How Sage Helps to Implement Goppa Codes and the Mceliece Public Key Crypto System

Common cryptographic methods, especially Public Key Crypto Systems, PKCS based on difficulty to factor large integers or to compute the discrete logarithm, commonly deployed today will not resist attacks using quantum computers once these are operational. However, there are alternatives like hash based digital signature schemes, lattice based cryptography, or multivariate-quadratic-equations public-key cryptography. Here, the authors present ways to judiciously implement code based cryptography exemplied by the McEliece PKCS based on Goppa Codes. They will show how the open source computer algebra system SAGE can guide the implementation of the PKCS say on FPGAs.

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