The community of users and developers have expressed their concern about the future of Bitcoin in the face of the advent of quantum computing. To date, concerns have focused mainly on the SHA-256 algorithm, a cryptographic function that regulates the mining of the cryptoasset and converts any block of data into a fixed-length string of characters. This hash function serves, through proof of work, to preserve the integrity of the protocol, specifically the authenticity of the blocks and the legitimacy of transactions on the network. It also helps verify transactions, avoiding double-spending events. 

However, there is a second line of defense for Bitcoin against quantum, focused not on protecting the BTC ledger, its distribution and integrity, but on the signing of transactions with the currency and the guarantee of exclusive possession over them through securely encrypted private keys. 

According to this line of development, wallets would need to adopt (how urgently is not yet known) signature algorithms resistant to quantum attacks, and be able to preserve the privacy and security of users who use bitcoin.  

How do bitcoin wallets work today? 

Today, Bitcoin wallets incorporate the scheme called Elliptic Curve Digital Signature Algorithm (ECDSA) to generate digital signatures capable of validating transactions on the network.  

According to bitcoin.it, a source of technical information on the cryptocurrency, this signature algorithm used by wallets depends on the hash function used by Bitcoin (SHA-256), but is not identical to it. 

In order to achieve protection for wallets, they need an algorithm that encrypts the generation and use of user keys. The same page that documents Bitcoin comments: “ECDSA signature and verification algorithms use some fundamental variables that are used to obtain a signature and the reverse process of obtaining a message from a signature.” 

The computational power of today's computers means that ECDSA is sufficient for now to ensure that funds in a bitcoin address can only be spent by its rightful owner(s), and that the relationship between public and private signatures cannot be easily decrypted.  

However, the ability of quantum computer algorithms to factor numbers and solve mathematical problems could render this algorithm obsolete at some point, which would have implications.  

For example, data leaks with user keys that would facilitate access to private wallets and the theft of funds. In other words, a massive theft of bitcoin and cryptocurrencies during the social climax of quantum technology, when people capable of handling it efficiently have access to it at the same time. 

Given this latent danger, what can be done to protect bitcoin wallets? 

Cryptographers, even pre-Bitcoiners, have been thinking for years about possible solutions for post-quantum cryptography. This is because the quantum concern is not new, and it affects technological society as a whole.  

In 1994, Peter Shor demonstrated how quantum computers were “capable of breaking all digital signature schemes that are used today.” 

Following the above demonstrations, a group of technicians and developers asked themselves the following question: what kind of digital signature algorithms remain secure in the era of quantum computers? 

According to Buchman, “There are several candidates for post-quantum signature schemes. The most efficient ones are NTRU, SFLASH and the Merkle scheme.   ”

NTRU is an encryption system that uses polynomials (a type of mathematical equation) to protect sensitive information. One of its advantages is that it is fast and requires little memory, making it efficient and resistant to attacks by quantum computers. 

SFLASH is a symmetric key cryptographic scheme designed to be efficient on resource-constrained devices.

SFLASH is designed to be a very fast signature system, both for signature generation and verification. It is much faster than RSA in signing and much easier to implement on smart cards without any arithmetic coprocessor, for example. 

Courtois, Goubin and Patarin, technical paper on SFLASH. 

The Merkle scheme, on the other hand, is one whose “security is based on the absence of collisions between an arbitrary cryptographic hash function and an arbitrary single-signature algorithm.” According to the paper by Buchman and company, the Merkle scheme has competitive efficiency, and progress has been made in applying this scheme to Bitcoin cryptography using the OP_CAT operation code. Bitcoin has used the Merkle scheme since its origins.

However, the introduction of OP_CAT and a quantum-proof Merkle scheme would help improve verification processes in the Bitcoin protocol. 

The solution to achieving more secure post-quantum bitcoin wallets would then be to integrate signature schemes resistant to greater processing power, which may come in the future. These new schemes would improve the Elliptic Curve Digital Signature Algorithm (ECDSA) or replace it entirely. 

Developers can find a way to use these signature patterns with Bitcoin wallets, positively affecting the security and the way they generate keys to prevent guessing of the private key from the public key, or the so-called “elliptic discrete logarithm problem.”