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Abstract:

Public-key cryptography is one of the fundamental ingredients in modern protocols for computer-based communications and data storage. The security of public-key cryptosystems is based on the intractability of some algebraic problems, such as the discrete logarithm or the integer factorization: the best algorithms for solving such problems with classical computers have exponential run-time, making the decryption without key unfeasible. However, in the last decades, a new concept, theorized in the 70s, has been developed and improved: the quantum computer. Despite quantum technologies are still immature, new powerful algorithms have already been published and some of them can solve in polynomial run-time the (assumed) intractable problems mentioned above. Hence, from now on, new quantum-resistant algorithm will be required.