A lower bound for the number of Egyptian fractions
(with Sandro Bettin, Loïc Grenié, and Giuseppe Molteni)
https://arxiv.org/abs/2509.10030
Caution: Published copies might be slightly different from the copies stored here. Always check the published article.
Implementation of a Post-Quantum Anonymous Verifiable Credential Framework
(with Davide Margaria, Alessandro Pino, Andrea Vesco, Giuseppe D'Alconzo, Antonio J. Di Scala, and Enrico Guglielmino)
QSNS 2025
https://zenodo.org/records/14848814
Sneaking up the Ranks: Partial Key Exposure Attacks on Rank-Based Schemes
(with Giuseppe D'Alconzo, Andre Esser, and Andrea Gangemi)
CBCrypto 2025
https://eprint.iacr.org/2024/2070
A note on the power sums of the number of Fibonacci partitions
Discrete Analysis (2025)
https://doi.org/10.19086/da.137601
Smaller public keys for MinRank-based schemes
(with Antonio J. Di Scala)
Journal of Mathematical Cryptology 19 (2025), 20240008
https://doi.org/10.1515/jmc-2024-0008
Counting numbers that are divisible by the product of their digits
(with Qizheng He)
Journal of Number Theory 272 (2025), 34–59
https://doi.org/10.1016/j.jnt.2025.01.002
On the number of solutions to a random instance of the permuted kernel problem
Journal of Complexity 86 (2025), 101898
https://doi.org/10.1016/j.jco.2024.101898
On the number of residues of certain second-order linear recurrences
(with Federico Accossato)
Comptes Rendus Mathématique 362 (2024), 1365–1377
https://doi.org/10.5802/crmath.647
MiRitH: Efficient Post-Quantum Signatures from MinRank in the Head
(with Gora Adj, Stefano Barbero, Emanuele Bellini, Andre Esser, Luis Rivera-Zamarripa, Javier Verbel, and Floyd Zweydinger)
IACR Transactions on Cryptographic Hardware and Embedded Systems (2024), 304–328
https://doi.org/10.46586/tches.v2024.i2.304-328
On the index of appearance of a Lucas sequence
The Ramanujan Journal 63 (2024) 1199–1223
https://doi.org/10.1007/s11139-023-00811-4
On the distribution of the entries of a fixed-rank random matrix over a finite field
Finite Fields and Their Applications 93 (2024) 102333
https://doi.org/10.1016/j.ffa.2023.102333
RLWE and PLWE over cyclotomic fields are not equivalent
(with Antonio J. Di Scala and Edoardo Signorini)
Applicable Algebra in Engineering, Communication and Computing 35 (2024), 351–358
https://doi.org/10.1007/x00200-022-00552-9
Finding differential trails on ChaCha by means of state functions
(with Emanuele Bellini, Juan Grados, and Rusydi H. Makarim)
International Journal of Applied Cryptography 4 (2024)
https://doi.org/10.1504/IJACT.2024.10063705
On the inverse of a Fibonacci number modulo a Fibonacci number being a Fibonacci number
Mediterranean Journal of Mathematics 20 (2023) 333
https://doi.org/10.1007/s00009-023-02518-8
On the greatest common divisor of n and the nth Fibonacci number, II
(with Abhishek Jha)
Canadian Mathematical Bulletin 66 (2023), 617–625
https://doi.org/10.4153/S0008439522000595
A note on the distribution of weights of fixed-rank matrices over the binary field
Finite Fields and Their Applications 87 (2023), 102157
https://doi.org/10.1016/j.ffa.2022.102157
Zeckendorf representation of multiplicative inverses modulo a Fibonacci number
(with Gessica Alecci and Nadir Murru)
Monatshefte für Mathematik 201 (2023), 1–9
https://doi.org/10.1007/s00605-022-01724-y
Pairwise modular multiplicative inverses and Fibonacci numbers
INTEGERS 23 (2023), article A3
http://math.colgate.edu/~integers/vol23.html
MR-DSS – Smaller MinRank-based (Ring-)Signatures
(with Emanuele Bellini, Andre Esser, and Javier Verbel)
PQCrypto 2022: Post-Quantum Cryptography, Lecture Notes in Computer Science, vol. 13512, pp. 144–169
https://doi.org/10.1007/978-3-031-17234-2_8
An estimator for the hardness of the MQ problem
(with Emanuele Bellini, Rusydi H. Makarim, and Javier Verbel)
Progress in Cryptology—AFRICACRYPT 2022, Lecture Notes in Computer Science, vol. 13503, pp. 323–347
https://doi.org/10.1007/978-3-031-17433-9_14
A survey on coefficients of cyclotomic polynomials
Expositiones Mathematicae 40 (2022), 469–494
https://doi.org/10.1016/j.exmath.2022.03.002
Greatest common divisors of shifted primes and Fibonacci numbers
(with Abhishek Jha)
Research in Number Theory 8 (2022), 65
https://doi.org/10.1007/s40993-022-00365-2
Practical complexities of probabilistic algorithms for solving Boolean polynomial systems
(with Stefano Barbero, Emanuele Bellini, and Javier Verbel)
Discrete Applied Mathematics 309 (2022), 13–31
https://doi.org/10.1016/j.dam.2021.11.014
On the divisibility of the rank of appearance of a Lucas sequence
International Journal of Number Theory 18 (2022), 2145–2156
https://doi.org/10.1142/S1793042122501093
On the number of residues of linear recurrence
Research in Number Theory 8 (2022), 7
https://doi.org/10.1007/s40993-021-00305-6
The largest entry in the inverse of a Vandermonde matrix
(with Jeffrey Shallit and Shun Zhang)
Linear and Multilinear Algebra 70 (2022), 5634–5641
https://doi.org/10.1080/03081087.2021.1922337
Membership in random ratio sets
Indagationes Mathematicae 33 (2022), 1326–1333
https://doi.org/10.1016/j.indag.2022.08.007
On the l.c.m. of shifted Lucas numbers
Indagationes Mathematicae 33 (2022), 1001–1011
https://doi.org/10.1016/j.indag.2022.04.006
On the exponents in the factorizations of r consecutive numbers
Quaestiones Mathematicae 45 (2022), 1221–1228
https://doi.org/10.2989/16073606.2021.1938277
Practical central binomial coefficients
Quaestiones Mathematicae 44 (2022), 1141–1144
https://doi.org/10.2989/16073606.2020.1775156
A note on the natural density of product sets
(with Sandro Bettin and Dimitris Koukoulopoulos)
Bulletin of the London Mathematical Society 53 (2021), 1407–1413
https://doi.org/10.1112/blms.12506
Additive bases and Niven numbers
Bulletin of the Australian Mathematical Society 104 (2021), 373–380
https://doi.org/10.1017/S0004972721000186
On the l.c.m. of shifted Fibonacci numbers
International Journal of Number Theory 17 (2021), 2009–2018
https://doi.org/10.1142/S1793042121500743
On the least common multiple of shifted powers
Journal of Integer Sequences 24 (2021), article 21.7.3
https://cs.uwaterloo.ca/journals/JIS/VOL24/Sanna/sanna7.html
On the least common multiple of random q-integers
Research in Number Theory 7 (2021), 16
https://doi.org/10.1007/s40993-021-00242-4
On the condition number of the Vandermonde matrix of the nth cyclotomic polynomial
(with Antonio J. Di Scala and Edoardo Signorini)
Journal of Mathematical Cryptology 15 (2021), 174–178
https://doi.org/10.1515/jmc-2020-0009
Greedy approximations by signed harmonic sums and the Thue–Morse sequence
(with Sandro Bettin and Giuseppe Molteni)
Advances in Mathematics 366 (2020), 107068
https://doi.org/10.1016/j.aim.2020.107068
On the l.c.m. of random terms of binary recurrence sequences
Journal of Number Theory 213 (2020), 221–231
https://doi.org/10.1016/j.jnt.2019.12.004
A note on product sets of random sets
Acta Mathematica Hungarica 162 (2020), 76–83
https://doi.org/10.1007/s10474-019-01014-4
On numbers divisible by the product of their nonzero base b digits
Quaestiones Mathematicae 43 (2020), 1563–1571
https://doi.org/10.2989/16073606.2019.1637956
Least common multiple of polynomial sequences
(with Danilo Bazzanella)
Rendiconti del Seminario Matematico Università e Politecnico di Torino 78 (2020), n° 1, 21–25
Directions sets: A generalization of ratio sets
(with Paolo Leonetti)
Bulletin of the Australian Mathematical Society 101 (2020), 389–395
https://doi.org/10.1017/S0004972719000959
Practical numbers among the binomial coefficients
(with Paolo Leonetti)
Journal of Number Theory 207 (2020), 145–155
https://doi.org/10.1016/j.jnt.2019.07.005
On the number of distinct exponents in the prime factorization of an integer
Proceedings of the Indian Academy of Sciences 130 (2020), 27
https://doi.org/10.1007/s12044-020-0556-y
p-adic denseness of members of partitions of N and their ratio sets
(with Piotr Miska)
Bulletin of the Malaysian Mathematical Sciences Society 43 (2020), 1127–1133
https://doi.org/10.1007/s40840-019-00728-6
Waring’s theorem for binary powers
(with Daniel Kane and Jeffrey Shallit)
Combinatorica 39 (2019), 1335–1350
https://doi.org/10.1007/s00493-019-3933-3
Practical numbers in Lucas sequences
Quaestiones Mathematicae 42 (2019), 977–983
https://doi.org/10.2989/16073606.2018.1502697
On the p-adic denseness of the quotient set of a polynomial image
(with Piotr Miska and Nadir Murru)
Journal of Number Theory 197 (2019), 218–227
https://doi.org/10.1016/j.jnt.2018.08.010
On numbers n with polynomial image coprime with the nth term of a linear recurrence
(with Daniele Mastrostefano)
Bulletin of the Australian Mathematical Society 99 (2019), 23–33
https://doi.org/10.1017/S0004972718000606
On numbers n relatively prime to the nth term of a linear recurrence
Bulletin of the Malaysian Mathematical Sciences Society 42 (2019), 827–833
https://doi.org/10.1007/s40840-017-0514-8
Small values of signed harmonic sums
(with Sandro Bettin and Giuseppe Molteni)
Comptes Rendus Mathématique 356 (2018), 1062–1074
https://doi.org/10.1016/j.crma.2018.11.007
On the greatest common divisor of n and the nth Fibonacci number
(with Paolo Leonetti)
Rocky Mountain Journal of Mathematics 48 (2018), 1191–1199
https://doi.org/10.1216/RMJ-2018-48-4-1191
The density of numbers n having a prescribed G.C.D. with the nth Fibonacci number
(with Emanuele Tron)
Indagationes Mathematicae 29 (2018), 972–980
https://doi.org/10.1016/j.indag.2018.03.002
The moments of the logarithm of a G.C.D. related to Lucas sequences
Journal of Number Theory 191 (2018), 305–315
https://doi.org/10.1016/j.jnt.2018.03.012
A note on primes in certain residue classes
(with Paolo Leonetti)
International Journal of Number Theory 14 (2018), 2219–2223
https://doi.org/10.1142/S1793042118501336
Central binomial coefficients divisible by or coprime to their indices
International Journal of Number Theory 14 (2018), 1135–1141
https://doi.org/10.1142/S1793042118500707
On the k-regularity of the k-adic valuation of Lucas sequences
(with Nadir Murru)
Journal de Théorie des Nombres de Bordeaux 30 (2018), 227–237
https://doi.org/10.5802/jtnb.1025
On the closure of the image of the generalized divisor function
Uniform Distribution Theory 12 (2017), 77–90
https://doi.org/10.1515/udt-2017-0016
A coprimality condition on consecutive values of polynomials
(with Márton Szikszai)
Bulletin of the London Mathematical Society 49 (2017), 908–915
https://doi.org/10.1112/blms.12078
Distribution of integral values for the ratio of two linear recurrences
Journal of Number Theory 180 (2017), 195–207
https://doi.org/10.1016/j.jnt.2017.04.015
p-adic quotient sets
(with Stephan Ramon Garcia, Yu Xuan Hong, Florian Luca, Elena Pinsker, Evan Schechter, and Adam Starr)
Acta Arithmetica 179 (2017), 163–184
https://doi.org/10.4064/aa8579-4-2017
The quotient set of k-generalised Fibonacci numbers is dense in Q_p
Bulletin of the Australian Mathematical Society 96 (2017), 24–29
https://doi.org/10.1017/S0004972716001118
A factor of integer polynomials with minimal integrals
Journal de Théorie des Nombres de Bordeaux 29 (2017), 637–646
https://doi.org/10.5802/jtnb.994
On numbers n dividing the nth term of a Lucas sequence
International Journal of Number Theory 13 (2017), 725–734
https://doi.org/10.1142/S1793042117500373
On the p-adic valuation of Stirling numbers of the first kind
(with Paolo Leonetti)
Acta Mathematica Hungarica 151 (2017), 217–231
https://doi.org/10.1007/s10474-016-0680-4
The p-adic valuation of Lucas sequences
The Fibonacci Quarterly 54 (2016), 118–124
https://www.fq.math.ca/54-2
On the p-adic valuation of harmonic numbers
Journal of Number Theory 166 (2016), 41–46
https://doi.org/10.1016/j.jnt.2016.02.020
Counting arithmetic formulas
(with Edinah K. Gnang and Maksym Radziwiłł)
European Journal of Combinatorics 47 (2015), 40–53
https://doi.org/10.1016/j.ejc.2015.01.007
On the number of arithmetic formulas
International Journal of Number Theory 11 (2015), 1099–1106
https://doi.org/10.1142/S1793042115500591
On the sum of digits of the factorial
Journal of Number Theory 147 (2015), 836–841
https://doi.org/10.1016/j.jnt.2014.09.003
Covering an arithmetic progression with geometric progressions and vice versa
International Journal of Number Theory 10 (2014), 1577–1582
https://doi.org/10.1142/S1793042114500456
On the exponential sum with the sum of digits of hereditary base b notation
INTEGERS 14 (2014), article A36
https://www.integers-ejcnt.org/vol14.html
On the asymptotic density of the support of a Dirichlet convolution
Journal of Number Theory 134 (2014), 1–12
https://doi.org/10.1016/j.jnt.2013.07.012
Uncertainty principles connected with the Möbius inversion formula
(with Paul Pollack)
Bulletin of the Australian Mathematical Society 88 (2013), 460–472
https://doi.org/10.1017/S0004972712001128
On arithmetic progressions of integers with a distinct sum of digits
Journal of Integer Sequences 15 (2012), article 12.8.1
https://cs.uwaterloo.ca/journals/JIS/VOL15/Sanna/sanna3.html
A new elementary proof of the inequality ϕ(n) > π(n)
Notes on Number Theory and Discrete Mathematics 18 (2012), No. 3, 35–37
https://nntdm.net/volume-18-2012/number-3/35-37