# Quantum Computing’s Triumph: Calculating and Storing All SHA-256 Values Introduction

Quantum computing, with its immense computational power, holds the potential to revolutionize various fields. In this article, we delve into a captivating scenario where a quantum computer calculates all possible SHA-256 values and the implications of storing this vast dataset in a quantum-enhanced database.

Part 1: Quantum Calculation of SHA-256 Values

The SHA-256 algorithm is widely used for cryptographic purposes due to its collision resistance and security properties. Calculating all possible SHA-256 values using classical computers would be an astronomical task, requiring immense time and resources. However, a quantum computer harnesses quantum bits or qubits, offering a parallelism that classical bits lack. Here’s how a quantum computer could achieve this feat:

1. Quantum Superposition: In a quantum superposition, qubits can represent multiple states simultaneously. A quantum computer can prepare an initial state that encodes a range of inputs.
2. Quantum Gates: Quantum gates manipulate qubits’ states based on quantum logic. Quantum operations can be applied in parallel to all possible input states, thanks to superposition.
3. Quantum Entanglement: Entanglement allows qubits to be correlated in ways that classical bits cannot. Quantum operations on one qubit can affect the state of another, enabling complex calculations.
4. Grover’s Algorithm: Grover’s algorithm is a quantum search algorithm that can search through an unsorted database of N items in √N steps. Applied to the SHA-256 problem, it could speed up the search for matching values.

By leveraging these principles, a quantum computer could calculate all possible SHA-256 values exponentially faster than classical computers, demonstrating the potential of quantum computing’s computational superiority.

Part 2: The Quantum Database Challenge

Storing all SHA-256 values presents a colossal data challenge. Each SHA-256 value is a 256-bit string, resulting in an enormous dataset. To understand the size of the required database, we’ll calculate it using basic principles:

1. Size of a Single Value: A SHA-256 value is 256 bits, or 32 bytes.
2. Number of Possible Values: Since SHA-256 produces a 256-bit output, there are 2^256 possible values.
3. Database Size Calculation: To store all possible values, we multiply the size of a single value by the number of possible values.

Calculating the database size:

`Database Size = Size of a Single Value × Number of Possible Values= 32 bytes × 2^256`

Converting to a more human-readable format:

`Database Size ≈ 1.1579209 × 10^77 bytes ≈ 9.2633672 × 10^77 bits`

This astronomical number demonstrates the sheer magnitude of data that would need to be stored to accommodate all possible SHA-256 values.

How much storage is required to “hack” passwords?

The hypothetical scenario of a quantum computer calculating and storing all SHA-256 values exemplifies the incredible potential of quantum computing. Quantum principles like superposition and entanglement, along with specialized algorithms, empower quantum computers to perform calculations that were once considered insurmountable.

While the idea of storing such massive datasets in quantum databases is intriguing, it also underscores the challenges posed by the sheer volume of data. These challenges extend beyond calculations and storage to considerations of security, cryptography, and quantum database management.

However, we can assume that passwords have limited length, and limited character use.

If we assume that all English characters (both uppercase and lowercase), numbers, and special characters are allowed in passwords, the total number of possible combinations for passwords of different lengths can be calculated using the formula:

`Number of Combinations = (Total Number of Characters) ^ (Length of Password)`

Where:

• `Total Number of Characters` = 26 (English lowercase letters) + 26 (English uppercase letters) + 10 (digits) + (number of special characters)
• `Length of Password` represents the length of the password.

Let’s calculate the number of combinations for passwords of different lengths:

For a password with eight characters:

`Total Number of Characters = 26 + 26 + 10 + (number of special characters)Number of Combinations = (26 + 26 + 10 + number of special characters) ^ 8`

For a password with nine characters:

`Total Number of Characters = 26 + 26 + 10 + (number of special characters)Number of Combinations = (26 + 26 + 10 + number of special characters) ^ 9`

And so on, up to a password with twenty characters.

The storage required for such a database, is given in the following table:

Length of PasswordTotal Number of CharactersNumber of Combinations (10^N)Memory Storage Required
895 (26 + 26 + 10 + 33)3.87 x 10^14≈ 2 GB
995 (26 + 26 + 10 + 33)1.27 x 10^17≈ 5 GB
1095 (26 + 26 + 10 + 33)4.13 x 10^19≈ 16 GB
1195 (26 + 26 + 10 + 33)1.35 x 10^22≈ 540 GB
1295 (26 + 26 + 10 + 33)4.40 x 10^24≈ 18 TB
1395 (26 + 26 + 10 + 33)1.44 x 10^27≈ 571 TB
1495 (26 + 26 + 10 + 33)4.71 x 10^29≈ 19,200 TB
1595 (26 + 26 + 10 + 33)1.53 x 10^32≈ 62,000 TB
1695 (26 + 26 + 10 + 33)4.98 x 10^34≈ 203,000 TB
1795 (26 + 26 + 10 + 33)1.62 x 10^37≈ 660,000 TB
1895 (26 + 26 + 10 + 33)5.29 x 10^39≈ 2,150,000 TB
1995 (26 + 26 + 10 + 33)1.73 x 10^42≈ 7,030,000 TB
2095 (26 + 26 + 10 + 33)5.64 x 10^44≈ 22,900,000 TB

Which shows that for certain passwords sizes, if the hashing algorithm is solved once by a quantum computing, we don’t really need a huge storage size to keep the results and use them whenever we wanted to “hack” a password.