Quantum Computing and Satoshi’s Treasure

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30 Oct 2023
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Photo Super-quantum-computer by — mviamonte


Introduction 🚀

Quantum computing is a cutting-edge technology that promises to revolutionize the fields of science, engineering, cryptography, and many more. Quantum computers use the principles of quantum mechanics to perform calculations that are impossible or extremely difficult for classical computers. Quantum computers have the potential to solve some of the most complex and important problems in the world, such as climate change, drug discovery, artificial intelligence, and encryption.

But quantum computing also poses a threat to some of the existing cryptographic systems that are widely used today, such as public-key cryptography. Public-key cryptography is the basis of many digital protocols and applications, such as secure communication, digital signatures, and cryptocurrencies. Public-key cryptography relies on mathematical problems that are easy to solve in one direction, but hard to solve in the reverse direction. For example, it is easy to multiply two large prime numbers, but hard to factorize their product. These problems are called “one-way functions” or “trapdoor functions”.

However, quantum computers can use special algorithms, such as Shor’s algorithm and Grover’s algorithm, to break some of these one-way functions in polynomial time. This means that quantum computers can potentially decrypt messages, forge signatures, and steal private keys that are currently considered secure by classical computers. This would have serious implications for the security and privacy of many digital systems and users.

One of the most interesting and controversial cases of quantum computing and cryptography is Bitcoin and Satoshi’s wallet. Bitcoin is the first and most popular cryptocurrency, created by an anonymous person or group using the pseudonym Satoshi Nakamoto in 2009. Bitcoin uses public-key cryptography to generate addresses and transactions on a decentralized network of nodes. Each address is associated with a private key that allows the owner to spend the bitcoins stored in that address. The private key is a secret number that must be kept safe and never revealed to anyone.

Satoshi Nakamoto is the mysterious creator of Bitcoin, who has never revealed his or her identity or whereabouts. Satoshi is also the owner of the first and largest Bitcoin address, which contains about 1 million bitcoins, worth about $60 billion as of October 30, 2023. This address is often called “Satoshi’s wallet” or “Satoshi’s treasure”. Satoshi has never moved or spent any of these bitcoins since 2009, leading to many speculations and theories about his or her motives, intentions, and fate.

Some people believe that Satoshi is dead, missing, or retired from the Bitcoin project. Some people believe that Satoshi is waiting for the right moment to reveal himself or herself, or to use his or her bitcoins for a noble cause. Some people believe that Satoshi is actually a group of people, a government agency, or an artificial intelligence. No one knows for sure who Satoshi is or what he or she plans to do with his or her bitcoins.

But what if quantum computers could crack Satoshi’s wallet and steal his or her bitcoins? What if someone could use quantum computing to impersonate Satoshi and manipulate the Bitcoin network? What if quantum computing could render Bitcoin obsolete or insecure? These are some of the questions that we will explore in this article.


Quantum Computing and Cryptography 🔐

Quantum computing is a branch of computer science that studies how to use quantum mechanical phenomena, such as superposition and entanglement, to perform computations that are beyond the capabilities of classical computers. Quantum computers operate on quantum bits or qubits, which can exist in a superposition of two states: 0 and 1. This means that a qubit can be both 0 and 1 at the same time until it is measured and collapses to one of the states. A qubit can also be entangled with another qubit, which means that their states are correlated even when they are separated by large distances.

Quantum computers can use these properties to perform parallel operations on multiple qubits at once, which gives them an exponential speedup over classical computers for certain types of problems. For example, a quantum computer with n qubits can represent 2^n possible states at once, while a classical computer with n bits can only represent one state at a time.

One of the most important applications of quantum computing is cryptography, which is the science of creating and breaking codes that protect information from unauthorized access or modification. Cryptography is essential for many digital systems and services, such as online banking, e-commerce, email, social media, cloud computing, and blockchain.

One of the most widely used cryptographic techniques is public-key cryptography, which allows two parties to communicate securely without sharing a secret key beforehand. Public-key cryptography uses two types of keys: public keys and private keys. A public key is a number that can be freely shared with anyone, while a private key is a secret number that must be kept by the owner. A public key and a private key are mathematically related, but it is very hard to derive the private key from the public key.

Public-key cryptography enables two main functions: encryption and digital signatures. Encryption is the process of transforming a message into an unreadable form, using a public key. Only the owner of the corresponding private key can decrypt the message and recover the original form. Digital signatures are the process of proving the authenticity and integrity of a message, using a private key. The owner of the private key can generate a signature that can be verified by anyone using the public key. The signature proves that the message was not altered or forged by anyone else.

Public-key cryptography relies on the assumption that certain mathematical problems are hard to solve, even for powerful classical computers. These problems are called “one-way functions” or “trapdoor functions”, because they are easy to compute in one direction but hard to invert in the other direction. For example, it is easy to multiply two large prime numbers, but hard to factorize their product. Another example is finding the discrete logarithm of a number in a finite field, which is easy to do with exponentiation, but hard to do with logarithms.

However, quantum computers can use special algorithms, such as Shor’s algorithm and Grover’s algorithm, to break some of these one-way functions in polynomial time. This means that quantum computers can potentially decrypt messages, forge signatures, and steal private keys that are currently considered secure by classical computers.

Shor’s algorithm is a quantum algorithm that can efficiently factorize large numbers and find discrete logarithms. Shor’s algorithm can break many public-key cryptosystems that are based on these problems, such as RSA, Diffie-Hellman, ElGamal, and DSA. Shor’s algorithm works by reducing the factorization or discrete logarithm problem to a period-finding problem, which can be solved by using quantum Fourier transform and phase estimation.

Grover’s algorithm is a quantum algorithm that can efficiently search an unsorted database or a large search space. Grover’s algorithm can break many symmetric-key cryptosystems that are based on brute-force attacks, such as AES, DES, and SHA-256. Grover’s algorithm works by using amplitude amplification and inversion to increase the probability of finding the desired element.

The threat of quantum computing to cryptography is not hypothetical or theoretical. Quantum computers already exist and are being developed by various organizations and companies, such as IBM, Google, Microsoft, Intel, Amazon, Alibaba, and D-Wave. Some of these quantum computers are available for public access through cloud platforms or online interfaces. For example, IBM offers a service called IBM Quantum Experience, which allows users to run experiments on real quantum devices or simulators.

However, quantum computers are still in their infancy and face many challenges and limitations. Quantum computers are very sensitive to noise and errors, which can affect their performance and accuracy. Quantum computers also require very low temperatures and high isolation to operate properly. Quantum computers also have limited scalability and availability, as they are very expensive and complex to build and maintain.

The current state-of-the-art quantum computer is Google’s Sycamore processor, which has 53 qubits and achieved quantum supremacy in 2019. Quantum supremacy is the milestone when a quantum computer can perform a task that is impossible or impractical for a classical computer. Google claimed that Sycamore could perform a specific random sampling task in 200 seconds, while a classical supercomputer would take 10,000 years.

However, quantum supremacy does not mean that quantum computers can break cryptography or solve any problem faster than classical computers. The task that Sycamore performed was designed to be hard for classical computers but easy for quantum computers. It was not a useful or meaningful task for any practical application. Moreover, Sycamore’s result was disputed by IBM, which argued that a classical supercomputer could perform the same task in 2.5 days with enough memory and optimization.

The current estimate for breaking RSA-2048 encryption with Shor’s algorithm is about 20 million qubits and several hours of runtime. The current estimate for breaking AES-256 encryption with Grover’s algorithm is about 6 billion qubits and several years of runtime. These estimates assume ideal conditions and ignore many technical details and challenges. Therefore, it is unlikely that quantum computers will be able to break cryptography anytime soon.
However, this does not mean that we should ignore or underestimate the threat of quantum computing to cryptography. Quantum computing is advancing rapidly and unpredictably, and it could reach a point where it could pose a serious risk to many cryptographic systems and applications. Therefore, we need to prepare for the post-quantum era by developing new cryptographic schemes that are resistant to quantum attacks.

Post-Quantum Cryptography 🔒

Post-quantum cryptography is a branch of cryptography that studies how to design and implement cryptographic schemes that are secure against both classical and quantum attacks. Post-quantum cryptography aims to replace or complement the existing public-key cryptosystems with new ones that are based on different mathematical problems that are hard to solve even for quantum computers. Some of these problems are:

  • Lattice-based cryptography: This is based on finding the shortest vector or the closest vector in a high-dimensional lattice, which is a regular grid of points in a vector space. Lattice-based cryptography can support encryption, digital signatures, key exchange, and fully homomorphic encryption, which allows performing arbitrary computations on encrypted data without decrypting it.
  • Code-based cryptography: This is based on decoding a linear error-correcting code, which is a way of adding redundancy to a message to detect and correct errors. Code-based cryptography can support encryption and digital signatures and is very fast and efficient.
  • Multivariate cryptography: This is based on solving a system of multivariate polynomial equations, which are equations that involve more than one variable and have a degree higher than one. Multivariate cryptography can support encryption, digital signatures, and key exchange, and is very compact and flexible.
  • Hash-based cryptography: This is based on finding collisions or preimages of a cryptographic hash function, which is a function that maps any input to a fixed-length output in a one-way and unpredictable manner. Hash-based cryptography can support digital signatures and is very simple and secure.
  • Isogeny-based cryptography: This is based on finding isogenies between elliptic curves, which are smooth curves that have a group structure. Isogeny-based cryptography can support key exchange and is very elegant and resistant to quantum attacks.

These are some of the main candidates for post-quantum cryptography, but there are also others, such as quantum cryptography, which uses quantum physics to create and distribute secret keys. Post-quantum cryptography is an active and exciting area of research, and there are many challenges and opportunities for developing new schemes, standards, and applications.

One of the most important initiatives for post-quantum cryptography is the NIST Post-Quantum Cryptography Standardization project, which started in 2016 and aims to select and standardize one or more post-quantum cryptosystems for public use by 2024. The project has received 69 submissions from researchers around the world and has narrowed them down to 15 finalists and 8 alternates in the third round of evaluation. The project considers various criteria for selecting the candidates, such as security, performance, functionality, usability, and compatibility.

The NIST Post-Quantum Cryptography Standardization project is expected to have a significant impact on the future of cryptography and cybersecurity, as it will provide guidance and confidence for adopting post-quantum cryptosystems in various domains and applications. The project will also foster innovation and collaboration among researchers, developers, and users of post-quantum cryptography.


Quantum Computing and Bitcoin 💰

Bitcoin is the first and most popular cryptocurrency, created by an anonymous person or group using the pseudonym Satoshi Nakamoto in 2009. Bitcoin uses public-key cryptography to generate addresses and transactions on a decentralized network of nodes. Each address is associated with a private key that allows the owner to spend the bitcoins stored in that address. The private key is a secret number that must be kept safe and never revealed to anyone.

Bitcoin transactions are recorded in a public ledger called the blockchain, which is maintained by the network of nodes through a consensus mechanism called proof-of-work. Proof-of-work is a process that requires nodes to solve a hard mathematical puzzle to create new blocks of transactions and earn rewards in bitcoins. Proof-of-work ensures that the blockchain is secure, consistent, and immutable.

Bitcoin has many advantages over traditional currencies and payment systems, such as decentralization, transparency, anonymity, low fees, global accessibility, and limited supply. Bitcoin has also attracted many users, investors, enthusiasts, developers, and critics around the world. Bitcoin has become a phenomenon that has influenced the fields of economics, finance, politics, sociology, and technology.

But Bitcoin also faces many challenges and limitations, such as scalability, volatility, regulation, security, and environmental impact. Bitcoin also faces the threat of quantum computing, which could potentially compromise its cryptographic foundations and undermine its security and value.
Quantum computing could affect Bitcoin in two main ways: by breaking its public-key cryptography and by accelerating its proof-of-work. Both of these scenarios could have serious consequences for Bitcoin and its users.


Breaking Bitcoin’s Public-Key Cryptography 🔓

Bitcoin uses two types of public-key cryptography: the Elliptic Curve Digital Signature Algorithm (ECDSA) and the Elliptic Curve Diffie-Hellman (ECDH). ECDSA is used to generate digital signatures for Bitcoin transactions, while ECDH is used to generate shared secrets for encrypted communication between nodes.

ECDSA and ECDH are based on the discrete logarithm problem on elliptic curves, which is finding the scalar multiplier of a point on a curve. This problem is believed to be hard to solve for classical computers, but it can be broken by quantum computers using Shor’s algorithm.
If quantum computers could break ECDSA and ECDH, they could potentially steal bitcoins from any address that has ever been used or revealed its public key. This includes addresses that have been spent from, reused, or published online. Quantum computers could also forge transactions and signatures, and impersonate nodes on the network.

The most vulnerable target for quantum attacks is Satoshi’s wallet, which contains about 1 million bitcoins that have never been moved since 2009. Satoshi’s wallet is composed of multiple addresses that have revealed their public keys in the blockchain. If quantum computers could crack these keys, they could access Satoshi’s bitcoins and spend them as they wish.
This would not only cause a huge loss for Satoshi but also a major shock for the Bitcoin community and market. The sudden movement of Satoshi’s bitcoins could trigger panic, speculation, and volatility among Bitcoin users and investors. It could also raise questions about the identity and motives of Satoshi and the attacker. It could even undermine the credibility and legitimacy of Bitcoin as a decentralized and secure currency.


Accelerating Bitcoin’s Proof-of-Work 💨

Bitcoin uses proof-of-work as a consensus mechanism to secure the blockchain and prevent double-spending attacks. Proof-of-work requires nodes to solve a hard mathematical puzzle that involves finding a nonce that makes the hash of a block header lower than a target difficulty. The difficulty is adjusted every 2016 block to maintain an average block time of 10 minutes.

Proof-of-work is designed to be hard to solve but easy to verify, and it requires a lot of computational power and energy to perform. Proof-of-work ensures that the longest chain of blocks is the valid one and that no one can alter or rewrite the history of transactions.
However, quantum computers could use Grover’s algorithm to speed up the search for the nonce and solve the proof-of-work puzzle faster than classical computers. Grover’s algorithm can provide a quadratic speedup over classical brute-force search, which means that it can reduce the number of trials needed to find the nonce by a factor of the square root.

If quantum computers could accelerate proof-of-work, they could potentially gain an unfair advantage over classical miners and dominate the network. Quantum computers could generate blocks faster than the rest of the network, and create a longer chain of blocks that would be accepted as the valid one. Quantum computers could also launch 51% attacks, which are attacks that allow a malicious entity to control more than half of the network’s hashing power and manipulate the blockchain.
51% attacks could enable quantum computers to double-spend bitcoins, censor transactions, reverse confirmations, and fork the blockchain. These attacks could compromise the integrity and reliability of Bitcoin as a distributed ledger and a medium of exchange.


Quantum-Resistant Bitcoin 🛡️

Quantum computing poses a serious threat to Bitcoin and its cryptography, but it does not mean that Bitcoin is doomed or defenseless. Bitcoin can adapt and evolve to resist quantum attacks by implementing new solutions and protocols that are based on post-quantum cryptography.
One possible solution is to replace ECDSA and ECDH with post-quantum alternatives, such as lattice-based or hash-based schemes. These schemes could provide similar or better functionality and security than ECDSA and ECDH, without being vulnerable to Shor’s algorithm. However, these schemes also have some drawbacks, such as larger key sizes, slower performance, or limited functionality.

Another possible solution is to use quantum-proof addresses, which are addresses that do not reveal their public keys until they are spent from. These addresses could prevent quantum computers from stealing bitcoins from unused or unspent addresses, as they would not have enough time to crack their keys before they are invalidated by the network. However, these addresses also have some limitations, such as requiring users to never reuse or publish their addresses online.

A third possible solution is to use quantum cryptography, which is cryptography that uses quantum physics to create and distribute secret keys. Quantum cryptography could provide a high level of security and privacy for Bitcoin transactions and communication, as it could detect and prevent any eavesdropping or tampering by quantum computers. However, quantum cryptography also has some challenges, such as requiring special hardware, infrastructure, and protocols.

These are some of the possible solutions for quantum-resistant Bitcoin, but there are also others, such as changing the proof-of-work algorithm, implementing a hard fork, or creating a new cryptocurrency. Each solution has its own advantages and disadvantages, and none of them is perfect or easy to implement. Therefore, the choice of the best solution depends on various factors, such as feasibility, compatibility, efficiency, and acceptance.


Conclusion 🏁

Quantum computing is a powerful and promising technology that could have a huge impact on many fields and applications, including cryptography and Bitcoin. Quantum computing could potentially break Bitcoin’s public-key cryptography and accelerate its proof-of-work, which could compromise its security and value. However, quantum computing could also inspire Bitcoin to adapt and evolve to resist quantum attacks by implementing new solutions and protocols that are based on post-quantum cryptography.

Quantum computing and Bitcoin are both fascinating and controversial phenomena that have sparked a lot of interest and debate among researchers, developers, users, and observers. Quantum computing and Bitcoin are both challenging and inspiring each other to reach new heights of innovation and excellence.

What do you think about quantum computing and Bitcoin? Do you think quantum computing will break or boost Bitcoin? Do you think Bitcoin will survive or succumb to quantum attacks? Do you think Bitcoin will adopt or ignore post-quantum cryptography? Let me know your thoughts in the comments below. Thank you for reading this article. 😊


📌Originally posted on - medium


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📚 Sources:

(1) Proof Of Keys Day And Quantum Computing - Bitcoin Magazine | Bitcoin Magazine
(2) There will eventually be the biggest treasure hunt in history for ... | Reddit
(3) Quantum Computing and Satoshi's Sunken Treasure | SoundCrypto | SoundCrypto


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