The Future of Cryptography with Quantum Computing

Here is an excellent presentation by Professor Andris Ambainis (@aambainis) on the aspects of cryptography and encryption in the future with quantum computers:

The main issues are with the asymmetric public key cryptography and the way quantum computing is good at factorization and solving discrete logarithms which are supposed to be the difficult part of the RSA algorithm:

He outlines the following alternative algorithms which are still hard to solve for quantum computers:

The only issue with those algorithms appears to be the key size:

Algorithm Public key size (bits) Private key size (bits)
Ring-LWE 6,595 14,000
NTRU 6,130 6,747
Rainbow 991,000 740,000
Hash signature 36,000 36,000
McEliece 37,674,480 77,742,169
SIDH 3,071 3,072

To me it feels like the computational power and the memory capacity of secure elements today is no longer the main issue.

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