7 citations · 10 across the 8 of their papers we have counts for
9 papers
Numerical and Statistical Analysis of Aliquot Sequences
Kevin Chum, Richard K. Guy, Michael J. Jacobson +1
We present a variety of numerical data related to the growth of terms in aliquot sequences, iterations of the function . First, we compute the geometric mean of th…
Removable Weak Keys for Discrete Logarithm Based Cryptography
Michael John Jacobson, Prabhat Kushwaha
We describe a novel type of weak cryptographic private key that can exist in any discrete logarithm based public-key cryptosystem set in a group of prime order where has…
A note on the security of CSIDH
Jean-François Biasse, Annamaria Iezzi, Michael J. Jacobson
We propose an algorithm for computing an isogeny between two elliptic curves defined over a finite field such that there is an imaginary quadratic order sat…
Unconditional Class Group Tabulation of Imaginary Quadratic Fields to
A. S. Mosunov, M. J. Jacobson
We present an improved algorithm for tabulating class groups of imaginary quadratic fields of bounded discriminant. Our method uses classical class number formulas involving theta-…
Practical improvements to class group and regulator computation of real quadratic fields
Jean-François Biasse, Jacobson John Michael
We present improvements to the index-calculus algorithm for the computation of the ideal class group and regulator of a real quadratic field. Our improvements consist of applying t…
Security Estimates for Quadratic Field Based Cryptosystems
Jean-François Biasse, Jacobson John Michael, Silverster K. Alan
We describe implementations for solving the discrete logarithm problem in the class group of an imaginary quadratic field and in the infrastructure of a real quadratic field. The a…