On February 11th, 2009, Satoshi Nakamoto published his groundbreaking paper “Bitcoin: A Peer-to-Peer Electronic Cash System” and referenced it in his first post titled “Bitcoin open source implementation of P2P currency” on the P2P foundation forum. It identified all the trust that’s required to make conventional currency work as it’s root problem and concluded that the solution is an e-currency based on cryptographic proof, without the need to trust a third party middleman, money can be secure and transactions effortless.
In the code that was provided for download as “Bitcoin v0.1” at http://www.bitcoin.org Satoshi Nakamoto embedded a quote which was unalterably planted into the genesis block of Bitcoin: “The Times 03/Jan/2009 Chancellor on brink of second bailout for banks.” The text was a headline article in the London Times about the British government's failure to stimulate the economy post-2007-08 and was carved into Bitcoin block 0 on the same day as news of a bank bailout broke.
Since then, Bitcoin underwent an unprecedented transformation from a currency known only by a handful of P2P enthusiasts and specialists to a currency with a market cap that topped $ 1 trillion in 2021 and exhibits world-wide adoption. It’s defining characteristics of being fully decentralized, trust- and permissionless, and with a strictly limited supply, enabled this development.
However, the prospect of digital currency with the anonymous characteristics of cash could not be really fulfilled with Bitcoin and other crypto currencies. Bitcoin users send their private payment data in plain text to the public blockchain. Although Bitcoin and other crypto currencies hide identities behind pseudonyms (public keys), there are efficient methods of deanonymizing Bitcoin users, as researchers at the University of Luxembourg have already shown in 2014. In the past, various cryptocurrency projects have addressed this issue through the utilization of advanced cryptographic techniques, with ZCash and Monero being the most prominent ones.
But now a new generation of computers threatens the Bitcoin system and also it’s privacy enhancing successors like ZCash and Monero: quantum computers. A traditional computer processes information by encoding it in 0s and 1s. For example, if we have a sequence of thirty 0s and 1s, it has about one billion possible values. Traditional computers can only be in one of those billion states at a time. But quantum computers can be in a quantum combination of all these states simultaneously, called superposition. So a quantum computer can perform one billion or more copies of a calculation at the same time.
Therefore, quantum computers will be superior to conventional machines when it comes to finding something in a large amount of data, such as private keys of Bitcoins and other crypto currencies. The public key of Bitcoin and other cryptocurrencies that rely on Elliptic Curve Digital Signature Algorithm (ECDSA) derives from the private key by mathematical functions. These mathematical functions are practically irreversible for conventional computers so that a public key from a private key can be easily calculated using a standard key generation algorithm. Still, the calculation in the other direction is practically impossible with conventional computers.
However, powerful quantum computers, in addition to their ability to perform a large number of calculations simultaneously, will use algorithms such as Shor’s algorithm to derive a private key from a public key within minutes/ seconds instead of thousands of years.
A class of cryptographic primitives which allows for construction of quantum-secure algorithms to be used for cryptocurrencies are pure symmetric cryptography primitive functions. The high plausibility of believing truly quantum-secure algorithms can be formulated with this class stems from the long-standing research conducted in the field of cryptanalysis of symmetric cryptographic primitives. The application of these however led to transaction sizes which were too large for a truly decentralized system where anyone could easily participate by joining the network with his PC or laptop and trustlessly check every transaction by themselves up to now.
What in God’s name is truly needed is thus a cryptocurrency solution guaranteeing strong privacy, being post quantum secure with highest plausibility, while using proofs that are small in size for being stored on a public ledger and cheap to communicate for matching the computational capabilities of the nodes operating the network...