CROSS-REFERENCE TO RELATED APPLICATIONS

The subject matter is related to U.S. Patent Application Nos. PCT/US2019/012537 and PCT/US2019/012556 and the disclosures of which are expressly incorporated by reference herein.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention relates to authentication and security, and more particularly to a physically unclonable function (PUF). The PUF is also a temperature sensor.

2. Description of the Related Technology

A physical unclonable function (sometimes also called physically unclonable function), or PUF, is a physically-defined “digital fingerprint” that serves as a unique identity for a device. A PUF is based on unique physical variations which occur naturally during manufacturing. A PUF is embodied in a physical structure. PUFs are implemented in integrated circuits and are used in applications with high security requirements, more specifically cryptography.

https://en.wikipedia.org/wiki/Physical_uncloneable_function

U.S. Patent Application No. PCT/US2019/012537 entitled “Hypercomputation with Programmable Matter” shows a system that provides a new way of computing exploiting the electrical and acoustic properties of piezo materials for computation.

U.S. Patent Application No. PCT/US2019/012556 entitled “Secure Programmable Matter” shows a method for performing secure computation using a solid volume of material to which a number of electrodes are attached.

References to systems that exploit the physical properties of disordered systems for authentication purposes date back to Bauder in 1983 and Simmons in 1984. Naccache and Fromanteau provided an authentication scheme in 1992 for memory cards. The terms POWF (physical one-way function) and PUF (physical unclonable function) were coined in 2001 and 2002, the latter publication describing the first integrated PUF where, unlike PUFs based on optics, the measurement circuitry and the PUF are integrated onto the same electrical circuit (and fabricated on silicon).

Over 40 types of PUF have been suggested. These range from PUFs that evaluate an intrinsic element of a pre-existing integrated electronic system to concepts that involve explicitly introducing random particle distributions to the surface of physical objects for authentication. All PUFs are subject to environmental variations such as temperature, supply voltage and electromagnetic interference, which can affect their performance. Therefore, rather than just being random, the real power of a PUF is its ability to be different between devices, but simultaneously to be the same under different environmental conditions on the same device.

From 2010 to 2013, PUFs gained attention in the smartcard market as a promising way to provide “silicon fingerprints”, creating cryptographic keys that are unique to individual smartcards. PUFs are now established as a secure alternative to battery-backed storage of secret keys in commercial FPGAs, such as the Xilinx Zynq Ultrascale++ and Altera Stratix 10.

PUFs depend on the uniqueness of their physical structure. This structure should depend on random physical factors introduced during manufacturing. When the factors are unpredictable and uncontrollable, it is virtually impossible to duplicate or clone the structure.

PUFs may implement challenge-response authentication to evaluate this microstructure. When a physical stimulus is applied to the structure, it reacts in an unpredictable (but repeatable) way due to the complex interaction of the stimulus with the physical microstructure of the device. A specific challenge and its corresponding response together form a challenge-response pair or CRP. The device's identity is established by the properties of the microstructure itself. As this structure is not directly revealed by the challenge-response mechanism, such a device is resistant to spoofing attacks.

Using a fuzzy extractor or key extractor PUFs can also be used to extract a unique strong cryptographic key from a physical structure. The same unique key is reconstructed every time the PUF is evaluated. The challenge-response mechanism is then implemented using cryptography.

PUFs can be implemented with a very small hardware investment. Unlike a ROM containing a table of responses to all possible challenges, which would require hardware exponential in the number of challenge bits, a PUF can be constructed in hardware proportional to the number of challenge and response bits. In some cases, PUFs can even be built from existing hardware with the right properties.

Unclonability means that each PUF device has a unique and unpredictable way of mapping challenges to responses, even if it was manufactured with the same process as a similar device, and it is infeasible to construct a PUF with the same challenge-response behavior as another given PUF because exact control over the manufacturing process is infeasible. Mathematical unclonability means that it should be very hard to compute an unknown response given the other CRPs or some of the properties of the random components from a PUF.

Note that a PUF is “Unclonable” using the same physical implementation, but care must be taken to protect against other forms of attack such as side-channel analysis or that a model can't be used to predict a response.

In many applications it is important that the output is stable. Error correction may be required if the PUF is used for a key in cryptographic algorithms to correct any errors caused by the underlying physical processes and reconstruct exactly the same key each time under all operating conditions. In principle there are two basic concepts: Pre-Processing and Post-Processing Error Correction.

Strategies have been developed which lead a static random-access memory (SRAM) PUF to become more reliable over time without degrading the other PUF quality measures such as security and efficiency. Research at Carnegie Mellon University into various PUF implementations found that some error reduction techniques reduced errors in PUF response in a range of −70 percent to −100 percent. Research at the University of Massachusetts Amherst to improve the reliability of SRAM PUF-generated keys posited an error correction technique to reduce the error rate.

PUF technology can be licensed from several companies including eMemory, ICTK, Intrinsic ID, Invia, QuantumTrace and Verayo. PUF technology has been implemented in several hardware platforms including Microsemi SmartFusion2, NXP SmartMX2, Coherent Logix HyperX, InsideSecure MicroXsafe, Altera Stratix 10, Redpine Signals WyzBee and Xilinx Zynq Ultrascale+.

Not all proposed PUFs are unclonable and many have been attacked successfully in a laboratory environment. A research team from Technical University of Berlin was able to clone an SRAM PUF within 20 hours using tools readily available in university failure analysis labs. In this work only SRAM cells of a microcontroller were read out.

University research has shown that delay-based PUF implementations are vulnerable to side-channel attacks and recommends that countermeasures be employed in the design to prevent this type of attack. Also, improper implementation of a PUF could introduce “backdoors” to an otherwise secure system. In June 2012, Dominik Merli, a scientist at Fraunhofer Research Institution for Applied and Integrated Security (AISEC) further claimed that PUFs introduces more entry points for hacking into a cryptographic system and that further investigation into the vulnerabilities of PUFs is required before PUFs can be used in practical security-related applications. The presented attacks are all on PUFs implemented in insecure systems, such as FPGA or SRAM. It is also important to ensure that the environment is suitable for the needed security level.

In 2015, studies have also emerged claiming it is possible to attack certain kinds of PUFs with low-cost equipment in a matter of milliseconds. A team at Ruhr Universitat of Bochum, Germany demonstrated a method to create a model of XOR Arbiter PUFs and thus be able to predict their response to any kind of challenge. Their method requires only 4 CRPs which even on resource constrained devices should not take more than about 200 ms to produce. Using this method and a $25 device or a near-field communication (NFC) enabled smartphone, the team was able to successfully clone PUF-based radio frequency ID (RFID) cards stored in the wallet of users while they were in their back pockets.

The attacks mentioned above range from invasive to non-invasive attacks. One of the most celebrated types of non-invasive attacks is machine learning (ML) attacks. From the beginning of the era of PUFs, it has been doubted if these primitives are subject to this type of attacks. In the lack of thorough analysis and mathematical proofs of the security of PUFs, ad hoc attacks against PUFs have been introduced in the literature. Consequently, countermeasures presented to cope with these attacks are less effective. In line with these efforts, it has been conjectured that PUFs can be considered as circuits, being provably hard to break. In response, a mathematical framework has been suggested, where provable ML algorithms against several known families of PUFs have been introduced.

Along with this provable ML framework, to assess the security of PUFs against ML attacks, property testing algorithms have been reintroduced in the hardware security community and made publicly accessible. These algorithms trace their roots back to well-established fields of research, namely property testing, machine learning theory, and Boolean analysis.

Mobile and embedded devices are becoming ubiquitous, interconnected platforms for everyday tasks. Many such tasks require the mobile device to securely authenticate and be authenticated by another party and/or securely handle private information. Indeed, smartphones have become a unified platform capable of conducting financial transactions, storing a user's secure information, acting as an authentication token for the user, and performing many other secure applications. The development of powerful mobile computing hardware has provided the software flexibility to enable convenient mobile data processing. However, comparable mobile hardware security has been slower to develop. Due to the inherent mobility of such devices, the threat model must include use cases where the device operates in an untrusted environment and the adversary has a degree of physical access to the system. The current best practice for providing such a secure memory or authentication source in such a mobile system is to place a secret key in a non-volatile electrically erasable programmable read-only memory (EEPROM) or battery backed SRAM and use hardware cryptographic operations such as digital signatures or encryption. This approach is expensive both in terms of design area and power consumption. In addition, such non-volatile memory is often vulnerable to invasive attack mechanisms. Protection against such attacks requires the use of active tamper detection/prevention circuitry which must be continually powered. As described inPhysical Uncloneable Functions and Applications: A Tutorial, Charles Herder, Meng-Day (Mandel) Yu, Farinaz Koushanfar, and Srinivas Devadas, 2014.

In the physical world, the development of high-quality fake art, jewelry, watches and fashion increases the need for manufacturers to demonstrate authenticity to maintain trust with their customers and to make it harder for third parties to create counterfeit products.

Physical Unclonable Functions (PUFs) are one way to provide such solutions both for the digital and physical world. The main advantages of traditional PUFs over traditional cryptographic techniques are:No secret key is stored in non-volatile memory where it could be discovered. Instead a PUF takes advantage of tiny differences in manufacture of, for example, a silicon chip whereby each is unique. Because these differences are random and outside of human control, it is practically impossible, even for the manufacturer, to make an exact copy.It is not necessary to trust a third party. If, for example, a secret key is created by a manufacturer the purchaser has to trust that party has not made a duplicate or retained some means to break the cryptographic key. While that possibility may be remote, a PUF does not have this disadvantage.PUFs can be constructed from cheaper components and consume less power than solutions that depend on EEPROM or SRAM memory.The secret key disappears when power is off.As the key is derived from the material itself any attempt to surreptitiously modify is likely to change the physical characteristics.

Authentication is the process between a prover, e.g., a hardware token or smart card, and a verifier, such as a secure server or bank, which confirms the identities, using corroborative evidence, of one or both parties. With the Internet-of-things (IoT), there are a growing number of applications that require low cost authentication. Physical Unclonable Functions (PUFs) are hardware security and trust primitives that can address issues related to low cost because they can potentially eliminate the need for non-volatile memory (NVM).

One instance of a PUF extracts randomness from variations in the physical and electrical properties of integrated circuits [IC], which are unique to each IC, as a means of generating digital secrets (bitstrings). The bitstrings are generated on-the-fly, thereby eliminating the need to store digital copies of them in NVM and are (ideally) reproducible under a range of environmental variations. The ability to control the precise generation time of the secret bitstring and the sensitivity of the PUF entropy source to invasive probing attacks (which act to invalidate it) are additional attributes that make them attractive for authentication in embedded hardware.

Resistors are common elements of electrical networks and electronic circuits and are ubiquitous in electronic equipment. A resistor is a passive two-terminal electrical component that implements electrical resistance as a circuit element. In electronic circuits, resistors are used to reduce current flow, adjust signal levels, to divide voltages, bias active elements, and terminate transmission lines, among other uses. High-power resistors that can dissipate many watts of electrical power as heat, may be used as part of motor controls, in power distribution systems, or as test loads for generators. Fixed resistors have resistances that only change slightly with temperature, time or operating voltage. Variable resistors can be used to adjust circuit elements (such as a volume control or a lamp dimmer), or as sensing devices for heat, light, humidity, force, or chemical activity. Practical resistors as discrete components can be composed of various compounds and forms. Resistors are also implemented within ICs. The electrical function of a resistor is specified by its resistance: common commercial resistors are manufactured over a range of more than nine orders of magnitude. The nominal value of the resistance falls within the manufacturing tolerance, indicated on the component.

It is known that electronic devices such as resistors may exhibit a temperature dependence of electrical resistance. The temperature coefficient of resistance describes the relationship between the resistive property of a component and the temperature of the component. The higher the coefficient, the greater an increase in electrical resistance for a given temperature increase.

A draw-back to current temperature sensing technology available for use in IoT applications is a vulnerability to security attacks and/or falsification. Traditional systems may allow an attacker to substitute the temperature sensor and the device responsible for authenticating and encrypting the reading may not know that it has been substituted. Furthermore, a faulty reading may not be detected.

SUMMARY OF THE INVENTION

It is an object to provide a security token based on a physical unclonable function (PUF). It is a further object to provide a security token which may be used as a secure temperature sensor. It is an object to eliminate the current distinction between PUF security token and analog temperature sensor. A security token is a device or component used to store or generate a value to be used in a security application such as an authentication or encryption application. It is a further object is to improve the security of analog temperature sensors such that a PUF based security token is a temperature sensor and the temperature sensor is a PUF based security token. It is a further object to reduce the vulnerability of temperature sensing devices by combining the functions of temperature sensor and cryptographic key generation such that it is resistant to substitution or modification. It is analogous to die-packs used to secure cash in transit. If activated the die makes the cash unusable. Similarly, any attempt to modify the resistors causes the temperature sensor/PUF to fail.

With proliferation of electronic devices, and with billions of IoT devices communicating with other devices, there is a pressing and growing need for robust secure key generation. In an ideal world every such device would have a unique ‘fingerprint’ that is impossible to spoof, clone, or hack. Such secure key generation may be used in a multi-layered security framework.

PUF based security tokens may advantageously be:Stable (able to perform consistently as required under different and variable environmental conditions for the lifetime of the device that it is securing).Affordable (able to be produced, maintained and disposed of at a price whereby customers can justify the additional upfront, ongoing and end of life cost and suppliers can make a profit) and requiring minimal energy consumption and zero maintenance).Secure (provides robust protection against attempts to clone, spoof or hack and does not require trust in a third party).

The PUF based security token may be constructed from a cluster of large, SMD or on-chip resistors. Due to manufacturing and other variations, no two resistors are expected to exhibit precisely the same physical properties. It is not suitable to rely on actual resistance values to define a PUF because resistors are sensitive to and react to temperature variations. Resistors may be selected for uses which have reasonable consistent temperature coefficients of electrical resistance. The property of electrical resistance may be utilized to compare the values of two or more resistors to specify a bit in a PUF generated security key. Multiple resistor sets may be used to specify multiple bits, for example, to specify a 128-bit key. By adding more resistors, longer and thus more secure keys can be generated for cryptographic or authentication functions. According to a feature of the resistor components, they are responsive to changes in temperature. In addition to relying on differences in resistance to specify elements of a key, one or more of the same resistor components may be used as a temperature sensor. This will result in a temperature sensor function linked to the PUF based security key so that both the key generation and temperature sensing are stable, affordable, and secure. The PUF based security token may be used for key generation, and once a key is generated, it can then be used for other purposes such as authentication and encryption.

The PUF based security token may provide a single response. Each time a PUF is queried, it may produce some stable responses and some unstable ones. These unstable ones, or noise, may be filtered out with error correction.

The PUF based security token may be implemented with a thin film 10K Ohm 50V 100 mW 1% tolerance rated −55° to +155 C.

It is a further object to provide a secure temperature sensing element. It has been found that the elements of a resistor network PUF may be utilized for temperature sensing. The temperature sensing may be accomplished by monitoring electrical properties of one or more resistors in the PUF structure. For example, resistors may have a property that varies with temperature. As long as the resistance varies in a known manner, the resistance may be determined by voltage drop across the resistor, and the voltage drop may be mapped into a temperature reading. According to an embodiment, different resistors may have different temperature responses. We use the relationship between the resistor clusters to generate the cryptographic key. We use one or many resistor clusters to measure temperature. Then we sign the temperature reading with the cryptographic key. If you change a resistor so that the temperature is different from the correct temperature, then it will also affect the PUF such that it will construct the wrong cryptographic key.

Any product can be counterfeited given sufficient incentive. High value physical products such as luxury handbag designs are targets for counterfeiting. The total trade in fake products is estimated at around $4.5 trillion, and fake luxury merchandise accounts for 60% to 70% of that amount, ahead of pharmaceuticals and entertainment products and representing perhaps a quarter of the estimated $1.2 trillion total trade in luxury goods.

One response to the threat of counterfeiting is to track products using a vendor database or blockchain from manufacture to end-of-life. LVMH Moet Hennessy-Louis Vuitton, a Société Europeenne (“LVMH”) has launched the AURA platform, developed by Microsoft and ConsenSys with product tracking and tracing services based on blockchain technology.

A PUF based security token can protect against counterfeit physical high value products in combination with NFC and a vendor database or blockchain technology.

In this instance, a PUF based security token embedded tag is either attached to or embedded in the product if practical (e.g., into the lining of a handbag) and/or is incorporated into a certificate of authenticity passport (e.g. for a piece of jewelry). In very high value items, two PUF based security token devices could be associated with the same product, one attached to the product and a second embedded in the certificate of authenticity passport.

The manufacturer creates the first record in the blockchain when the product is manufactured which includes a digital signature DigSigSK(PropM(O)) signed with a private key (SK) that included the PUF based security token associated with the Object to track (O).

At each subsequent event, such as shipment, delivery into store and first sale, the PUF based security token can be queried using a Standard Measuring Device (M) comprising an app and NFC to verify the product's authenticity before the event is added to the blockchain. In this instance we store the public key (PK) in the App that is paired to the manufacturer's private key (SK).

Using the Manufacturer's Public Key (PK) and the Standard measurement Apparatus (M), the testing device applies the following decision rule:

If DigSigSK(PropM(O))

is valid, and if for the object O on the item it holds that

PropM(O)=PropM(O),

then the testing device accepts the tag, otherwise not.

To supplement the scheme, anti-tamper technology can be used to prevent a genuine PUF based security token being added to a fake product. When we stimulate the PUF based security token we get a unique response which cannot be cloned. The Standard measurement Apparatus (M) can be used to repeat the original test, the results of which are embedded in the digital signature previously stored on the blockchain. Because the public key derived from the unique response is stored in the blockchain it cannot be manipulated.

In essence the solution is key-free and security-free. Source: Towards Secret-Free Security by Ulrich Rührmair, April 2019.

One benefit of this system is that it can be retro-active. Owners of high-value items can take them to the store or a trusted third party where a PUF based security token embedded tag can be retrofitted, or a certificate of authenticity passport issued, as applicable. If the PUF based security token is lost, stolen or damaged this can be recorded in a vendor database or blockchain and a replacement tag issued by the store or trusted third party.

Another benefit of the system is that authentication can take place anywhere and at any time without any need for online access or real-time verification by a central authority.

A further benefit is that because the system is integrated with a vendor database or blockchain additional information such as product data can be recorded.

An alternative approach that achieves the same outcome, is that hashed values of PropM(O) can be signed and contained in the PUF based security token. Testing will determine which approach is faster and more efficient.

With sufficient incentive any piece of software or hardware will eventually be hacked, cloned or spoofed.

In an ideal world, every computing device would have a unique ‘fingerprint’ that is impossible to guess. Without rock-solid authentication trust is impossible. Secure cryptographic key generation is a vital first step in a multi-layered security framework to protect against data loss, ransomware and other damage. According to Sophos two out of three organizations fell victim to one or more cyberattack in 2018 despite the fact that 26% of IT team's time is spent on cyber-security and 91° A of organizations were running up to date protection. The result—stolen data, wasted time, financial cost and damage to reputation.

In the physical world more than 1 in 4 consumers unknowingly purchase fake products online. The Global Brand Counterfeiting Report 2018 says the amount of total counterfeiting globally had reached 1.2 Trillion USD in 2017 and is bound to reach 1.82 Trillion USD by the year 2020 which includes counterfeiting of all equipment/products from defense equipment to watches.

It is an object to provide a security element to enhance a vendor database or blockchain by offering irrefutable unclonable ID's either integrated into a product or as a ‘passport’ where that is impractical e.g. luxury watches. The passport will also enhance the ability to create a second-hand market. Swiss luxury watchmaker Audemars Piguet said it would launch a second-hand business in 2018, becoming the first big brand to announce plans to tap into a fast-growing market for pre-owned premium watches. Use of a passport involves the establishment of a token to be associated with an item to be tracked but does not require the item to be retrofitted.

A PUF security element as disclosed may be used to track and trace an item to be secured. This can be done by integrating a PUF security element into the item or by incorporating the PUF security element into a separate passport. Why can't a counterfeiter simply copy the bag with an identical serial number? What happens if a thief were to steal a genuine PUF based security token embedded tag and attempt to sell it with a counterfeit?

It is an object to provide a structure useful as a Physical Unclonable Function security element (“PUF Security Element”) that produces a response which is unique to that specific instance when stimulated because of tiny variations in the material. The variations in the materials of the PUF Security element may provide a secret key which may be used in authentication. There is no need for a physical key to be inserted in memory at manufacture. Therefore, security is enhanced by eliminating a trusted third party to insert a key in the material.

It is a further object to provide a PUF Security element that does not include an inserted key that is subject to detection in the absence of any stimulation, thereby eliminating certain attack vectors.

It is a further object to provide a PUF Security Element that may interact using symmetric or asymmetric architecture. It is a further object to provide a PUF Security Element that may be used to generate a public/private key pair. A private key remains secret. The public key can be shared without compromising security. With a symmetric architecture the key is shared. A request encrypted with the public key can only be decrypted by the specific PUF Security Element which may yield the private key.

It is an object to incorporate use of blockchain to enables a user to have one PUF Security Element linked to many products manufactured by different companies.

A hybrid blockchain may be used which will make the public key/serial number relationship visible and immutable. One backend function will be to look for suspicious transactions. Then if a secret was somehow compromised, multiple fakes could not share the same serial number/PUF Security Element without raising an alert.

A private component (hereafter called a private manufacturer database) may record details of ownership and be used by companies to understand their customer purchasing habits as well as provide extra security if either the PUF Security Element (tag) or the product is lost or stolen. The usual privacy laws and processes will apply.

The private blockchain could extend the public key/serial number combination to hold a hash of a user password or biometric data such as a fingerprint. This would tie the product and owner together.

An object authentication system may require that a user first register to participate using a communication device such as a smart phone. A user may install an app and register to participate in the authentication system. The user may then verify that a product is authenticated; record acquisition of a product protected by a PUF Security element; record a transfer of a product protected by a PUF security element; register a notification that a product protected by the PUF security element has been lost or stolen; and register a notice that a product they previously recorded acquisition of may or may not be validly transferred between third parties. As an alternative to interacting with the authentication system through a smartphone app, a vendor, seller, or service provider may have the capability to accomplish the foregoing operations through a terminal.

A temperature sensing security token may include a first resistor having a first side connected to a voltage source, a second resistor having a first side connected to the voltage source, an analog comparator having a first input connected to a second side of the first resistor and a second input connected to a second side of the second resistor and an output that represents at least one bit of a key, and an analog to digital converter having an input connected to the second side of the first resistor wherein an output of said analog to digital converter is related to temperature by a temperature coefficient of resistivity of the first resistor. The first resistor and the second resistor may have the same nominal resistance. The first resistor, the second resistor and the analog to digital comparator may be encased in the same package. The package may be configured to inhibit inspection and discovery of components contained in said package. A processor may be connected to a key register and to a temperature table wherein said processor may be configured to store the key bits in the key register and is configured to store data corresponding to temperature. The processor may be configured to store a time stamp associated with an entry in the temperature table. A communications interface may be connected to the processor.

The security token may include a multiple bit security element where each bit is an output of a comparator having a first input connected to a first electrical circuit and a second input connected to a second electrical circuit wherein the first electrical circuit and the second electrical circuit are characterized by electrical components having the characteristics of a PUF. The electrical components may be resistors. The comparator may be connected to the first electrical circuit and the second electrical circuit to compare the resistance of at least one resistor in the first electrical circuit to the resistance of at least one resistor in the second electrical circuit. An analog to digital converter may be connected to at least one resistor in the first electrical circuit and wherein the at least one resistor may have a temperature coefficient of resistivity corresponding to an expected range of variations in temperature detectable by an output of the analog to digital converter. A processor configured to read each bit and compose a multi-bit security key. The processor may be programed to store a value corresponding to the output of the analog to digital converter. The corresponding value may be the value read or a conditioned or calculated value. The processor may be programed to store a timestamp associated with said value corresponding to the output of the analog to digital converter. An addressable switch may be connected to a plurality of electrical resistors and the switch may be controlled by the processor to select the resistor(s) connected to the comparator.

A method for generating a secure temperature reading may include the steps of providing a plurality of first resistors having resistive values based in part on physical properties not practically predictable or cloneable, providing a plurality of second resistors having resistive values based in part on physical properties not practically predictable or cloneable, generating a key having a plurality of bits where each bit is specified by comparing resistive values of one of said first resistors with resistive values of one of the second resistors, sensing ambient temperature by sampling voltage drop across at least one of the resistors and converting the voltage drop to a digital representation of temperature, and using the key to digitally sign the digital representation of the temperature. The key may be used to generate at least one key of an asymmetric key pair. The step of sensing ambient temperature may be done by taking a plurality of samples of voltage drop across a plurality of resistors, converting the plurality of voltage drops to a plurality of preliminary digital representations of temperature, combining the plurality of preliminary digital representations of temperature into the representation of temperature value. A plurality of digital representations of temperature may be accumulated in a storage device and periodically transmitted or be transmitted on demand.

The above objects and advantages of the invention are illustrative, and not exhaustive, of those that can be achieved by the invention. Thus, these and other objects and advantages of the invention will be apparent from the description herein, both as embodied herein and as modified in view of any variations which will be apparent to those skilled in the art.

