Quantum Physics and Cyber Security

Article by Amit Rao, McMaster University

In the field of cyber security, the world is secured by the RSA-2048 standard. However, as computer architecture and algorithms advance, the security held by the RSA standard could be broken allowing for immense vulnerability of many personal data. One known technology that can break the encryption set by RSA is through the use of quantum computers.

RSA which is an acronym for Rivest-Shamir-Adleman which is a public-key encryption method. The idea behind RSA encryption utilizes the product of two prime numbers to generate the encrypting key [1]. Since the product is made up of two prime numbers, only those prime numbers can be a factor for that product. Therefore, in order to decrypt the product, knowledge of the prime factors needs to be known. In the encryption process if the prime factors used are relatively small then it can still be broken through with today’s technology.

RSA-2048 uses prime factors that are composed of 2048 bits which is an incredibly large value and guessing the prime factors that make up the large product is essentially impossible with today’s technology [1]. With this a user can send their public encryption key to successfully encrypt the key, and even if someone has access to the public key, without the prime factors they will essentially be unable to decrypt the contents being locked.

Although RSA-2048 is currently a good method for security, the safety net can be broken through with the advancement of quantum computers [2]. This was shown by the Shor’s algorithm where by guessing a factor, the factor can then be put in a superposition of values raised to a series of integers. By applying a quantum fourier transform, the period of related remainders due to your initial guess can be found. If the period of found from the initial guess is even – it can be used to find a common denominator with the initial guess related to the original prime product enabling you to find the prime factors needed [2].

This is only achieved through the use of quantum computing as the superposition of states allows quantum computing to perform calculations on all inputted states at the same time and by applying a quantum fourier transform on all the states, the frequency of the states with the same remainder can be found. This is much quicker than classical computers as classical computers need to perform these calculations one by one whereas quantum computers can calculate it at the same time.

Although quantum computers are still in development, shor’s algorithm was created in 1994 showing the strength of quantum computers already [2].

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