Cosmic coding and transfer storage (COSMOCATS) for invincible key storage

doi:10.21203/rs.3.rs-2588477/v1

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Cosmic coding and transfer storage (COSMOCATS) for invincible key storage

https://doi.org/10.21203/rs.3.rs-2588477/v1

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published 30 May, 2023

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Thus far, a perfectly secure encryption key storage system doesn't exist. As long as key storage is connected to a network system, there is always a chance that it can be cracked. Even if storage is not continually connected to a network system; it is repeatedly necessary for an individual to access storage to upload and download the data; hence there is always a loophole with every conventional encryption key storage system. By utilizing the penetrative nature of cosmic-ray muons, the COSMOCAT (Cosmic coding and transfer) technique may tackle this problem by eliminating the requirement for any network connection to data storage. COSMOCAT was invented for post quantum key generation and distribution technique for wireless near field communication. However, in its first stage of development, COSMOCAT relied on standard comparators and Global Positioning System (GPS) or other Global Navigation Satellite Systems (GNSS) for key generation. Temporal jitters of the signals outputted from comparators and frequency fluctuations in GPS-disciplined oscillators degraded the key strength and the efficiency of both the key generation and distribution. New strategies are tested in this paper to improve these factors. As a result, the key strength and the key authenticating rate limit are respectively improved by 4 orders of magnitude and more than 5 orders of magnitude. As a consequence, it has become possible to propose a practical methodology for a new key storage and authentication which has the potential to be an impregnable defense against any kind of cyber/physical attack to data storage. Practical applications of COSMOCATS-based symmetric-key cryptosystems to an electronic digital signing system are discussed by introducing, as an example, a system for cryptocurrency implementation.

Physical sciences/Physics/Particle physics

Physical sciences/Physics/Particle physics/Experimental particle physics

Physical sciences/Engineering/Electrical and electronic engineering

Physical sciences/Mathematics and computing/Computational science

Physical sciences/Mathematics and computing/Computer science

Physical sciences/Mathematics and computing

Physical sciences/Mathematics and computing/Information technology

While quantum computing promises unprecedented speed and power for processing data, it also poses new risks to public key encryption. As this technology advances over the next decade, its new capabilities could be exploited to break standard encryption methods that are widely used to protect customer data, complete business transactions, and provide secure communications.  New schemes are urgently required to prepare for the transition to post-quantum cryptography so that potentially vulnerable data, algorithms, protocols, and systems can be properly protected.

With all architectural solutions using cryptographic keys stored in cloud storage, there is a limit to the degree of security assurance that the cloud consumer can expect to get; this is due to the fact that the logical and physical organization of the storage resources are entirely under the control of the cloud provider¹. In particular, the cloud service client’s assets are susceptible to key leakage and key corruptions. Loss of a client’s encryption key results in severe security issues². Potential attackers may have the power to generate a new re-encryption key from stored re-encryption keys³. Even if the keys are protected from cyberattacks, the storage system is still vulnerable since, unless it's physically protected inside an underground safe without an entrance, there is always a possibility that a third person could physically access and steal the storage assets or the storage itself. Therefore, an uncrackable encryption key storage system cannot exist in the conventional sense and thus, several security protocols have been established to minimize data storage security weaknesses⁴. However, if we could safely send keys (without using any physical route such as Ethernet cables, Wi-Fi, optical fibers, Bluetooth etc.) from an internet connected server to storage facilities that are completely concealed inside an inaccessible underground safe, (totally isolated from the outside environment), then we could realize an invincible data storage system which would be entirely safe from security threats since it would be impossible to conduct either physical or cyber-attacks on this system.

Quantum key distribution (QKD) has been proposed as a guaranteed and secure method to share private keys between the sender and the receiver. However, in 2016, Yuen reviewed the problems associated with QKD security⁵. Accordingly, a white paper from the National Cyber Security Centre (NCSC), UK, proposed a halt to QKD development⁶ due to the following concerns regarding QKD:

(A) Security research such as authentication is not incorporated into QKD research

(B) In order to build a network with QKD, it is necessary to set up a relay point which relies on classical physics, so it is not unconditionally secure.

(C) Attack methods that may target QKD devices are also being researched, but such research does not guarantee complete security. An unknown loophole may exist.

(D) Updating QKD equipment requires hardware replacement.

QKD may offer highly secured key distribution in principle, but in practice, it cannot be used for upgrading the security of data storage. From the point of view of practicality, there might be more value in researching an alternative methodology with stronger security potential which can be retrofitted to the currently available system.

COSMOCAT has been invented as a post-quantum key generation and distribution scheme for near field communication under a common key cryptosystem⁷. The process is as follows: by recording the muon's arrival times, sequences of true random numbers (TRNs) are obtained. If the sender and receiver are close enough (≤10 m) to each other to detect the same muons, then after subtraction of the muon's TOF between the sender and the receiver, identical numerical sequences can be independently taken from data recorded at both of the COSMOCAT sensors located at the sender and the receiver locations. Thus, both the sender and the receiver can hold the same TRN sequences (called cosmokeys) without having to physically exchange the data. The number of digits that can be used for cosmokeys depends on precision of measuring the moment the cosmic muons are detected.

Pseudo random number generators are cost-effective, but if the algorithm that generates the numbers is stolen by hackers, they can be easily decrypted if attackers can correctly predict future number sequences. COSMOCAT essentially realizes a method to obtain a one-time pad which is independently known by only the sender and the receiver and which cannot be cracked; thus, COSMOCAT qualifies as an information-theoretic security technique. Nevertheless, in its first iteration, COSMOCAT was using GPS-disciplined oscillators (GPS-DO) for time synchronization to generate keys for encoding. GPS and other GNSS have enabled widespread adoption of Positioning, Navigation, and Timing (PNT) services in many applications across modern society. However, the following drawbacks exist when using the GPS-based timing system:

(A) GPS-DOs are usually steered to the GPS time every few minutes, thus the resultant frequency output is strongly influenced by frequency fluctuations of local oscillators. These fluctuations degrade the performance of COSMOCAT.

(B) GPS signals are unavailable in underground environments.

(C) Since GPS signals are low-power and unencrypted, there is a vulnerability to interference, jamming, and spoofing. While interference arises from unintentionally produced RF waveforms that raise the effective noise in the receiver processing, jamming is caused by intentionally producing these RF waveforms. Spoofing is caused by unintentional, intentional or malicious RF waveforms that mimic true signals to cause a range of effects: from incorrect PNT outputs to receiver malfunction. Therefore, GPS-dependent disruption or interference with PNT systems has the potential (as it was used in its first iteration) to have adverse impacts on the otherwise excellent security ofCOSMOCAT.

There are several techniques which could be employed to better enhance the independency and the accuracy of timing used in COSMOCAT. These techniques include (1) direct universal time coordinate (UTC) dissemination e.g., via optical fibers, (2) atomic clocks, and (3) cosmic time calibration (CTC)⁸. All of these techniques offer timing precision of a few ns or better, however they are either (1) costly or (2) have a tendency to drift after being used for long periods of time. Amongst all of these techniques, the cheapest and the most stable solution is CTC. For the second iteration of COSMOCAT described in this work, (A) we replaced the comparator used in the prior work with the constant fraction discriminator (CFD) and improved the key strength and key generation efficiency by 4 orders of magnitude and more than 5 orders of magnitude, respectively. (B) Based on this key generation efficiency, an unbreakable underground key storage security system was designed using a combination of COSMOCAT and CTC by employing one of the major features of COSMOCAT: the penetrative nature of muons (which can automatically generate cosmokeys) to locations deep underground. (C) A protocol for authentication of the encrypted data with the keys stored in the storage in the underground safe is proposed with an introduction on how this could be applied to a digital signing system in cryptocurrency operations.

In this section, the basic principles of COSMOCATS along with two key results (1. improvements in key strength and key generation and 2. distribution efficiency) will be outlined. Then the newly created COSMOCATS (the procedures followed at the sender's side and the storage side) will be discussed more in detail in the next section.

COSMOCAT has two features. (1) COSMOCAT can duplicate and triplicate numerical sequences of TRNs in different locations. If someone tries to duplicate a 24-digit TRN numerical sequence in different locations with the world’s best random number generating machine (generating 250 trillion random numbers per second)⁹ but without data transfer, it would take 3,000 years to accidently generate the same combination of the numbers. On the other hand, since the cosmic ray muon's travelling speed (~ c) and the traveling path (straight) are well known, COSMOCAT can generate 2 or more identical 24-digit TRNs in different locations within one second without physically transferring the TRNs. It is known that cosmic ray muons have a random arrival time distribution: one event occurs completely independently from the occurrence of another event. Ahlen et al. (1992)¹⁰ evaluated 407,420 high-energy muon arrival times, and found that there were no indications of deviations or time anisotropies in nanosecond to second time scales. (2) COSMOCAT can deliver the same numerical sequences of TRNs between the aboveground facility and a concealed underground vault. Cosmic-ray muons are penetrative, and they have been applied to imaging gigantic objects such as volcanoes¹¹, ocean¹², cyclones¹³, tectonics¹⁴, earthquake retrodiction¹⁵, Egyptian pyramids¹⁶, the Great Wall of China¹⁷ as well as underground/underwater positioning¹⁸ and navigation¹⁹, precise time synchronization²⁰.

Principle of COSMOCATS. The COSMOCATS system consists of the sender's COSMOCAT sensor, the receiver's COSMOCAT sensor, and the receiver's storage. In the COSMOCATS scheme, (1) if the sender knows the receiver at the storage site will detect the same muons, (2) if the sender knows the distance between the sender and the receiver, and (3) if the time is accurately synchronized between the sender and the receiver, then the sender can predict the muon's arrival time at the receiver's detector. Cosmokeys are defined as timestamps generated by the muons passing through both the sender's sensor and the receiver's sensor. In COSMOCATS, these timestamps (in units of ps) are used as cosmokeys. The muon's arrival timestamp (t) can be described by using a numerical sequence (N_i) as follows:

$$t=\sum _{i}^{}{N}_{i}\times {10}^{-i}\left[\text{s}\right], \left(1\right)$$

where N can have a value from 0 to 9. The numerical sequence N_i is used as a cosmokey. When a muon event is observed, (at either the sender's COSMOCAT sensor or the receiver's COSMOCAT sensor) timestamps are automatically issued respectively at the sender and the receiver locations. However, in general, many of these timestamps do not match between the sender and the receiver since many of the muons do not pass though both of the sensors. The cosmokey generation rate can be calculated from the frequency of the muons which pass through both the sender's sensor and the receiver's sensor (f_µ):

R _CK = f_µ = ΦS, (2)

where S is the effective detection areas of COSMOCAT sensor and Φ is the muon flux integrated over the solid angular region (Ω) formed by the sender's COSMOCAT sensor and the receiver's COSMOCAT sensor and the energy range between the cutoff energy (E_c) and infinity:

Φ =${\int }_{{\varphi }_{0}}^{{\varphi }_{0}+{\Delta }\varphi }{\int }_{{\theta }_{0}}^{{\theta }_{0}+{\Delta }\theta }{\int }_{{E}_{c}}^{\infty }I(E,\theta , \varphi )dEd\theta d\varphi$, (3 − 1)

=${\int }_{{\varphi }_{0}}^{{\varphi }_{0}+{\Delta }\varphi }{\int }_{{\theta }_{0}}^{{\theta }_{0}+{\Delta }\theta }I(\theta , \varphi )d\theta d\varphi$, (3 − 2)

where the angular region defined between (A) φ₀ and φ₀ + Δφ, and (B) θ₀ and θ₀ + Δθ are respectively (A) small zenith and (B) azimuth angles formed by the sender's COSMOCAT sensor and the receiver's COSMOCAT sensor. If Δφ << φ₀ and Δθ << θ₀, the cosmokey generation rate is:

R _CK = ISΩ ∼ IS²D^− 2, (4)

where I is the intensity of the muons arriving from the zenith angle θ₀, and D is the distance between the sender's sensor and the receiver's sensor. The value of E_c in Eq. (3) depends on the thickness (d gcm^− 2) of the material located above the sensors. For example, if the thickness of a concrete slab located above the sensors is 1 m, E_c will be 400 MeV, and if a steel plate with a thickness of 50 cm is added, E_c will be 1.1 GeV²¹. Considering the most frequent energy of the cosmic muons range from 1 to 3 GeV, the muon flux is almost the same as the open-sky flux in an underground safe underneath a regular building or a house. The integrated open-sky muon flux (Φ₀) is ~ 10² m^− 2s^− 1, and here we define the open-sky muon rate with:

f ₀ = Φ₀S. (5)

The timestamps are recorded in the receiver's sensor at this rate and are eventually transferred and stored in storage also at this rate. Then, a square of the ratio:

G ₁ = R_CK f₀ ^− 1, (6)

can be defined as the cosmokey matching rate between the sender and the receiver. Due to temporal jitters of the signals outputted from comparators and frequency fluctuations in clocks used in COSMOCAT, generated cosmokeys do not always match between the sender and the receiver. Therefore, the factor (r_CK) coming from this effect needs to be considered, also. Consequently, the actual cosmokey matching rate is:

G ₂ = r_CKG₁= r_CKR_CK f₀ ^− 1, (7)

Due to fluctuations in time measurements, the length of each cosmokey ranges from four to six digits. TRN sequences with 15 digits to 40 digits are required in order to generate sufficiently strong encryption keys (48 bit to 128 bit). For this purpose, several cosmokeys should be combined. Therefore, the actual keys used for encrypting data would be a numerical sequence of cosmokeys: {t₁, t₂, ...t_n}. However, the keys combined at the sender's detector and the keys combined at the storage detector generally don’t match since R_CK< f₀. Therefore, the storage user (sender) needs to encode the data for N_TRIAL times, where N_TRIAL is the number of trials required to independently generate the same encryption key between the sender and the receiver, and given by N_SENDER x N_RECEIVER, where:

N _SENDER = N_RECEIVER = nG₂ ^− 1!/ n!(nG₂ ^− 1-n)!, (8)

and where n is the number of combinations of the generated cosmokeys required to generate encryption keys. Here it was assumed that S is the same for the sender and the receiver. In other words, one key out of N_TRIAL keys can be used as an encryption key. For example, if G₂ is 0.2, and n = 3, then the sender and the receiver would respectively need to encode the data around 5x10² times so that one out of ~ 2x10⁵ trials would match the key generated in the storage.

A more detailed procedure will be described in the following section by introducing an example case, but the basic concept of encoding, key storing, and authentication will be outlined here for the purpose of explaining the experimental results. The procedures the storage user needs to follow are:
(A) Encode the data for N_trial times with the timestamps (N_i (t₀)) generated at t = t₀. The encoding rate is f₀ ^− 1.

(B) Every time the key is used for encoding, this key is erased.

Meanwhile, in the storage facility,

The authentication procedure for the storage user is as follows:

(D) Send a set of N_trial encoded data to the storage facility.

As can be seen in Eq. (8), if we can reduce n, we can drastically reduce N_trial; hence the key generation rate in storage could be drastically upgraded. Since the comic muon flux cannot be changed, G₂ can be increased by improving a geometrical configuration and detection efficiency of the COSMOCAT system.

Improvements in cosmokey generation. During the current timing measurements, naturally occurring cosmic-ray muon events are detected with 2 vertically aligned detectors. In order to confirm the performance of the key generation with CFD, the muon's time of flight (TOF) was measured for two different distances: D = 120 cm and D = 240 cm. Since muons arrive only from the upper hemisphere, with this detector configuration, the muons always pass through the top detector first and the bottom detector second. For the purpose of demonstrating key distribution to an underground safe, a lead plate with a thickness of 3 cm was inserted between the sender's and the receiver's detector. In order to separate the problem associated with the frequency fluctuations of the local clock from the problem involving temporal jitters of the signals outputted from comparators, COSMOCAT sensors were wired with RG50 co-axial cables to guarantee the time synchronization between sensors. Scintillation photons are generated in the plastic scintillator (ELJEN 200) and then travel through an acrylic light guide to be processed by the photomultiplier tube (PMT). The signal pulses outputted from the photomultiplier tubes (PMTs) (Hamamatsu R7724) were discriminated by CFDs (KAIZU KN381) in order to reduce the temporal jitter with this process. Also, while 1m x 1m scintillators were used in the prior work, much smaller (W x W = 20 cm x 20 cm) scintillators with a thickness of 2 cm were used for the current testing to improve the timing accuracy. Therefore, Ω in Eq. (4) were respectively 28 msr and 7 msr for D = 120 cm and D = 240 cm. Travel distances of the photons in the scintillator (λ_i) tend to vary as a function of time since the distance between the PMT and the muon's hitting point within the scintillator varies for each event. Therefore, the maximum time and the minimum time between the moment when the scintillation photons arrive at the sender's photocathode and the moment when the scintillation photons arrive at the receiver's photocathode are respectively:

[Dc^− 1 + λc_ν ^− 1]_MAX=(D² + 2xW²)^1/2c⁻¹+1.4Wc_ν ^− 1 (8 − 1)

[Dc^− 1 + λc_ν ^− 1]_MIN= Dc^− 1 (8 − 2)

where c_ν is the speed of light in material with a refractive index of ν ( c_ν = c /1.49 for a plastic scintillator). If we employ the parameters used for the prior work (W = 1 m and D = 70 cm), the values for [D(τ)c^− 1 + λ(τ)c_ν ^− 1]_MAX and [D(τ)c^− 1 + λ(τ)c_ν ^− 1]_MIN are respectively ~ 12.2 ns and ~ 2.3 ns; hence, in the previous geometrical configuration, there was an uncertainty of timing of ~ 10 ns at the most. On the contrary, the setup employed in the current work (W = 20 cm and D = 120 cm, 180 cm and 240 cm) reduces this uncertainty to, at most, a value of ~ 1 ns. The time resolution of the time to digital converter (TDC) used for the current experiment (ScioSence TDC-GPX) was 27 ps. The block diagram designed for the current experiment is shown in Fig. 1.

Figure 2 compares the TOF distribution obtained in the prior work with the TOF distribution obtained in the current work. The distance between these COSMOCAT sensors are changed (120 cm and 240 cm) in order to confirm the time resolution of the current system. In this figure, the distribution of the time displacements between the event occurrence recorded by the sender's COSMOCAT sensor and the event occurrence recorded by the receiver's COSMOCAT sensor (associated with the storage) |Δt_RECEIVER- Δt_SENDER| are shown. The timing accuracy was ~ 1ns (S.D.). Since the distances between the sender's COSMOCAT sensor and the receiver's COSMOCAT sensor were 120 cm and 240 cm, the muon's TOF were respectively expected to be 4 ns and 8 ns; the measurement results are in agreement with these expectations. In the prior work, not only was the TOF spectrum much broader than the current work, but also there was a large discrepancy between the expected peak location and the measured peak location. As shown in Fig. 2, although the TOF value of 2 ns was expected for D = 70 cm, the peak of the TOF spectrum was located at ~ 20 ns. As a matter of fact, in the previous work, there were three peaks at ~ 2 ns, ~ 20 ns, and ~ 45 ns where the 20-ns peak was largest, and the other two peaks are difficult to see in the current presentation (for more detail, see Fig. 5B of Tanaka (2023)⁷). This was due to the systematic fluctuations in the GPS-DO's frequency. The wide range of the TOF spectrum came from (A) temporal jitters of the comparator output signals and (B) frequency fluctuations of the GPS-disciplined oscillators (GPS-DO). A large discrepancy between the expected peak location and the measured peak location came from the time offset between GPS-DOs.

In the prior work, as a consequence of discrepancies in TOF, the time series of N_{3 ≤ i≤6} (4 digits) were used as cosmokeys. In contrast, Fig. 2 indicates that there is a potential that the time series of N_{3 ≤ i≤8} (6 digits) can be used as cosmic keys. In order to generate encryption keys with 20 digits and 24 digits, N_trial would be respectively 53,130 and 4,845 for a given G = 0.2 with the prior and current COSMOCAT system. With the upgraded COSMOCAT, N_trial would be reduced by an order of magnitude, and the key would be 10,000 times stronger. f_µobserved for these distances (120 cm, and 240 cm) were respectively ~ 0.1 Hz and ~ 0.02 Hz. Since the value G₂ depends on the broadness of the TOF spectrum, N_trial can be further improved and will be discussed in the following paragraph.

R _CK can be derived by integrating the time spectrum (blue filled circles) shown in Fig. 2 over the time range between 0 and the given time window (T_W) such that:

$${R}_{\text{C}\text{K}}={\int }_{0}^{{T}_{\text{W}} \text{n}\text{s}}f\left(t{\prime }\right)dt{\prime } \left(9\right)$$

where f(t') is the event frequency at t'. The value of Eq. (9) for T_W=100 ns was 20 m^− 2 sr^− 1s^− 1 in the prior work. Figure 3A shows r_CKR_CK as a function of T_W (120 cm and 180 cm) measured in the current work. There was no large distant-dependent difference in r_CKR_CK. For T_W =1 ns, r_CK =0.58 for 120 cm and r_CK =0.49 for 240 cm; for T_W =3 ns, r_CK =0.87 for 120 cm and r_CK=0.77 for 240 cm. Figure 3B shows G₂ as a function of Ω for different T_W. Consequently, N_trial could be drastically reduced. For example, if we compare N_trial for the same geometrical configuration with the prior work (Ω ~ 1sr), the N_trial values required for the sender to share encryption keys in the storage with digits of 20 digits in the prior work and 24 digits in the current work are respectively 53,130 and 70.

Authenticating rate limit. As was described in the previous section, in order to authenticate the sender's data with the key stored in storage, the storage user needs to send a set of N_trial encoded data to the key storage facility. In the key storage facility, the N_trial encoded data will be authenticated by verifying the N_storage timestamps. If the detector size of the sender's COSMOCAT sensor and that of the receiver's COSMOCAT sensor are the same, and if the data encryption at the sender and the key generation at storage are conducted in the same time period, N_storage = N_trial. In the prior work, 53,130 x 20 digits = 1,062,600 patterns in the encoded data need to be verified (to find a match) with the 1,062,600 patterns of the keys stored in storage. The time required to verify 10¹² patterns is 25 seconds, and thus the authentication rate limit would be 0.04 per second with a currently commercially available graphic card: Gigabyte GeForce RTX 2080 Ti Turbo 11GB Graphics Card²². However, if we use N_trial, a value achieved by the current work, the number of patterns we would need to verify would only be 3x10⁶ patterns for 24 digit keys; hence the authentication rate limit would reach a rate of 12,000 per second. This is an improvement by more than 5 orders of magnitude.

Time synchronization scheme. Degradation of the cosmokey length due to temporal jitters of the signals outputted from comparators was solved. In order to replace GPS with another device, we need an alternative wireless ns-level time synchronization scheme. However, the currently available wireless time synchronization technique is RF-based and offers only a microsecond-order time synchronization precision^23,24. Not only does RF fall short of the precision requirements of COSMOCAT, but also RF cannot penetrate matter sufficiently to reach the underground safe location.

Recently, the cosmic time synchronizer (CTS) was developed²⁰ as a wireless underground/underwater time synchronization technique, but the time synchronization precision was limited to ~ 100 ns. The easiest way to synchronize the sender's clock and the receiver's clock at the storage site is by wiring these clocks. However, if this strategy was used for COSMOCATS, the remaining physical traffic between the sender and the storage may reduce the security level of the system. Therefore, it is better to keep the storage physically separated at a distance at least while encoding files on the server and generating encryption keys in the storage. Therefore, the cosmic time calibrator (CTC) scheme is employed in this work.

Figure 4 shows a diagram of the setup for the CTC-based COSMOCATS system. In this system, COSMOCATS timestamps are issued by local oscillators called OCXOs (oven controlled crystal oscillators). Since the frequency of OCXO outputs drifts in a different way between the sender's OCXO and the receiver's OCXO, the timestamps issued by the same muons could be recorded as different timestamps between the sender's OCXO and the receiver's OCXO. However, in this system, this difference is retrospectively corrected with another pair of muon sensors that are prepared in the vicinity of the COSMOCATS system.

CTC uses cosmic ray muons as calibration signals to correct local clocks associated with COSMOCAT sensors. If the sender's local clock is defined as the standard clock (labeled as Clock 0) then its successive clock is named here as Clock 1. The times measured by Clock 0 and Clock 1 are respectively labeled with τ and t. Since most of a cosmic-ray muon's Lorentz factor is much larger than 1, it is reasonable for us to approximate the time (T) required for cosmic-ray muons to travel a distance between Detector 0 and Detector 1 to be Dc^− 1. Consequently, if a cosmic-ray muon passes through Detector 0 and Detector 1, then the moment when the muon has passed through Detector 1 is measured by Clock 1 (t) as:

t = τ + Dc^− 1 + δτ (10)

δτ comes from the relative drift of Clock 1 measured with Clock 0. Since D is known, δτ can be derived from t and τ. The information of τ can be associated with the data when the sender encodes the data with the COSMOCAT system, and can be sent to the storage receiver when the senders authenticate their encrypted data. The muon rate is limited, and the OCXO doesn't drift so far within a short period of time (Fig. 5A). In order to remove effects from the comparators/geometrical configuration of the setup, signals from a clock generator (Technoland N-TM 715) split with a fan-out circuit (Technoland N-TM 605) instead of signals from the scintillation detectors were fed into TDC shown in Fig. 4. In Fig. 5B, a standard deviation calculated from 9 independent runs of OCXO is shown as a function of time. If the CTC steering frequency is < 0.1 Hz, > 99.7% of the time stamps can be corrected by finding coincident events within a time window of t_W = 10 ns for the muon that passed through Detector 0 and Detector 1. Figure 5C shows magnified view of temporal fluctuations acquired in another OCXO run within the time rage between 0 and 5 seconds with a sampling rate of 10 Hz (the data shown in Figs. 5A and 5B are sampled at 1 Hz). In this specific case, a standard deviation within this time range was 349 ps, indicating that CTC would work satisfactory for the COSMOCATS system.

The clock correction errors due to the accidental coincidence can be neglected. As can be seen in Eq. 11, the time window set for finding coincidence events is generally much shorter than the open-sky muon's arrival rate (f₀ ^− 1):

t _W < < f₀ ^− 1. (11)

Therefore, the accidental coincidence is negligible if we use four CTC sensors, and if we look for four-fold coincidence events such that:

T = 0.25 t_W³ f₀ ^− 4, (12)

where T is the accidental coincidence interval. For example, if t_W=10^− 8 s, and f₀ = 10² Hz, the accidental coincidence would occur every 2.5 x 10¹⁵ seconds. The following procedure describes the CTC process: (A) TTL pulses outputted from OCXO are continuously counted by the scaler respectively at Detector 0 and Detector 1. These count numbers are respectively defined as N₀ and N₁. (B) Once τ information (N₀) is sent to Clock 1, Dc^− 1 + δτ is calculated from Eq. (11), and it is then subtracted from t (N₁). By repeating this process, Clock 0 and Clock 1 can be resynchronized in a retrospective way with a precision of < < 10 ns as is indicated in Figs. 5B and 5C. The correction time intervals are equivalent to the key generation time intervals and the authenticating time intervals that are generally much shorter than 5 s.

Application of COSMOCATS. The caveat of the COSMOCATS system is that the storage is invincible only when files are being encoded on the user's server and encryption keys are being generated in storage. However, there are several useful applications of this storage system which can be used to generate an electronic digital signature. The electronic digital signature system is an essential concept in modern society: integral to cryptocurrency, e-commerce websites, social media, banking apps and any other exchange of sensitive data. Here we consider a model of cryptocurrency using COSMOCAT and issued by a fictitious organization called COSMOBANK as an example. In this scenario, storage is located inside the underground safe of a bank called “COSMOBANK”. This underground safe is built in the COSMOBANK building and there is no entrance; hence no human can access the underground safe. Therefore, this safe is physically protected. The cryptocurrency called cosmocurrency is issued by COSMOBANK. Cosmocurrency functions like cash. Cosmocurency encrypts the data showing its value (10 USD, 100 USD, etc.) with the COSMOCATS system equipped for COSMOBANK. The key used for encrypting each cosmocurrency is used as an identification number of each cosmocurrency.

Issuing process. The procedure to issue the cosmocurrency is as follows. The aboveground COSMOCAT sensor encrypts the cosmocurrency data and the encrypted cosmocurrency is transferred to the COSMOBANK server that is connected to the internet. At the same time, the underground COSMOCAT sensor located inside the safe records the timestamps and transfers them to storage. CTC is used for recording the time calibration information which is later used for the authentication process. Neither physical nor cyber connections exist between the aboveground server sensor to storage. Therefore, at this stage, the identification numbers (24-digit encryption keys) of the cosmocurrency cannot be leaked. Also, since cosmocurrency is strongly encrypted in this process, any spying third party that managed to access the cosmocurrency data (protected by 24-digit keys) doesn't have a possibility of tampering with the cosmocurrency. (It would take approximately one million years to crack with a currently commercially available graphic card: Gigabyte GeForce RTX 2080 Ti Turbo 11GB Graphics Card²²)

Authenticating process. The authenticating process would be required when a transaction is performed with cosmocurrency. At this stage, there are physical connections between the COSMOBANK server and the underground storage. The physical connection for uploading from the COSMOBANK server to the underground storage is one way. The device that can be used for this purpose is e.g., a USB-based DataBridge²⁵. A DataBridge is a security device that connects terminals with a USB cable and allows one-way data transfer only while the terminals are connected. Therefore, it is impossible to download the keys from the storage on the server's side. Even if the data bridge itself is cracked, the data on this traffic is already highly encrypted. The physical connection for downloading data from this storage is an RG50 coaxial cable. If the data are successfully authenticated by the key in the storage, (A) the key in this storage is erased, and (B) a TTL pulse is outputted to the COSMOBANK server. After this authentication process, COSMOBANK will know the corresponding cosmocurrency is the authentic currency.

This authenticating process guarantees the security of cosmocurrency for the following reasons: (A) the cosmocurrency users cannot duplicate this currency since the same cosmocurrency used for the second transaction cannot be authenticated, and (B) eavesdroppers would get no useful data since information related to encryption keys is not included in this TTL pulse. The cosmocurrency issuing and authenticating processes are summarized in the diagram shown in Fig. 6. The aforementioned protocol indicates that once the encrypted data like cosmocurrency are generated, these can be used not only for virtual currency but also for other electronic digital signing processes on other occasions for other purposes.

The majority of other cryptocurrency uses digital signatures and cryptocurrency mining to store data on a public ledger that cannot be altered retroactively without altering all subsequent blocks: blockchains that use the hashing algorithm. As security and privacy of a blockchain solely depends on the hashing and digital signatures, a number of researchers^{26,27,28,29,30,31,32} have discussed about how the fast progress of quantum computing has opened up the possibilities of attacks on blockchains through Grover’s and Shor’s algorithms. ECDSA is mainly used as a way to sign digitally. It uses the logarithmic problem for security which cannot be solved by classical computers, making it secure for now, but this security will be compromised with the advancement of quantum computing. Moreover, the most criticized issue of this system is excessive energy consumption³³. There is a report that the amount of energy consumed by bitcoin mining exceeds the electricity consumed in dozens of countries³⁴. It is clear that the mining process will have various environmental consequences due to the excessive amount of energy consumption required. By following the aforementioned COSMOCAT-based protocol, the safety of issuing currency and transactions will be guaranteed and thus, centralized cash management will be possible. As a result, the standard public ledger distributed within a peer-to-peer computer network can be discarded; hence the mining process can be removed from cryptocurrency.

In conclusion, it was shown that COSMOCAT has the potential to realize invincible key storage that enables ultra-high security electronic digital signing. While the advantage of symmetric-key cryptosystems is that they are invulnerable against quantum computers and that processing is faster than public-key cryptosystems, the disadvantage is that it requires careful handling of keys. This is because no matter how complicated the encryption is, if the key is stolen, anyone can decrypt the data. Since the encryption side and the decryption side must have the same key, the possibility of key leakage increases as the number of holders increases. The COSMOCATS system solved these problems. The COSMOCATS system takes advantage of two major features of COSMOCAT: strong penetrability to underground locations and capability to generate multiple TRN sequences at a distance without transferring these sequences. Consequently, we can construct a new symmetric-key cryptosystem between aboveground locations and concealed underground locations. It is anticipated COSMOCATS will contribute towards the establishment of a new system for postquantum electronic digital signing including cryptocurrency that doesn't require blockchains; hence helping ensure unprecedented levels of security for users and cutting energy consumption problems.

Contributions

H.K.M.T. wrote the text. H.K.M.T. prepared the figures. H.K.M.T. reviewed the manuscript.

Corresponding author

Correspondence to Hiroyuki K. M. Tanaka.

Ethics declarations

Competing interests

The authors declare no competing interests.

Data Availability

The datasets used and/or analyzed during the current study available from the corresponding author on reasonable request.

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No competing interests reported.

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Cosmic coding and transfer storage (COSMOCATS) for invincible key storage

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Introduction

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Φ =\({\int }_{{\varphi }_{0}}^{{\varphi }_{0}+{\Delta }\varphi }{\int }_{{\theta }_{0}}^{{\theta }_{0}+{\Delta }\theta }{\int }_{{E}_{c}}^{\infty }I(E,\theta , \varphi )dEd\theta d\varphi\), (3 − 1)

=\({\int }_{{\varphi }_{0}}^{{\varphi }_{0}+{\Delta }\varphi }{\int }_{{\theta }_{0}}^{{\theta }_{0}+{\Delta }\theta }I(\theta , \varphi )d\theta d\varphi\), (3 − 2)

Discussion

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