Digital key distribution protected by recorded quantum noise

Abstract

A system to secure digital in-transit communication is disclosed. It includes true random bits generation, a secure digital key distribution and an encryption system for broad use. It offers post quantum-resistant characteristics. The system uses true random bits generated from vacuum quantum fluctuations. The distribution of these bits is protected by recorded quantum noise and works in standard communication channels.

Description

[0001] DIGITAL KEY DISTRIBUTION PROTECTED BY RECORDED QUANTUM NOISE Inventor: Geraldo A Barbosa Summary of InvenƟon Technical Problem The coexistence of encrypƟon and quantum computers raises difficult mulƟ-disciplinary problems, theoreƟcal and pracƟcal. These are current challenges, because "harvest now, decrypt later" operaƟons are currently in effect. Quantum Key DistribuƟon (QKD) [WI], [BB], [SA], [QK], [ZH], all purely quantum, offer uncondiƟonal security (assuming correct implementaƟon) and will solve the needs of large organizaƟons. However, many pracƟcal and technological aspects plague QKD: it is slow, distance limited, needs quantum channels and is very costly - not affordable or pracƟcal for broad commercial use. NIST is starƟng to offer encrypƟon soluƟons posited as quantum-resistant. However, uncondiƟonal security and guarantees of invulnerability cannot be offered. The soluƟons are based in the belief that the determinisƟc computaƟonal complexiƟes employed are sufficient to withstand quantum computer aƩacks – even if quantum capabiliƟes are sƟll immature and soŌware to be used is yet to be wriƩen: hƩps: / / www.technologyreview.com / 2023 / 01 / 06 / 1066317 / whats-next-for-quantum-compuƟng / [MI]. However, the current speed up for construcƟon of powerful quantum computers indicates potenƟal risks The fundamental problem with all current classical security protocols is that they are like determinisƟc “Turing” machines, regardless of their complexity levels: there is a determinisƟc processing rouƟne (such as the ones performed by a classical computer) that, in principle, provides some security. Apart from the classical OTP protocol, with truly random keys, these cannot offer uncondiƟonal security. The security of OTP, by definiƟon and contrast, rests on the true randomness of the encrypƟon keys. SoluƟon to Problem This disclosure shows a soluƟon to the described problem. The reported security of the disclosed system rests on truly random processes to cloak the fast,flexible, secure key distribuƟon. This soluƟon does not belong to the class of QKD systems. This distribuƟon starts once with a shared key between users. AŌer encrypƟon keys are disƟlled from the distributed random sequences, informaƟon confidenƟality is guaranteed by using the OTP encrypƟon protocol. All subsequent key distribuƟon is automaƟcally accomplished with our protocols and with no need for couriers (that is, physically carried by someone): Whenever needed, freshly shared secret keys are delivered to guarantee security. This automaƟc secure renewal of keys is a novel feature. The security level offered by our system is calculated using InformaƟon Theory elements. Although this system offers a standalone technology, it can coexist with classical security protocols when needed for legal purposes: For example, streams of coded random bits covered with recorded quantum noise could be sent as the message by the NIST “Module-Laƫce-based Key-EncapsulaƟon Mechanism Standard (FIPS 203)” [FI]. The noisy message is the ulƟmate security layer. The disclosed system offers strong encrypƟon for broad applicaƟons, and these can coexist with quantum computers. These ideas produced a pracƟcal secure communicaƟon system for cell phones, computers, IoT and IIoT devices. DIGITAL KEY DISTRIBUTION PROTECTED BY RECORDED QUANTUM NOISE Inventor: Geraldo A Barbosa Advantageous Effects of InvenƟon In this disclosure, communicaƟons are encrypted, sent, and decrypted via any means of telecommunicaƟons or combinaƟons thereof, whether public (e.g., internet) or private (e.g., private Ethernet,fiber opƟc network, and satellite). The encrypƟon security rests on three pillars: [1] The use of generated random signals that are of quantum origin and are truly random, with no generaƟon rule. Therefore, even a quantum computer cannot discover the generated keys being transmiƩed because no generaƟon rules exist. This property creates the quantum-resistant technology. [2] The secure key distribuƟon protected by recorded quantum noise and the disƟllaƟon processes set the probability for discovery of each encrypƟon bit by an aƩacker at the pracƟcal guessing level . [3] The classical OTP encrypƟon process is known to be mathemaƟcally unbreakable. The developed system solves the problem of cost, speed and range limitaƟon that plagues the QKD technologies. At the same Ɵme, it incorporates non-determinisƟc features into its protocols: the key distribuƟon signals are cloaked by recorded quantum noise in a way that the useful informaƟon in the signals cannot be extracted by any aƩacker without the key possessed by the users and constantly renewed. This is an informaƟonal advantage of the users over the aƩacker. Besides being a technical soluƟon, it is available for broad use, due to the low cost compared with QKD. Background Art This disclosure refers to the use of physical noise intertwined with or superposed to encoded signals to create a protected communicaƟons system composed of secure key distribuƟon, encrypƟon and decrypƟon capabiliƟes. This system for secure key distribuƟon disclosed here evolved from a line of encrypƟon research that has taken place over more than 20 years. For some references, see H. P. Yuen, A. M. Kim, ''Classical noise-based cryptography similar to two-state quantum cryptography'', Physics LeƩers A volume 241, pp.135-138 (1998) [YK], G. A. Barbosa E. Corndorf, P. Kumar, and H. P. Yuen, “Secure communicaƟon using mesoscopic coherent states''”, Phys. Rev. LeƩ. volume 90, No 22, pp.227901, 2003. doi: 10.1103 / PhysRevLeƩ.90.227901 [AE], G. A. Barbosa, “Fast and secure key distribuƟon using mesoscopic coherent states of light, Physical Review A, volume 68, p.052307, 2003. doi: 10.1103 / PhysRevA.68.052307 [FAST], G. A. Barbosa, "InformaƟon theory for key distribuƟon systems secured by mesoscopic coherent states", Physical Review A 71, 062333 (2005) [IN], US 7,333,611 B1, 2008, Inventors: H. P. Yuen P. Kumar, and G. A. Barbosa [AL], G. A. Barbosa and J. van der Graaf, “Untappable Key DistribuƟon System: a One- Time-Pad Booster'', ENIGMA — Brazilian Journal of InformaƟon, Security and Cryptography, volume 1, pp. 16-27 (2015). doi:10.17648 / enig. v2i1.43 [BG], G. A. Barbosa, Patent: US 7,831,050 B2. - November 9, 2010 [PF]. Very briefly, [YK] presented the possibility of a cryptographic key agreement via classical noise, with security similar to that of the two-state quantum cryptosystem but with the advantage of signal amplificaƟon. This is not possible with QKD due to the non-cloning theorem of W. WooƩers, W. Zurek, "A Single Quantum Cannot be Cloned", Nature volume 299 (5886), pp 802–803 (1982) [WZ]. DIGITAL KEY DISTRIBUTION PROTECTED BY RECORDED QUANTUM NOISE Inventor: Geraldo A Barbosa StarƟng in the year 2000, a theoreƟcal study and pracƟcal implementaƟon of an encrypƟon system [AE] exploited the use of quantum noise in an opƟcal channel. Many papers and studies were developed along the lines given by [AE], a small sample being given by [SH] and references therein. Shortly aŌer [AE], [FA] and [IN] presented a key distribuƟon system with protecƟon also given by the quantum noise in an opƟcal channel and discussed security aspects. A quantum formalism was used to calculate the aƩacker probability or error -- a "measure" of the security level of the key distribuƟon process. Ref. [BG] revisited the system presented in [FA] adding many security details, including privacy amplificaƟon, and thefiber opƟcs modulaƟon / demodulaƟon system. This embodiment deviated from above, eliminaƟng the need for opƟcal channels and the need for quantum calculaƟons to define the security level. Going digital The proliferaƟon of digital technology sƟmulates the transposiƟon of many ideas in [FA] to digital key distribuƟon systems. As digital signals are classical, the security procedures use elements of classical staƟsƟcs and classical protocols, differently from systems using opƟcal channels. OpƟcal channels demand expensive modulaƟon and demodulaƟon systems when compared with gateways for digital communicaƟons. Besides addressing a wide network already established for mulƟple users (i.e., digital), simplicity, low cost, and unbreakable security are drivers for secure digital communicaƟons. The disclosed system establishes the reconcepƟon of a technology for opƟcal channels for applicaƟon via expansive generic digital channels. The security system embodied here combines concepts from IT and Physics to uniquely apply quantum noise to the cloaking of digital key distribuƟon. Data is subsequently a one-Ɵme pad (OTP) encrypted with encrypƟon keys disƟlled from the distributed random keys. While the technology may use disƟnct physical random number generators, the one used here includes an original truly-random key generator. The in- transit security is provided by recorded quantum noise and uses an automated secure key replenishment with no need for couriers - and not relying on PKI protocols. It is fast, with no range limitaƟon, is channel- agnosƟc, and is affordable. Its security level is calculated using the mutual informaƟon funcƟon. This system offers strong encrypƟon for broad applicaƟons and that can coexist with quantum computers. A pracƟcal secure communicaƟon system was created for cell phones, computers, IoT and IIoT devices. It is supported by the basic components: [1] a truly random bit generator, which extracts quantumfluctuaƟons from a coherent laser beam. These fluctuaƟons generate random keys for encrypƟon as well as purely random numbers to cloak the transmiƩed signals. [2] protocols for safe random key distribuƟon and disƟllaƟon of encrypƟon keys, without the need for couriers. These protocols include recorded quantum noise superposed over the transmiƩed digital signals, cloaking the carried informaƟon. From these components, communicaƟons are encrypted, sent, and decrypted using any means of telecommunicaƟons, whether public (e.g., internet) or private (e.g., private Ethernet,fiber opƟc network, and satellite) and fulfilling the three pillars earlier presented. DIGITAL KEY DISTRIBUTION PROTECTED BY RECORDED QUANTUM NOISE Inventor: Geraldo A Barbosa Detailed DescripƟon of the InvenƟon The technology disclosed in the Summary is supported by the existence of 1) a random bit generator, 2) a generic network, that includes Private Network (VPN), for groups of users. 3) protocols for safe random key distribuƟon and disƟllaƟon of encrypƟon keys, without the need for couriers. These components are disclosed: 1) Random bit generator The physical principles on which the random bit generator was created are disclosed to reveal the true quantum nature of the random keys used: The source of entropy for the random bit generator is the quantum electromagneƟcfield. See FIG 1. The generaƟon of bits (keys) uses opƟcal quantum fluctuaƟons in a laser (01) beam. A light beam from a laser, configured to yield a coherent state, presents spontaneousfluctuaƟons of photon numbers of an uncontrollable character. These fluctuaƟons of quantum origin are also known as “opƟcal shot noise”. To have a full quantum characterisƟc, these samplings must be done within a coherence Ɵme of the electromagneƟcfield. ExtracƟon of random bits, or random numbers (a set of bits defines a number), is done by sampling lightfluctuaƟons with a fast detector (02), occurring within a very short Ɵme window defined by the digiƟzaƟon electronic speed of the Analog-to-Digital Converter (04). Using a laser (01) with a long coherence Ɵme (Ɵme where the laser keeps a constant phase and conƟnuously taking light intensity samples within short Ɵme windows of duraƟon , fluctuaƟons of intensity can be seen. These are directly associated with photon number withfluctuaƟons . In quantum mechanics the photon number operator and the phaseoperator do not commute [MW]. This leads, through a Heisenberg-like uncertainty, to large fluctuaƟons when In this generator, signalfluctuaƟons (06) occurring above or below the average are recorded and represent the desired bits (07). This quantum entropy source produces bits in a completely different process than those processes used by pseudo-random generators, which employ algorithms producing random-like sequences of bits. Pseudo random sources have a determinisƟc characterisƟc at the core, and regardless of complexity, bits are produced by rules. Quantum computers may use the rules to obtain the used keys. However, quantum computers will notfind paƩerns produced from our technology because its source of keys is quantum and because the key distribuƟon process is cloaked by recorded quantum noise, yielding no paƩern. The laser (01) has a small frequency bandwidth corresponding to coherence Ɵme much longer than the detecƟon system Ɵme resoluƟon. This allows fast light samplings where the photons in the mode are in the same phase. Consequently, the obtained staƟsƟcs have a quantum origin. DIGITAL KEY DISTRIBUTION PROTECTED BY RECORDED QUANTUM NOISE Inventor: Geraldo A Barbosa The detector (02) has a large frequency bandwidth allowing sensiƟvity to fastfluctuaƟons within the photon ensembles. The amplifier (3) gain (G) must produce signals well above the electronic background to allow collecƟon of opƟcal noise while negaƟng electronic noise contribuƟon. The analog-to-digital converter (ADC) (04) is configured to be fast and possesses sufficient digital resoluƟon to sense the voltagefluctuaƟons from the amplifier. The FPGA (05) configuraƟon is fast to process the inflow signals. Important characterisƟcs of this random number generator include: (1) The entropy source for bit generaƟon is the quantumfluctuaƟon of the laserfield. (2) ConƟnuous operaƟon: range. (3) Configurable to increase speed; it just depends on electronics. (4) A stable system: no interferometry is used. (5) MiniaturizaƟon is possible. (6) MulƟple uses: Secure communicaƟons, games, staƟsƟcal simulaƟons, etc. (7) Composed of commercial off-the-shelf parts. FIG 2 compares some Physical Random Number Generators with the generator described in this disclosure. It qualitaƟvely contrasts bandwidth, construcƟon simplicity, presence of radioacƟvity. No comparison is made with “quantum random generators” based on the response of pixel detectors such as digital camera detectors, because these belong to a disƟnct category: their sampling Ɵmes are much longer than the coherence Ɵme of the LED source of light. The coherence Ɵme of LED sources is very short. Therefore, each sampling averages over mulƟple coherence Ɵmes of the source, which leads to randomness connected to classical staƟsƟcs (disconnected from any quantum associated phase, that was averaged out). PragmaƟc approaches are used when checking for randomness of generators. These include mulƟple staƟsƟcal tests of randomness. One should be saƟsfied if no determinisƟc paƩerns are found with these tests. For example, the NIST suite of tests [NI] is widely used. The disclosed generator passes the NIST tests for relaƟvely short as well as for long random sequences, and other tests such as the Diehard baƩery of tests [GM] and TestU01 [ES]. 2) CommunicaƟon network FIG 3A, FIG 3B, and FIG 3C, exemplify the secure network and a Virtual Private Network (VPN) that defines connecƟons with a team (two users are shown in the example but more users are possible). CommunicaƟon can be made from one-to-one user to one-user-to-many. See FIG 3A. The secure network has a central staƟon (10) where keys are generated within the generator (11) stored on a server (13), in a key vault (14) and sent to users using noise coded signals (15). Keys are coded with an iniƟal secret (called a “base”) shared by the users and the central staƟon. Recorded quantum noise is added to the coded key signals (15) which are sent to a team of users. This step uses the protocol TX. DIGITAL KEY DISTRIBUTION PROTECTED BY RECORDED QUANTUM NOISE Inventor: Geraldo A Barbosa See FIG 3B. The coded key signals (15) are transmiƩed by a generic network (16) to the users. See FIG 3C. The noisy coded signals are received at the user staƟon (17) by a computer (18) (or mobile device), using the protocol RX. The protocols RX / PA eliminate the noise, then extract and disƟll the sent keys to produce thefinal encrypƟon keys. The disƟlled encrypƟon keys (19) are inserted into an external memory (e.g., pendrive) to be used in the cell phone (20) app (or IIoT devices). CommunicaƟon through the app (Quantum Communicator), with a default OTPencrypƟon is then secured among users. The safe storage of encrypƟon keys (fresh or used keys) is external: keys are not stored on the app or mobile device. Decrypted documents are also kept on external physically secure memories. The system allowsflexibility: if company policy is that copies of informaƟon exchanged between employes should be stored in a central locaƟon, the informaƟon may be restored as necessary. 3) Protocols The protocols presented in these embodiments are just examples of protocols to achieve the described funcƟonality and, in no way exhaust the possibility of mulƟple variants leading to similar results, as synthesized in the CLAIMS. Protocol TX TX designates the protocol to send noisy encoded keys (15) from the key generator (at staƟon TX) to a generic receiving staƟon RX (17) (at the user posiƟons). The objecƟve of this protocol is to generate and securely transfer a sequence of bits to the receiving staƟon. To achieve such goal, the bits to be sent are encoded in a -ary level of values (called -ary coding). These levels are also called bases. Recorded quantum noise numbers are added to each encoded bit defined by the -ary coding: The process starts by acquiring a sequence of random bits from the key generator (11). These are the fresh raw random bits to be sent in a secure way (signals (15)) to RX. The operaƟonal meaning of “secure “at this point is that the bits sent are cloaked with the combinaƟon of coding and added recorded quantum noise. Another sequence of random numbers represenƟng each possible value of the -ary set of levels, the bases (in same number as the number of bits ), is also produced by the random generator (11). The encoding is described below. Noiseless encoding The protocol TX involves a determinisƟc encoding of bits by the basis followed by addiƟon of recorded quantum noise. Encoding starts defining the noiseless encoding funcƟon : . DIGITAL KEY DISTRIBUTION PROTECTED BY RECORDED QUANTUM NOISE Inventor: Geraldo A Barbosa This encoding funcƟon produces numbers with a separaƟon distance and depend on whether the basis is odd or even. For a visualizaƟon of the encoding funcƟon, a coding wheel is used here. See FIG 4. Choosing an even number of bases , is the number of bits (for example, defines a byte, making possible 256 base values). The choice of odd produces neighboring bits in the vicinity of the basis always with different parity. FIG 4 exemplifies a coding “wheel” with the choice . Usually, is of the order of hundreds. The external numbers in the wheel indicate base numbers (0 to 8, ) and the internal numbers are bits. Bits in neighboring bases have disƟnct parity from the bit at a parƟcular basis. FIG 5 describes aspects of the noiseless codificaƟon done by the coding wheel from FIG 4. It illustrates the basic noiseless encoding: “Base numbers" designate possible (random) numbers encoding bits. Symbol designates one basis: a number between 0 and . Bits in neighboring bases are separated by . In a same basis , bits and are separated by . The noiseless encoding of a bit by a basis is done by . The operaƟon constrains the range of levels used. Adding recorded quantum noise to the noiseless encoding AŌer the noiseless -ary encoding, where bits (or ) in neighboring bases are separated by , a random number , with amplitude (for example, ) is added to the encoded bit . The sequence of random numbers is also provided by the generator. is the neither the receiver nor the aƩacker knows their values. Although the -ary numbers (the bases ) these are known by the legiƟmate users but not by the aƩacker. The encoding is determinisƟc. However, is not known. Therefore, bits in neighboring bases, originally separated by , are covered by the added noise. Neither the user nor the enemy knows . As is uniformly distributed within the maximum amplitude used, the informaƟon of which signal represents a bit or is lost. In other words, each coded signal is independently cloaked by the recorded quantum noise. The noisy encoded signal to be transmiƩed is given by The size of the random numbers by an aƩacker probabilisƟc: the probability to get the correct noise level is (for example). There is no formaƟon rule for . Therefore, in a sequence of transmiƩed bits, the probability to get all correctly is , an exponenƟally decreasing value with DIGITAL KEY DISTRIBUTION PROTECTED BY RECORDED QUANTUM NOISE Inventor: Geraldo A Barbosa However, even ignoring the added noise, the aƩacker reaches one set of bases, either odd or even. This leads to his probability to obtain the correct bit as The probability to correctly acquire successive bits is The signal protecƟon from the coding random levels plus the noise , both unknown by the aƩacker. noise is essenƟal to cloak the -ary level used at each signal transmission; it cannot be eliminated from the channel by any means. Signals are sent to the user at staƟon RX (17). Protocol RX Signals (15) arrive at RX (17). The user knows the coding funcƟon , because he knows the basis used (the aƩacker does not know ). The user’s protocol RX subtracts the coding funcƟon from the received noisy coded signal and obtains the difference The signal contains is sƟll covered by noise. Due to the magnitude of the RX discards the noise by thefiltering ( example): This means that if the otherwise is . Bits are recovered. , are now known. The magnitude of was judiciously chosen to allow RX to extract , while aƩacker does not have enough informaƟon to obtain the noise values , basis or bits . Protocol PA (Privacy AmplificaƟon) and the Mutual InformaƟon FuncƟon The protocol [PA] is intended to eliminate any amount of informaƟon that an aƩacker could have acquired during the transmission process when this disclosed system is employed. Differently from an uncondiƟonal security proof, at the end of the PA protocol the Mutual InformaƟon funcƟon between the users and the aƩacker can be calculated, and the parameters connected with the security are adjusted to condiƟon . That is to say, the number of bits the aƩacker could obtain is 0 in the pracƟcal sense. One assumes that the aƩacker has a perfect copy of the transmission signals but no a-priori knowledge of the base bits , the bits , or the noise . In other words, the aƩacker records the total signals , and his goal is to obtain and . The lack of a-priori knowledge prevents the aƩacker the contents. These sets of bits, received by RX (17), will be used in the protocol PA (at TX (10) and RX (17)) to disƟll the encrypƟon bits and the new set of bases . Neither RX nor the aƩacker know the noise but, as will be shown, RX does not need to know to retrieve , differently from the aƩacker. DIGITAL KEY DISTRIBUTION PROTECTED BY RECORDED QUANTUM NOISE Inventor: Geraldo A Barbosa Generally, what the PA protocol used in the technology here disclosed does is to “shuffle” bits of and , wriƩen in the format of vector , where elements are bits and bases: and to produce a resultant new vector with random bit elements (for this shuffling of the vector , random numbers only known to TX and RX are used). The aƩacker could also know the general format of ; but does not know its components. Many disƟllaƟon procedures can be chosen [BG], with a complexity level to decrease the collision probability by choice of the “shuffling” procedure. This choice must be opƟmized to avoid excessive demands on the calculaƟon processing. AŌer this randomizaƟon, some bits can be erased, to discount bits that an aƩacker may have obtained during the transmission process or to guarantee a chosen security level (this is a step of the PA protocol used [PA]). The remaining bits, aŌer PA, are divided into one group , of the same size as the original , and another group of size . At the end of PA protocol for one sequence or cycle of bits sent, TX and RX know (new set of bases) and (fresh encrypƟon bits). The cycles TX and RX can be repeated, with freshly generated . Any number of encrypƟon bits can be generated as needed, by adding , obtained from new cycles TX / RX / PA: . Bits will be used to encrypt any informaƟon bit-by-bit (OTP encrypƟon). One assumes that the aƩacker has recorded all transmiƩed signals and knows the protocols used – however, neither are known to him. As data encrypted with OTP is unbreakable, the best hope for the aƩacker is to copy all informaƟon being transmiƩed from TX and try to obtain and , from which the aƩacker could aƩempt to replicate the PA protocol and to obtain . The security reported in this disclosure does not rely on the obscurity of the mechanisms or soŌware content. The encoding and noise addiƟon mechanisms are known by the aƩacker, but not the bases, keys, and added noise. It is assumed that modificaƟon of the protocols cannot be done by the aƩacker. It is also emphasized that staƟons TX and RX must have physical security (prevenƟng aƩacks on data-at-rest). The PA protocol is structured to destroy any correlaƟon between past and future encrypƟon bits. Therefore, even exploiƟng the encrypƟon of a known plaintext, the aƩacker is unable to obtain keys to be used in the future and cannot decrypt past data. Only the keys encrypƟng his own and known plaintext will be discovered. No informaƟon gain results. This is made possible by the process of conƟnuous injecƟon of entropy at every round: fresh bits are conƟnuously generated by the random generator. This reordered sequence does not end the security steps. The discounƟng of bits is another transformaƟon to eliminate any possible aƩacker's knowledge: The number of bits potenƟally DIGITAL KEY DISTRIBUTION PROTECTED BY RECORDED QUANTUM NOISE Inventor: Geraldo A Barbosa obtained by the adversary (esƟmated or calculable) is used to reduce the iniƟal number of bits to a smaller number : In other words, a number of bits sequence of length given by . An extra number of bits may parameter, as given by the amplificaƟon protocol [PA]: where is thefinal . This reduced number of bits is grouped in sizes as = The sequence of size is the sequence of fresh bits to be used for encrypƟon. The sequence of size will form the new bases set = for the next round of bitdistribuƟon. The new set of bases (length ) provides a renewed secret shared by TX and RX (a fresh informaƟon advantage) to yield a new round of fresh keys also sent from TX to RX. A secure repeatable fresh key distribuƟon cycle is then established. Perfect secrecy: Fresh keys are then acquired by TX and RX without using a courier. The aƩacker has no informaƟon on . This makes possible uƟlizaƟon of an automated OTP encrypƟon with secure keys achieving perfect secrecy level. It should also be emphasized that even if an aƩacker could obtain a sequence for one round, perhaps from a known-plaintext aƩack or by any other means, no past or future bit sequence is compromised; the PA protocol protects each round independently. CalculaƟng the Mutual InformaƟon: AŌer reducing the iniƟal number of bits from , (where the number of bits was iniƟally shared to create bases and fresh bits) to , the amount of informaƟon that may be known by the aƩacker is given by the Mutual InformaƟon , as derived in [PA]. It gives the informaƟon (in bits) leaked to the aƩacker: == iniƟal bits to , even with , the Mutual InformaƟon is reduced and it can be calculated in a range of values of pracƟcal values of interest. Usually, the number of discarded bits is much smaller than the number of transmiƩed fresh bits . FIG 6 shows the Logarithm of the Mutual InformaƟon as a funcƟon of the security parameter . The number DIGITAL KEY DISTRIBUTION PROTECTED BY RECORDED QUANTUM NOISE Inventor: Geraldo A Barbosa of bits possible to be obtained by the aƩacker, given by , can be set to a pracƟcal value of 0. Usually, the number of discarded bits is small compared with ; for example 300 in 1 Million. Kerckhoffs’ Principle The protocols TX, RX, PA and Replenisher are parts of the security strategy adopted to provide in-transit security for the disclosed technology. It was designed to follow Kerckhoffs’ Principle [KE], that states “a cryptographic system should be secure even if everything about the system, except for the key, is public knowledge”. Therefore, it is assumed that the enemy has the means to copy all signals sent from the Central StaƟon to any user if a public or unsecure channel is used. It should be emphasized that “unsecure channel” just means that the enemy can perfectly copy all signals running through it but it says nothing about the enemy’s ability to decode and discard the added noise or, in a sense, to decrypt the transmiƩedsignals to obtain bits sent.It should be emphasized that the protocols used in the embodiments described here conƟnuously inject physical entropy into the channel. This occurs not just through random bits but also during the coding process and in the added noise to each coded bit. Signals in the channel are physical signals represenƟng numbers; it is assumed that the enemy has the best detecƟon equipment to acquire the signals with perfect resoluƟon. However, as the protecƟon offered by the system described here is for in-transit communicaƟon only, aƩacks on informaƟon at-rest are beyond the scope of this system. The informaƟon at rest is assumed to be protected by the best procedures offered by the device makers (mobile and computer) and specialized companies (using hardware storage with pass-codes, access controls and so on). Decentralized encrypƟon FIGS 3A, FIG 3B, and FIG 3C shows a TX staƟon (10) and up to RX staƟons (17). The OTP encrypƟonworks between one-to-one users (say TX and one RX) but can also work between one-to (say TX toRX), or among any arbitrary number of users in the network. A decentralized possibility for encrypƟon [GR] based on the same set of encrypƟon keys is supported by the disclosed system and may be parƟcularly useful for a team with members. The disclosed system incorporates this decentralized use as follows: Assume that TX has distributed a certain number of coded base informaƟon with added noise random keys to users (who form a team) and that the soŌware will automaƟcally apply the same disƟllaƟon process given by the PA protocol (The coded base informaƟon is a pre-shared a sequence of random keys to form a set of -ary bases for one cycle of key distribuƟon).All team members will obtain the same set of fresh encrypƟon keys ( may be composed by manysequences), as shown in FIG 7. Procedure: Consider, for example, that randomly 20 lines (20 random numbers) in the long sequence of stored random bits, with the length of a message to be transmiƩed are chosen, by the sender user. The sender applies an operaƟon over these 20 lines: DIGITAL KEY DISTRIBUTION PROTECTED BY RECORDED QUANTUM NOISE Inventor: Geraldo A Barbosa , . The obtained sequence is the of bits -red to encrypt bit-by-bit the message: . The encrypted message is sent to the user with a header containing the numbering of the encrypƟonlines (that were “ ”-red). DecrypƟon is easily done by the user because he holds the originalsequence and can pick the right numbered 20 random sequences from the key list. The aƩacker does not know nor the content of any line. Even if the aƩacker could have obtained the order of lines in the header of the encrypted message , this is not usable informaƟon to retrieve the sequence of bits. The collision probability to have the same line chosen in another encrypƟon by any user can be computed as well as for a collision of all the lines. Very low probability values are obtained. In the decentralized use of a batch of keys, one esƟmate is that aŌer several (many) uses of this procedure of combining lines, all keys in the total number of keys would have been used at least once. The process must start from the beginning. In case of one-to-one users, the keys used for encrypƟon could be discarded immediately aŌer use. For the decentralized case, keys can be discarded only aŌer a renewing process for all users happens.

[0002] DIGITAL KEY DISTRIBUTION PROTECTED BY RECORDED QUANTUM NOISE Inventor: Geraldo A Barbosa CitaƟon List (alphabeƟzed) [AE] G. A. Barbosa E. Corndorf, P. Kumar, and H. P. Yuen, “Secure communicaƟon using mesoscopic coherent states”, Phys. Rev. LeƩ. volume 90, No 22, pp.227901, 2003. doi: 10.1103 / PhysRevLeƩ.90.227901. [AL] Northwestern University's patent, Inventors: H. P. Yuen P. Kumar, and G. A. Barbosa, [Patent] : US 7,333,611 B1, 2008. [BB] C. H. BenneƩ, G. Brassard, "Quantum cryptography: Public key distribuƟon and coin tossing", Proceedings of IEEE InternaƟonal Conference on Computers, Systems and Signal Processing, volume 175, page 8. New York, 1984. [BG] G. A. Barbosa and J. van der Graaf, “Untappable Key DistribuƟon System: a One-Time-Pad Booster'', ENIGMA — Brazilian Journal of InformaƟon, Security and Cryptography, volume 1, pp.16-27 (2015). doi:10.17648 / enig. v2i1.43. [ES] Pierre L’Ecuyer & Richard Simard, "TestU01: A SoŌware Library in ANSI C for Empirical TesƟng of Random Number Generators", ACM TransacƟons on MathemaƟcal SoŌware, 33: 22 (2007). [FA] G. A. Barbosa, “Fast and secure key distribuƟon using mesoscopic coherent states of light, Physical Review A, volume 68, p.052307, 2003. doi: 10.1103 / PhysRevA.68.052307. [FI] “Module-Laƫce-based Key-EncapsulaƟon Mechanism Standard, August 24, 2023”, NaƟonal InsƟtute of Standards and Technology (NIST), bibhƩps: / / doi.org / 10.6028 / NIST.FIPS.203.ipd. [GM] George Marsaglia, "The Marsaglia Random Number CDROM including the Diehard BaƩery of Tests of Randomness", Florida State University, 1995. [GR] J. van de Graaf. “Decentralized management of One-Time Pad key material for a group”, XIV Simpósio Brasileiro em Segurança da Informação e de Sistemas Computacionais, Belo Horizonte MG Brazil, SBSeg, pp.326-329, 2014. [IN] G. A. Barbosa, "InformaƟon theory for key distribuƟon systems secured by mesoscopic coherent states", Physical Review A 71, 062333 (2005). [KE] A. Kerckhoffs, "La cryptographie militaire". Journal des sciences militaires . IX: 5–83, January 1883. [MI] hƩps: / / www.technologyreview.com / 2023 / 01 / 06 / 1066317 / whats-next-for-quantum-compuƟng / [MW] L. Mandel and E. Wolf, "OpƟcal Coherence and Quantum OpƟcs" (Cambridge University Press, New York, 1995). [NIST] NIST, “A StaƟsƟcal Test Suite for Random and Pseudorandom Number Generators for Cryptographic ApplicaƟons”, NaƟonal InsƟtute of Standards and Technology, Special PublicaƟon 800-22, 2008. [PA] C. H. BenneƩ G. Brassard, C. Crepeau, U. M. Maurer, “Generalized Privacy AmplificaƟon''”, IEEE TransacƟons on InformaƟon Theory, volume 41, pp.1915-1923, 1995. doi: 10.1109 / 18.476316. [PF] G. A. Barbosa, [Patent]: US 7,831,050 B2. - November 9, 2010. [QK] S-K Liao et al., "Satellite-to-ground quantum key distribuƟon'', Nature volume 549, pages 43–47 (2017). [SA] M. Sasaki Et Al, Field test of quantum key distribuƟon in the Tokyo QKD Network, OpƟcs Express vol. 19, No 11, 10387 (2011). doi: 10.1364 / OE.19.010387. [SH] M. Sohma and O. Hirota , “Quantum Stream Cipher Based on Holevo–Yuen Theory”, Entropy , volume 24, pp.667-682 (2022). doi: 10.3390 / e24050667. [WI] S. Wiesner, "Conjugate Coding", SIGACT News. volume 15(1), pp.78–88. [WZ] W. WooƩers, W. Zurek, "A Single Quantum Cannot be Cloned". Nature volume 299 (5886), pp 802– 803 (1982). [YK] H. P. Yuen, A. M. Kim, “Classical noise-based cryptography similar to two-state quantum cryptography”, Physics LeƩers A volume 241, pp.135-138 (1998). DIGITAL KEY DISTRIBUTION PROTECTED BY RECORDED QUANTUM NOISE Inventor: Geraldo A Barbosa [ZH] L. Zhou, J. Lin, Y. Jing & Z. Yuan, Nature CommunicaƟons volume 14, No 928 (2023).

[0003] Description of Drawings - captions

[0004] FIG 1 - The diagram represents the steps involved in the used bit generation process: a coherent light beam from a laser (01) with long coherence time T is intensity-sampled by a fast detector (02) at instants tj within a short time window At (« T). The resulting current is amplified (G) (03). The analog signals pass to the Analog to Digital Converter (ADC) (04), the speed of which defines the sampling rate. The digitized voltage levels are classified as above or below average by the FRGA (05) with a programming that produces a stream of random voltages V+and V_ (06) representing the physical foitj (07). These digital signals are a record of quantum fluctuations - with no formation rule. Sequences of bits are generated for distinct functions (to be detailed in this disclosure): random bits a, to be distributed, groups of bits to create M encoding bases birand group of bits to represent random noise events N to cloak each encoded bit.

[0005] FIG 2 - Comparisons among some Physics I Random Number Generators and the generator described in this disclosure. A large bandwidth indicates that the circuitry is time -sensitive to signa i to a broad range of signal variations. Simplicity indications, such as the use of a single detector, usually implies lower initial and life-cycle cost and simpler maintenance.

[0006] FIG 3A - Exemplifies one part of the secure network with a Virtual Private Network (VPN) that defines connections to a team of users. The secure network has a central station (10) where the generator (11) described in this disclosure generates keys (12) that are stored in a main server (13) and key vault (14). These components allow key management and key replenishment whenever needed and through any channel. Keys are coded with an initial secret (a base) snared between the central stations and the users. Recorded quantum noise is added to the coded key signals and sent (15) to a team of users. This step uses the protocol TX.

[0007] FIG 3B - The noisy coded signals (15) are directed by a generic network (16) to the users.

[0008] FIG 3C - The noisy coded signals (15) are received at the user stations (17) by a computer (18) using the protocol RX. The protocols RX / PA in the computer eliminate the noise, extract and distill the sent keys to produce the final encryption keys. The encryption keys are inserted (19) into an external memory (e.g., pen drive) to be used in the ceil phone app (20) (or HoT devices). The cell phone encrypts and decrypt files using the OTP protocol. Hence communication is secured among users. Just to emphasize: The safe storage of encryption keys (fresh or used keys) is done externally by the users: keys are not stored on the device. The same applies to decrypted information; it is stored externally. The computer (18) also provides key replenishment to the users whenever needed. Central station (10) (shown in FIG 3A) may belong, for example, to a company securing communication among their employees. If company policy is that copies of information exchanged between employes should be centrally stored, the information and keys may be restored per company policy.

[0009] FIG 4 - The coding "wheel" illustrates the cycling accomplished by the operation Mod[f, M]). In this illustration, the coding "wheel" has an odd number of bases M = 2m+ 1, with m ~ 3, giving M — 9, and the possible random choices of bases k = 0,1,2,— 8. The neighboring bits to a given bit always have a different parity. FIG 5 ■ Basic noiseless encoding: "Base numbers" designate possible (random) numbers encoding bits. Symbol k designates one basis: a number between 0 and M — 1. Bits in neighboring bases are separated by 1. In a same basis k, bits 0 and 1 are separated by M / '2.

[0010] FIG 6 ■■ Logarithm of the Mutual Information as a function of the security parameter A.

[0011] FIG 7 - TX (22) sends to N RX (23) a sequence of coded bits with added noise. All stations perform the PA operations resulting in a sequence of fresh bits K.

Claims

AMENDED CLAIMS received by the International Bureau on 12 September 2025 (12.09.2025)Claim 1. A random key generation optoelectronic system, consisting of two or more identical detection systems, each of which is used to convert quantum fluctuations of a coherent electromagnetic field into random bits through a single signal light detector and to do so within a detection resolution time much shorter than the coherence time of the electromagnetic field. The final recorded quantum fluctuation outputs are routed to volatile memories and from these memories to an external memory using Direct Memory Access (DMA) protocol.”Claim 2. The system of Claim 1 , wherein the final recorded quantum fluctuation outputs result from amplification, digitization, bit identification, bit scrambling, and bit serializingto transform the signals into a true random bit sequence.Claim 3. A digital key distribution system (not QKD) with a truly random, non-deterministic structure, and which is resistant to post-quantum attacks and eavesdropping, and which generates and distributes sequences of true random bits to multiple users and groups.Claim 4. A set of protocols TX, RX, PA, and Replenisher used in digital key distribution of Claim 3, to allow for automatic key distribution to and among multiple users without using couriers (messengers).Claim 5. The protocol TX of Claim 4 uses recorded random numbers extracted from sequences of true random bits that are superposed bit-by-bit on an encoded bit signal. The final encoded bits with superposed noise form the noisy coded signals sent to users.Claim 6. In the protocol TX of Claim 4, the noisy coded signal of each bit is uncorrelated to the noisy coded signal added to any other bit.Claim 7. The protocol TX of Claim 4 allows the noisy coded signals generated to be transmitted on or between generic digital-agnostic communication channels, is independent of specific properties of optical channels.Claim 8. The protocol TX of Claim 4 allows the noisy coded signals to be transmitted without any distance limitation, other than network availability and constraints.Claim 9. The protocol RX of Claim 4 follows the protocol TX of Claim 4 and recovers bits from noisy coded signals regardless of the noise added to each encoded bit during TX.Claim 10. The protocol PA (Privacy Amplification Protocol) from Claim 4, follows the protocol RX of Claim 9 and "shuffles" the received signals. It distills new encryption bits and new encoding bases. The new encoding bases are used to distribute fresh random bits by protocol TX.Claim 11. In the protocol PA of Claim 10, distilled bits produced in one round of the PA protocol are uncorrelated with distilled bits produced in any other round.Claim 12. The protocol Replenisher from Claim 4 automatically renews keys whenever needed, using the TX, RX, and PA protocols and without using physical couriers (messengers).Claim 13. The system of Claim 3 also includes an application, Quantum Communicator (QC), residing on computing devices or mobile devices. QC uses fresh random encryption bits received from the protocol Replenisher, to decrypt any received data or encrypt any transmitted data.Claim 14. The application QC of Claim 13, wherein the default encryption is an automated one-time pad (OTP).Claim 15. The system of Claim 3, with the protocols TX, RX, PA, and Replenisher allows decentralized encryption for one-to-one and one-to-many communications.

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