Eike Kiltz investigates whether the data transmission methods used today are secure.

Can we mathematically prove that the encryption methods used in modern web browsers for secure data transmission are really safe? In other words, can we show that it would take at least several billion years to decrypt the data, even with the best and fastest computer? According to the current state of research: unfortunately, no.

**Seven unsolved problems**

Such proof would have dramatic consequences and brings us to the limits of our current knowledge. It would solve the famous P-NP problem, which is one of the seven unsolved problems in mathematics published by the Clay Mathematics Institute in 2000. The institute offered a prize of one million U.S. dollars for the solution of each of these problems.

Until the P-NP problem is solved, we cryptographers attribute the security of encryption methods to the difficulty of solving a well-understood mathematical puzzle. For example, we prove that decrypting data is at least as tricky as decomposing a large number into its prime factors. We can sleep easy because this so-called factorization problem is a challenging one, which many clever minds have tried to solve unsuccessfully.

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