Daniele Venturi

The principal aim of this notes is to give a survey on the state of the art of algorithmic number theory, with particular focus on the theory of elliptic curves.

Computational security is the goal of modern cryptographic constructions: the security of modern criptographic schemes stems from the assumption ...
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Eli Ben-Sasson, Dan Carmon, Swastik Kopparty, David Levit

Over finite fields $F_q$ containing a root of unity of smooth order $n$ (smoothness means $n$ is the product of small primes), the Fast Fourier Transform (FFT) leads to the fastest known algebraic algorithms for many basic polynomial operations, such as multiplication, division, interpolation and multi-point evaluation. These operations can ... more >>>

Eli Ben-Sasson, Dan Carmon, Swastik Kopparty, David Levit

Concretely efficient interactive oracle proofs (IOPs) are of interest due to their applications to scaling blockchains, their minimal security assumptions, and their potential future-proof resistance to quantum attacks.

Scalable IOPs, in which prover time scales quasilinearly with the computation size and verifier time scales poly-logarithmically with it, have been known ... more >>>