STNB2024(37a edició)
Post-quantum cryptography and number theory: a fruitful alliance
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Resumen
The successful building and deploy of a large scale quantum computer will render insecure most asymmetric current cryptographic primitives. With the drastic development of existing quantum technology it has become peremptory the analysis of new schemes which support quantum resistant primitives. For instance, in 2023 IBM has released Osprey (433 qubits) and announced that in about 5 years it will be available a quantum processor of 2000 qubits. This why the National Institute of Standards and Technology launched in 2017 a public contest to standardise post-quantum primitives, the first proposals been standardised in 2022. Three of them are based on the problem of finding shortest vectors over lattices attached to polynomial quotient rings and number fields.
The goal of this talk is to discuss how different ideas from algebraic number theory have been used to either "establish" security or to cryptanalyse different proposals, we will point out the impact that a proof of the Artin conjecture would bring to post-quantum cryptography, or the role that the Stickelberger ideal has brought into the security of cyclotomic based proposals. Rather presenting new results (which will be discussed by Carlo Sanna and Rodrigo Martín) we aim at calling for a collaboration between the number-theoretical and the cryptography community.
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