PoW with the new ingredient of cryptographic reputation. The same level of security compared to pure PoW can be achieved with a significant energy consumption reduction (of the order of 30\%) for the same security level. The proper implementation of a decentralized reputation protocol is suitable with an extra layer of mining security: Certified Mining.

We propose Ping-Pong Swaps: A secure pure peer-to-peer crosschain swap mechanism of tokens or cryptocurrencies that does not require escrow nor an intermediate trusted third party. The only technical requirement is to be able to open unidirectional payment channels in both blockchain protocols. This allows anonymous cryptocurrency trading without the need of a centralized exchange, nor DEX's in DeFi platforms, nor multisignature escrow systems with penalties. Direct peer-to-peer crosschain swaps can be performed without a bridge platform. This enables the creation of a global peer-to-peer market of pairs of tokens or cryptocurrencies. Ping-pong swaps with fiat currency is possible if banks incorporate simple payment channel functionalities. Some inmediate applications are simple and fast rebalancing of Lightning Network channels, and wrapping tokens in smartchains.

It has been known for some time that the Nakamoto consensus as implemented in the Bitcoin protocol is not totally aligned with the individual interests of the participants. More precisely, it has been shown that block withholding mining strategies can exploit the difficulty adjustment algorithm of the protocol and obtain an unfair advantage. However, we show that a modification of the difficulty adjustment formula taking into account orphan blocks makes honest mining the only optimal strategy. Surprinsingly, this is still true when orphan blocks are rewarded with an amount smaller to the official block reward. This gives an incentive to signal orphan blocks. The results are independent of the connectivity of the attacker.

The motivation of proposing and editing the Special Issue “Blockchain and cryptocurrencies” came from the inspirational invited and contributed talks at the 43rd annual A.M.A.S.E.S. conference held in Perugia in September 2019. All the papers have gone through the journal regular refereeing process under the same standards set by the journal, and nine contributions were finally accepted for publication. © 2021, The Author(s), under exclusive licence to Associazione per la Matematica Applicata alle Scienze Economiche e Sociali (AMASES).

Nakamoto doublespend strategy, described in Bitcoin foundational article, leads to total ruin with positive probability. The simplest strategy that avoids this risk incorporates a stopping threshold when success is unlikely. We compute the exact profitability and the minimal double spend that is profitable for this strategy. For a given amount of the transaction, we determine the minimal number of confirmations to be requested by the recipient that makes the double-spend strategy non-profitable. This number of confirmations is only 1 or 2 for average transactions and for a small relative hashrate of the attacker. This is substantially lower than the original Nakamoto number, which is about six confirmations and is widely used. Nakamoto analysis is only based on the success probability of the attack instead of on a profitability analysis that we carry out.

For a mining strategy we define the notion of "profit lag" as the minimum time it takes to be profitable after that moment. We compute closed forms for the profit lag and the revenue ratio for the strategies "selfish mining" and "intermittent selfish mining". This confirms some earlier numerical simulations and clarifies misunderstandings on profitability in the literature. We also study mining pairs of PoW cryptocurrencies, often coming from a fork, with the same mining algorithm. This represents a vector of attack that can be exploited using the "alternate network mining" strategy that we define. We compute closed forms for the profit lag and the revenue ratiofor this strategy that is more profitable than selfish mining and intermittent selfish mining. It is also harder to counter since it does not rely on a flaw in the difficulty adjustment formula that is the reason for profitability of the other strategies.

We study selfish mining in Ethereum. The problem is combinatorially more complex than in Bitcoin because of major differences in the reward system and a different difficulty adjustment formula. Equivalent strategies in Bitcoin do have different profitabilities in Ethereum. The attacker can either broadcast his fork one block by one, or keep them secret as long as possible and publish them all at once at the end of an attack cycle. The first strategy is damaging for substantial hashrates, and we show that the second strategy is even worse. This confirms what we already proved for Bitcoin: Selfish mining is most of all an attack on the difficulty adjustment formula. We show that the current reward for signaling uncle blocks is a weak incentive for the attacker to signal blocks. We compute the profitabilities of different strategies and find out that for a large parameter space values, strategies that do not signal blocks are the best ones. We compute closed-form formulas for the apparent hashrates for these strategies and compare them. We use a direct combinatorial analysis with Dyck words to find these closed-form formulas.