arXiv subjects

Andreas O. Bender

Publications and source records attributed to Andreas O. Bender.

4 recordsLinked to original sources

arXiv2018

qrypt0 - encrypted short messages exchanged between offline computers

A system is described for exchanging encrypted short messages between computers which remain permanently isolated from any network accessible to the attacker. The main advantage is effective protection of these computers from malware which could circumvent the encryption. For transmission, the ciphertext is passed between isolated and connected computers in the form of a QR code, which is displayed on and scanned from a screen. The security of qrypt0 therefore rests on the cryptography and the computer's physical isolation rather than on the computer security of the encrypting device.

cs.CR↗

arXiv2013

Representing an element in F_q[t] as the sum of two irreducibles

A monic polynomial in F_q[t] of degree n over a finite field F_q of odd characteristic can be written as the sum of two irreducible monic elements in F_q[t] of degrees n and n-1 if q is larger than a bound depending only on n. The main tool is a sufficient condition for simultaneous primality of two polynomials in one variable x with coefficients in F_q[t].

math.NT↗

arXiv2009

On quantitative analogues of the Goldbach and twin prime conjectures over F_q[t]

We study the number of ways to decompose a monic polynomial in F_q[t] of degree n as a sum of two monic irreducible polynomials in F_q[t]. Our principal result is an asymptotic formula for the number of such representations in the case when q is large compared to n. In its range of validity, this formula agrees with what is suggested by heuristic arguments from the rational setting. We also present similar results towards an analogue of the twin prime conjecture.

math.NT↗

arXiv2005

A potential analogue of Schinzel's hypothesis for polynomials with coefficients in Fq[t]

The Schinzel hypothesis essentially claims that finitely many irreducible polynomials in one variable over Z simultaneously assume infinitely many prime values unless there is an obvious reason why this is impossible. We prove that under a restriction on the characteristic of the finite field Fq and a smoothness assumption, finitely many irreducible polynomials in one variable over the ring Fq[t] assume simultaneous prime values after a sufficiently large extension of the field of constants.

math.NT↗