Publication
Efficient generation of prime numbers
Publications associées (43)
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Serge Vaudenay, Laurane Chloé Angélina Marco, Abdullah Talayhan
The Bitcoin architecture heavily relies on the ECDSA signature scheme which is broken by quantum adversaries as the secret key can be computed from the public key in quantum polynomial time. To mitigate this attack, bitcoins can be paid to the hash of a pu ...
2023A new elementary proof of the Prime Number Theorem
Let denote the number of prime factors of . We show that for any bounded one has [ \frac{1}{N}\sum_{n=1}^N, f(\Omega(n)+1)=\frac{1}{N}\sum_{n=1}^N, f(\Omega(n))+\mathrm{o}_{N\to\infty}(1). ] This yields a ...
2021Experiments with the Markoff Surface
Matthew De Courcy-Ireland, Sandy Lee
We confirm, for the primes up to 3000, the conjecture of Bourgain-Gamburd-Sarnak and Baragar on strong approximation for the Markoff surface modulo primes. For primes congruent to 3 modulo 4, we find data suggesting that some natural graphs constructed fro ...
TAYLOR & FRANCIS INC2020A spectral refinement of the Bergelson–Host–Kra decomposition and new multiple ergodic theorems
We investigate how spectral properties of a measure-preserving system (X, B, mu, T) are reflected in the multiple ergodic averages arising from that system. For certain sequences a :N -> N, we provide natural conditions on the spectrum sigma (T) such that, ...
2019System and method for providing a collective decentralized authority for sharing sensitive data
Jean-Pierre Hubaux, Bryan Alexander Ford, Jean Louis Raisaro, Zhicong Huang, Patricia Egger
A method of sharing private and/or sensitive data from plurality of data providers to a data user, the data user having a private key and a public key, the method comprising the steps of providing a first data set and encrypting the first data set at a ter ...
2018A PRACTICAL ANALYTIC METHOD FOR CALCULATING pi(x)
In this paper we give a description of a practical analytic method for the computation of pi(x), the number of prime numbers
American Mathematical Society2017LPN in Cryptography
The security of public-key cryptography relies on well-studied hard problems, problems for which we do not have efficient algorithms. Factorization and discrete logarithm are the two most known and used hard problems. Unfortunately, they can be easily solv ...
EPFL2017Some applications of smooth bilinear forms with Kloosterman sums
We revisit a recent bound of I. Shparlinski and T. Zhang on bilinear forms with Kloosterman sums, and prove an extension for correlation sums of Kloosterman sums against Fourier coefficients of modular forms. We use these bounds to improve on earlier resul ...
Maik Nauka/Interperiodica/Springer2017Signature Schemes Secure Against Hard-to-Invert Leakage
Side-channel attacks allow the adversary to gain partial knowledge of the secret key when cryptographic protocols are implemented in real-world hardware. The goal of leakage resilient cryptography is to design cryptosystems that withstand such attacks. In ...
Springer2016Sign changes of Kloosterman sums with almost prime moduli
We prove that the Kloosterman sum changes sign infinitely often as runs over squarefree moduli with at most 10 prime factors, which improves the previous results of Fouvry and Michel, Sivak-Fischler and Matomaki, replacing 10 by 23, 18 and 15, respectively ...
Springer Verlag2015