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Cipher-breaking refers to the process of deciphering or decoding a message that has been encoded with an encryption algorithm. In simple words, it's like trying to figure out the password to an encrypted message. In the context of AES encryption, breaking the cipher involves determining the key used to encrypt the data. This can be incredibly difficult, especially with sophisticated encryption methods like AES that use large key sizes. AES, or Advanced Encryption Standard, is often used because it provides a high level of security, making cipher-breaking a daunting task.

Breaking a cipher, particularly modern ones like AES, requires enormous computational power. Consider a machine with a million processors; even then, as per the given problem, it would take an unimaginable amount of time, around 10¹⁶ years, to crack the AES encryption. This highlights how secure AES encryption is against brute force attacks, where each possible key is tried until the correct one is found. This method of breaking ciphers is practically ineffective against AES, given current computational capabilities.

AES encryption, or Advanced Encryption Standard, is one of the most widely used encryption algorithms worldwide. It is employed to secure data and ensure confidentiality. AES was introduced by the National Institute of Standards and Technology (NIST) in the United States and has become a global standard for encryption.

AES encryption uses symmetric key cryptography, which means the same key is used for both encrypting and decrypting data. One of its main strengths is its versatility in key size. AES allows for 128, 192, or 256-bit keys, with the strength of the encryption increasing with larger keys. The 128-bit AES key alone provides a massive number of possible keys, making unauthorized decryption nearly impossible without significant advances in computational power.

In practical terms, AES encryption is used in a variety of applications, such as wireless communication, financial transactions, and secured data storage. Its efficiency and security make it a favorite choice for encrypting sensitive information.

Parallel computing is a type of computation where many calculations or processes are carried out simultaneously. It leverages multiple processors to perform complex computations more efficiently. This is crucial when dealing with tasks like cipher-breaking, where breaking down the task into smaller sub-tasks that can be executed simultaneously can significantly reduce the required time.

Modern computers often use parallel computing to enhance performance, particularly in tasks requiring large computation power, such as weather modeling, scientific simulations, and cryptography. In the scenario provided, a parallel computing setup with a million processors is employed to attempt breaking the AES encryption. However, given the current technological limits, even such a massive arrangement takes an impractical amount of time.

As technology progresses, parallel computing is becoming more sophisticated, with strategies such as grid computing and cloud computing being adopted. The ability to manage and distribute computing tasks across many processors opens up new possibilities for handling complex computations efficiently.

Doubling time is a concept rooted in Moore's Law, which predicts that computing power doubles approximately every 18 months. This principle is applied in forecasting the growth and improvement of computational abilities over time.

In the context of the given problem, we want to find out how long it will take for computers to become 10¹⁶ times faster to bring down AES cipher-breaking to a year. By using the doubling time concept, we understand that this involves 54 cycles of doubling the computational speed. This process involves determining the number of "doublings" or periods after which computing speed is expected to multiply to desired magnitudes.

The straightforward calculation entails dividing 54 cycles by the number of such cycles in a year (1.5 cycles per year), resulting in a timespan of approximately 81 years. This showcases how the exponential nature of technological advancement, guided by Moore’s Law, slowly chips away at massive computational challenges such as breaking advanced encryption.