Cryptographic encryption scheme based on metastable excited nuclei

Abstract

The novelty of quantum cryptography is that whenever a spy tries to eavesdrop the communication he causes disturbances in the transmission of the message. Ultimately this unavoidable disturbance is a consequence of Heisenberg’s uncertainty principle that limits the joint knowledge of complementary observables. We present in this paper a novel and highly speculative approach. We propose to replace Heisenberg uncertainties by another type of uncertainty, that characterizes the knowledge of the time at which an unstable nucleus decays. Previously developed protocols of quantum cryptography make it possible to refresh a key even in the case that we do not trust the carrier of the key. This scheme might do so as well.

Appendix: Production of a metastable Sn isotope of halflife 13.6 days

By bombarding natural Sn (composed of nine stable isotopes with mass between 112 and 124) with high energy protons, many radioactive nuclides of the elements Sb, Sn, In and Cd with half lives longer than 1 min can be formed (for instance more than 50 when the energy of the protons is 65 Mev (Hermanne et al. 2006)). Excitation functions, expressing the probability of the production in function of the particle energy, for 13 among them, all emitting $\gamma$-rays with energy above 100 keV, are documented in Ref. (Hermanne et al. 2006). One of these radionuclides is the metastable state $^{117{\rm m}}{\rm Sn}$ of the stable, naturally occurring, isotope 117Sn. The decay is characterized by a halflife $T _{1/2} = 13.6$ days¹² and the deexcitation from the metastable state to the ground state occurs through a cascade emission of a 156.0 keV $\gamma$-ray to an intermediate excited level followed by a 158.56keV $\gamma$-ray.

These transitions are characterized by high internal conversion rates which mean that the energy of the $\gamma$-rays is converted to electronic excitation states with high probability, which in turn induces several X-lines with energies between 25 and 29 keV.

The shape of the excitation function suggests that only a small fraction of the metastable state is formed by inelastic (p,p) scattering on 117Sn while the largest part is due to (p,pxn) reactions on 118,119,120 Sn. The contribution of decay of 117Sb (only 0.07 $\%$ decays to 117$^{\rm m}Sn$) can be neglected. For incident protons of 30MeV (a standard value for commercially available isotope production machines) a thick target yield of 1MBq/$\mu$Ah can be expected.¹³

Contaminating radio- or stable nuclides of Sb and In can be removed by a standard chemical separation step shortly after the end of bombardment. The production of the possibly disturbing co-produced Sn isotopes 113Sn ($T _{1/2}\,= \,115.1$ days); 119mSn ($T _{1/2}\,= \,293$ days), 121$^m$Sn ($T _{1/2}\,=\, 50$ years) and 123Sn ($T _{1/2}\,= \,129.2$ days) can be limited or avoided by working with enriched 118Sn targets. Moreover, isotopes with a long lifetime would be present in the placebo substance (Sect.  2, ii) in comparable proportions. Finally, it has to be remarked that for 117$^{\rm m}$Sn production an alternative to charged particle activation is (n,$\gamma$) caption in a fission reactor on enriched 116Sn targets.