Will using cryptography, among other things, remain safe in banks when quantum computers come into play? Answers to this question can be found in the research conducted by Dr. M. Michał Wroński from the Military University of Technology.

Many cryptographic algorithms are based on the discrete logarithm problem on elliptic curves. Until now, it has practically not been possible to break it (even in very small cases) using quantum methods. For now, the ciphers are safe.

“We are still far from breaking the discrete logarithm of ellipse curves for practical cases. But if this happens, modern cryptography, even the one used in banks, will be vulnerable to attacks, primarily using variants of the Shor algorithm. Therefore, extensive research on algorithms is currently underway. Resistance also to quantum computers ”- explains the meaning of his research, Major M. Michel Woronsky.

A scientist from the Institute of Mathematics and Cryptography demonstrated during the International Conference on Computing Science 2021 how the well-known discrete logarithm attack on elliptic curves can be converted into a form that can be solved by computers using quantum annealing (a type of computation that brings many quick solutions).

The scientist turned the key element of the so-called index method, which is the summation of dependencies between points of an elliptical curve, into a QUBO problem. This problem can then be solved by quantitative annealing.

For practical research, Dr. Wroński used remote access to a D-Wave computer. He managed to break the discrete logarithm problem of an elliptical curve set to an 8-bit field.

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The researcher admits that the implemented example is not great, but his quantum method has solved the biggest problem with discrete logarithms on elliptical curves so far.

“The research on transforming cryptographic problems into solvable ones using quantum annealing should continue dynamically, because thanks to this, significant progress can be made in this field of knowledge” – emphasizes the author.

You can read the source article “Index Calculation Method for Solving the Discrete Logarithm Problem of an Elliptical Curve Using Quantum Annealing” Here.

PAP – Science in Poland, Karolina Duszczyk

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