Template verification protocol

The key to any verification procedure is a protocol that can guarantee that no treaty accountable item undergoing verification is secretly modified or replaced with another object. Significant thinking has been invested into the concept of template verification, particularly at the US national laboratories and think tanks4,13,14. The high-level protocol has been either outlined in or been the basis of prior warhead verification publications in academia5,6,7,8 and in the US national laboratories14,15,16,17. Its basic steps can be summarized as follows:

1. The inspection party (inspectors) makes an unannounced visit to an ICBM site and randomly chooses a warhead from one of the missiles. The warhead enters the joint custody of the inspectors and the host country (hosts), and can be treated as the authentic template to which all future candidate warheads undergoing dismantlement and disposition will be compared. The warheads may be tagged with a unique measurement device to reduce the risk of diversions, as described by Fuller4. 2. The template is transported under the joint custody of the hosts and inspectors to the site where the candidate warheads (henceforth referred to as candidates) will undergo dismantlement, verification, and disposition. To increase the certainty that the template hasn’t been tampered with it could be isotopically taged, for example, using the nuclear material identification system18. 3. Both the template and the candidate undergo dismantlement by the hosts in an environment that cannot be observed directly by the inspectors, but from where no new objects can be introduced to or removed from. The fissile components of the weapons, also known as the pits, are extracted. Each pit is placed in a marked, opaque boxe. The remaining components are placed in a different, unmarked box. 4. The dismantlement area is made accessible to the inspectors. The inspectors use a simple Geiger counter to verify that the non-fissile, unmarked boxes do not contain any radioactive materials, thus confirming that the marked boxes indeed contain the pits. 5. The two marked boxes undergo epithermal transmission analysis. See Supplementary Note 3 for a discussion on aligning the objects while maintaining secrecy. The two-dimensional (2D) radiographs and the spectral signatures are compared in a statistical test. An agreement confirms that the candidate is identical to the template and thus can be treated as authentic. A disagreement indicates a hoaxing attempt.

The last step is key to the whole verification process, and is the focus of this work. The transmission measurement produces an effective image in a 2D pixel array made of scintillators that are sensitive to epithermal neutrons. Furthermore, by choosing a detector with a fast response time and knowing the time when the neutrons are produced, a TOF technique can allow an explicit determination of neutron energies.

Epithermal neutrons

The epithermal range refers to the neutron energy domain encompassed between the thermal energies of ~40 meV and fast neutron energies of ~100 keV. The energies of interest for this study are those of 1 ≤ E ≤ 10 eV. While the neutron interactions in the thermal regime are described by monotonic changes in cross sections, in the epithermal range the neutrons can trigger various resonant responses in uranium and plutonium. These are typically (n,fission) or (n,γ) reactions, resulting in the loss of the original neutron. A plot of total interaction cross sections in the epithermal range for five isotopes of interest can be seen in Fig. 1. For a radiographic configuration these interactions selectively remove the original neutrons of resonant energies from the transmitted beam and give rise to an absorption spectrum, resulting in unique sets of ~0.3 eV wide notches specific to each isotope. While the resonances are the most prominent features of the cross section, the continuum between the resonances also encodes information about the isotopic compositions of the target. These combined absorption features yield a unique fingerprint of a particular configuration of isotopics, geometry, and density distribution.

Fig. 1 Epithermal neutron interaction cross sections for plutonium isotopes. The legend lists the five isotopes of interest. For reference, WGPu is almost entirely made out of 239Pu and 240Pu, while RGPu contains significant contributions from 240,241,242,238Pu. Evaluated data taken from the JEFF-3.2 database28 Full size image

The key component of a nuclear weapon is its pit—the hollow plutonium sphere at the center of the assembly. This work focuses on the verification of the authenticity of the pit. A direct transmission imaging of the pit would reveal many of its secret parameters. Thus, an additional physical cryptographic barrier is necessary to achieve an ZK test. The barrier needs to be constructed such as to also allow for pit-to-pit comparisons that can detect any significant differences. These two simultaneous goals can be accomplished by the mass reciprocal mask of the pit. The reciprocal mask has a shape such that all the rays of epithermal neutrons in the beam transit the same combined areal density. A simple example of a reciprocal mask of a hollow shell could be a cube with the geometry of the said hollow shell subtracted. Thus, the aligned combination of the pit and the reciprocal will result in uniform areal density, producing an image in the detection plane, which is consistent with that of a flat object. A more optimal reciprocal for a hollow shell of internal and external radii r 1 and r 0 can be defined via its thickness along the beam axis \(d = D - 2\left( {\sqrt {r_0^2 - y^2} - \sqrt {r_1^2 - y^2} } \right)\) for y < r 1 and \(d = D - 2\sqrt {r_0^2 - y^2}\) for r 1 ≤ y ≤ r 0 , where D is the combined thickness observed by all particles in the beam, and y is the vertical coordinate. A combination of the pit and the reciprocal is illustrated in Fig. 2. The hosts can fit the pit and the reciprocal inside two opaque boxes, thus keeping their shape secret during times when they are accessible to the inspectors. The two boxes can then be aligned with each other, thus aligning the pit and the reciprocal for the transmission measurement. For a detailed discussion on the reciprocal geometries, as well as details on alignments see Supplementary Note 7. It should be noted that an assembly with a uniform areal density does not mean that the resulting image will be flat as well. Secondary processes, for example, neutron scattering, can distort the image and introduce some angular dependencies that hypothetically could contain information about geometric structures. For this reason detailed simulations are necessary to validate the concept and demonstrate information security. In the next sections we use Monte Carlo (MC) simulations to show that the transmission image produced for this configuration is identical to that of a uniform plate. This outcome guarantees that no geometric information is revealed by the transmission analysis. Even if the inspectors are capable of determining the incident flux in the neutron beam they will at most gain knowledge of an upper limit on the amount of total mass. The hosts can modify the mask to make that knowledge of no value: for example, the inspectors might determine that the mass of WGPu in the pit is <10 kg—this knowledge is useless, as the critical mass for a WGPu pit is approximately 6 kg.

Fig. 2 A diagram of the pit and its reciprocal mask in a radiographic configuration. The combined transmission image will be identical to that of a flat plate with a thickness equal to the external thickness of the mask Full size image

Isotopic hoax resistance

As the inspectors perform the radiographic interrogation of the pit, they need to ascertain that the isotopics and effective densities of the template and the candidate pits are identical. At a given pit orientation, this can be performed by comparing the epithermal spectra of the transmitted beam from the template and candidate measurements. The energy information can be acquired from the timing of the arrival of the neutrons, via the previously described TOF method to very high precision with either boron-doped microchannel plate detectors or 6Li-based LiCaAlF 6 scintillators19,20. For a further discussion see Supplementary Note 9. To study the system’s sensitivity to hoaxing, we consider a scenario where the WGPu pit has been replaced with a RGPu pit. MC simulations are performed for the configuration described in Fig. 2. The simulations were performed using the MCNP5 package, which has a fully validated neutron physics module21. The neutron energies were uniformly sampled in the 0 ≤ E ≤ 10 eV range. For this study the isotopic mass concentrations for RGPu was 40.8% 239Pu. For WGPu the fractions are 93% 239Pu, the remainder as 240Pu and trace amounts of the other isotopes. See Supplementary Note 5 for detailed listing of the isotopic concentration. For both the template and the hoax RGPu pit the inner diameter was 6.27 cm and the outer diameter was 6.7 cm—based on public domain estimates of a Soviet tactical thermonuclear warhead pit geometries22. The reciprocal was modeled in three dimensions along the previously described formula. The combined pit-reciprocal thickness was 5 cm.

Figure 3 shows the results of the MC simulation of an idealized detector exposed to the transmitted flux through a combination or a reciprocal mask and a WGPu pit, and a similar configuration where WGPu has been replaced by RGPu. The large spectral discrepancies are clear. The difference is primarily caused by the abundance of 242Pu in the RGPu, produced as a results of neutron capture in the reactor core. This manifests itself in deeper absorption lines at 4.2 and 8.5 eV, as well as generally increased absorption in the 5–8 eV range. It should be clarified that both the shape and the magnitude of the distribution are part of the hoax sensitivity. To achieve an absolute magnitude measurement, the inspectors can normalize the output to a parameter proportional to the incident neutron flux, such as the measurement time or the beam charge, as appropriate. The results have also been used to determine the number of incident neutrons to achieve a discrimination with a 5σ confidence. That number is n = 1 × 105 neutrons. See Methods for more detail.

Fig. 3 Spectra from transmitted epithermal flux simulations. The simulations were performed for 20.7 × 106 neutrons incident upon a valid WPGu-reciprocal and hoax RGPu-reciprocal configurations Full size image

Geometric hoax resistance

Geometric hoax resistance implies the use of 2D imaging to identify any significant geometric and/or isotopic differences between the template and the candidate, as a way of detecting cheating attempts. The detector described in Fig. 2 and modeled in the MC simulation, whose spectral output is shown in Fig. 3, can be pixelated to produce imaging data. Figure 4 shows the results of simulated epithermal transmission images for a WGPu template and RGPu hoax candidate scenarios. The 2D images show a clear difference, indicating that the candidate is a hoax and thus confirming the isotopic analysis described earlier. The one-dimensional projection of the two images’ radial distributions further shows the extent of the discrepancy. It should be noted that the non-flat image of the WGPu configuration is caused by the in-scatter of the epithermal neutrons, and doesn’t reveal any information about the object, as will be shown in the section on geometric information security. The imaging analysis described here focuses on a hoax scenario of modified isotopics. However, any changes in pit diameter(s) and/or density will result in nonuniformity in areal density as observed by the incident epithermal beam and will thus cause imaging inconsistencies similar to the ones described in Fig. 4.

Fig. 4 Epithermal neutron images in the detector for two configurations. a The valid WGPu-reciprocal scenario, b the RGPu-reciprocal hoax scenario, and c the radial distribution of the counts for both scenarios showing a clear discrepancy. The non-flat image of the WGPu configuration is caused by the in-scatter of the epithermal neutrons. The error bars reflect one sigma standard deviations Full size image

While the above discussion is indicative of the strength of the technique in detecting hoaxes, a proof of uniqueness is necessary. This means showing that for a given reciprocal a given image can be produced only by a unique object. This is not the case for a single projection, since transmission is only sensitive to the line integral along the beam axis. To exclude the possibility of geometric hoaxes with identical line integrals but consisting of a different three-dimensional manifold, multiple projections along the x-, y-, and z-axes may be necessary. For a spherically symmetric pit similar to the one treated in this work this could be achieved by multiple measurements at random angles. For a spherically non-symmetric objects three projections along the x-, y-, and z-axes may be sufficient—each requiring a reciprocal built for that projection. A more rigorous proof of uniqueness is part of future work, and could be based on the methodology of K-transforms as described in Kemp et al.8.

Geometric information security

Geometric information security refers to the notion that the inspectors will learn nothing about the pit geometry beyond what they already know. We assume that for the proof system to be ZK we need to only show that for an honest pit the combined pit-reciprocal transmission is identical to that of a flat, uniform plate of no geometric structure. This implies that the information content in the data cannot allow the inspectors to distinguish from a complex geometry (pit-reciprocal) and a flat object.

To show this, MCNP5 simulations have been performed for a simple flat plate of WGPu with an areal density equal to that of the pit-reciprocal configuration shown in Fig. 3. Similar to the analysis performed in the section on geometric hoax resistance the radial distribution of the counts of the two configurations are plotted in Fig. 5. The radial count distribution has error bars, which reflect the fluctuations that an inspector would observe for the scenario of 1 × 105 incident neutrons necessary for achieving a hoax detection at the 5σ confidence level. The large overlap of the errors shows the statistical identity of the two outcomes, and indicates that no useful geometric information can be extracted about the object.

Fig. 5 The radial distribution of epithermal neutron counts. The blue markers refer to the pit-reciprocal configuration, while the red markers refer to a flat plate of WGPu of equivalent thickness. The error bars reflect the expected one standard deviation fluctuations for a measurement necessary for the detection of a hoax at a 5σ confidence level. The comparison shows statistically identical distributions, indicating that no information about the pit-reciprocal geometry can be extracted Full size image

Isotopic information security

The isotopic composition of the plutonium pit can affect the reliability of the nuclear weapon23. Additionally, the knowledge about the abundance of particular isotopes can allow an observer to determine the methodology by which the fissile material was produced. Because of this and other considerations the information on isotopic composition can be of sensitive nature. Thus, a ZK proof system should not produce any data from which the isotopics of the pit-reciprocal configuration can be inferred beyond what is commonly known.

Just as the shape of the reciprocal mask protects the geometry of the pit, its isotopic composition can be used to mask the real isotopic concentrations in the pit itself. While the inspectors may use the spectral information to infer the isotopic ratios for the pit-reciprocal combination, it can be made impossible for them to infer the isotopic contributions of the pit itself. For a simple case consider a slightly modified version of the reciprocal than the one presented in Fig. 2, where the host has added an additional flat, cylindrical extension of unknown thickness and isotopic composition. It can be shown that multiple combinations of isotopics in the pit-reciprocal and the extension will produce the same spectrum. To show this computationally, MCNP5 simulations have been performed for the following three configurations: pit-reciprocal made out of WGPu, and a 2 cm extension of 41% enriched RGPu; pit-reciprocal and extension at intermediate 78% enrichment; and pit-reciprocal at low-intermediate 70% enrichment and extension made of super-grade plutonium. See Supplementary Note 5 for the full listing of concentrations corresponding to different enrichment levels used in these simulations. In the simulation incident epithermal neutron events were uniformly sampled in the [0,10 eV] range. The results of the simulations were used to determine the expected detector counts for achieving a 5σ hoax detection. The mean expected counts and the corresponding statistical errors are plotted in Fig. 6. The plots show no statistically significant differences. This proves that for this particular extension thickness the inspectors cannot determine the enrichment level to better than the 70–93% range. The function of the extension is somewhat analogous to that of the encryption/witness foil in tNRF-based warhead verification8. Just as the foil scrambles the isotopic-dependent signal, the extensions modify the signal in a way that is fixed between measurements but unknown to the inspector.

Fig. 6 Simulations of spectra of the transmitted epithermal neutron count mean values. The target consisted of a pit-reciprocal and an extension of various levels of 239Pu enrichment. The results show that the data would make it impossible to determine the enrichment of the pit beyond the 70–93% range. The error bars reflect the statistical uncertainty of an expected measurement with 1.0 × 107 incident neutrons, which is more than sufficient for achieving the 5σ hoax detection requirement Full size image