Explicit geometry and arithmetic of elliptic curves and application to cryptography

Cryptography: the science of secret messages? Today’s version of cryptography is much more complex. It provides protocols that we regularly use without even realizing it: sending emails, paying for purchases online or even using the telephone. “Cryptology gives us solutions every day, in a world where, with the development of means of communication, needs in terms of confidentiality and protection of privacy are constantly increasing,” explains Christophe Arène. Drawing on fundamental theorems developed over a century ago, he is exploring solutions for ensuring data integrity, authenticating identity and verifying digital signatures.
His initial results demonstrate how new “resistant” mathematical formulae can be built, paving the way to more secure cryptographic protocols.