The discrete logarithm problem over prime fields: the safe prime case. The Smart attack, non-canonical lifts and logarithmic derivatives

In this brief note we connect the discrete logarithm problem over prime fields in the safe prime case to the logarithmic derivative.Comment: 8 page

Solving discrete logarithms on a 170-bit MNT curve by pairing reduction

Pairing based cryptography is in a dangerous position following the breakthroughs on discrete logarithms computations in finite fields of small characteristic. Remaining instances are built over finite fields of large characteristic and their security relies on the fact that the embedding field of the underlying curve is relatively large. How large is debatable. The aim of our work is to sustain the claim that the combination of degree 3 embedding and too small finite fields obviously does not provide enough security. As a computational example, we solve the DLP on a 170-bit MNT curve, by exploiting the pairing embedding to a 508-bit, degree-3 extension of the base field.Comment: to appear in the Lecture Notes in Computer Science (LNCS

Cryptography Through the Lens of Group Theory

Cryptography has been around for many years, and mathematics has been around even longer. When the two subjects were combined, however, both the improvements and attacks on cryptography were prevalent. This paper introduces and performs a comparative analysis of two versions of the ElGamal cryptosystem, both of which use the specific field of mathematics known as group theory

On the closure of elliptic wedge operators

We prove a semi-Fredholm theorem for the minimal extension of elliptic operators on manifolds with wedge singularities and give, under suitable assumptions, a full asymptotic expansion of the trace of the resolvent.Comment: 22 pages, improved expositio