A gifted recent high school graduate has proposed an interesting and novel project ("Introducing Quaternions to Integer Factorization", Journal of Physical Science and Applications, Vol. 5, (2) (2015) pp.101-107) that seems to me to be a natural fit for Wolfram Groups. He (HuiKang Tong of Singapore) has opened up the concepts of the sum of four squares and the algebra of quaternions into the attempts to factor semiprimes (the product of two prime numbers) by generalizing Euler factorization of Gaussian integers to that of quaternion integers. Such factorization is important in the field of the cryptology based on RSA-type asymmetric public-key encryption, the security of which depends on incredibly long processing times to factor a huge semiprime.

Among the requirements for such an application, he cites the development of an algorithm to solve a set of bilinear equations that is significantly more efficient, and hopefully quite general, than the use of Gaussian elimination and brute force techniques. He also cites the need for more mathematically rigorous development of his somewhat intuitive conclusive steps in seeking a suitable quaternion pair of representations of the semiprime as a sum of four squares, which would easily factor the semiprime and immediately break RSA encryption.

His cited paper has an extensive list of references surveying the various fields involved, including six links to Wolfram MathWorld. Tong, HuiKang. "Introducing Quaternions to Integer Factorisation." Journal of Physical Science and Application 5.2 (2015): 101-107. A PDF of Tong's paper is attached.

The MathWorld references are: (editing in progress) Euler's Factorization Method. http://mathworld.wolfram.com/EulersFactorizationMethod.html http://mathworld.wolfram.com/GaussianInteger.html http://mathworld.wolfram.com/GaussianPrime.html

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