Abstract:
Methods of securing a cryptographic device against implementation attacks, are described. A disclosed method comprises the steps of obtaining a key ( 230 ) from memory of the cryptographic device; providing the key and a constant input ( 210 ) to an encryption module ( 240 ); deriving an output ( 250 ) of encrypted data bits using the encryption module ( 240 ); providing the output ( 250 ), the key ( 230 ) and an input vector ( 270 ) to a key update module ( 260 ); and using said key update module ( 260 ) to modify the key based on at least a part ( 270   a ) of the input vector ( 270 ) to derive an updated key ( 230   a ). This prevents the value of the key from being derived using the updated key or by using side-channel attacks because the input is constant for all keys. Additionally, by altering the input vector, the updated key is also altered.

Description:
FIELD 
       [0001]    This disclosure describes a method and integrated circuit for securing a cryptographic device, and in particular, a method for securing a cryptographic device against implementation attacks. 
       BACKGROUND 
       [0002]    Smart devices, in particular those with low power requirements, typically called passive smart devices, are widely used for authentication and access control. Examples of such devices include contactless smart cards, which are a subset of radio-frequency identification (RFID) tags. Such passive smart devices typically use an application specific integrated circuit (ASIC). 
         [0003]    Given the application of passive smart devices in security critical applications, cryptography is used to authenticate the passive smart device on use. Conversely, due to the desirability of the information that a passive smart device may hold or allow access to, they are also the focus of malicious attempted use. 
         [0004]    A lot of time and effort is spent in implementation and analysis of side-channel countermeasures within security integrated circuits (ICs) like smartcards. A side-channel attack is any attack based on information gained from the physical information of a cryptographic system. Such attacks are different from a software brute force attack or an exploit or weakness in the encryption algorithms. Side-channel attacks typically examine the internal operation of the system, such as the power drawn by the system, electromagnetic (EM) emissions or other ‘side-channels’ to determine patterns and implementation steps. One such known side-channel attack is differential power analysis (DPA). This may involve a malicious user studying traces of power usage during use of the device and, utilising statistical analysis, determining features of the encryption algorithms. 
         [0005]    With the use of currently available standardized algorithms and protocols, like the ones used in banking or e-government applications, attack scenarios for differential power analysis (DPA) (and differential fault attacks) are available, leading to devices implementing such protocols being threatened by such side-channel attacks (for example, because a varying input is always encrypted with the same (master) key, variations in the power signature of a system are solely or generally dependent on variations in the encryption algorithm). 
         [0006]    One solution to such attacks uses a method of re-keying. In such a method, a session key is derived from the master key, where subsequently this session key is used for the actual operation. This session key is changed regularly in order to decrease the amount of power traces that can be obtained from the device for a specific (master) key. 
         [0007]    A special instance of this re-keying has been applied within the CIPURSE protocol. In this approach the master key is used to derive an intermediate session key by using a random input and a function (called NLM (non-linear map)) that is easier to protect against implementation attacks. This intermediate session key is then used together with the master key to get to the used session key. (see reference US2010316217A1). The above solution to such DPA attacks relies on a random number agreement between the two parties. Such an approach prevents verification of previous transactions. In particular, it is not possible to repeat the sessions without the random numbers. 
         [0008]    A relatively new area of research is leakage resilient cryptography. In leakage resilience (LR), it is sought to avoid having the typical DPA scenario where it is possible to attack the key of a block cipher chunk-wise (i.e. in chunks, such as byte by byte) with a varying input for every execution. In the LR approach the block cipher is executed multiple times where the complete input vector is only used chunk-wise (e.g. 1 bit at a time) and copied to the whole input state of the block cipher. In every iteration the next input chunk is used as the input (again copied to the whole state). This limits the data-complexity, i.e. the number of traces which can be used for an attack, and creates a dependency between the side-channel information of the different key chunks. However, an adversary can still apply a DPA attack due to the N&gt;1 traces available per key. 
         [0009]    In summary, there are still issues in performing symmetric cryptography security services (e.g. IC authentication, secure communication, key update etc.) on a low-cost IC without implementation of heavy countermeasures and the need for detailed side-channel investigations. The following disclosure aims to address these problems. 
       SUMMARY 
       [0010]    According to a first aspect of the invention, there is provided a method for securing a cryptographic device against side-channel attacks, the method comprising: 
         [0011]    obtaining a key from memory of the cryptographic device; 
         [0012]    providing the key and a constant input of data bits to an encryption module; 
         [0013]    deriving an output of encrypted data bits using the encryption module; 
         [0014]    providing the output, the key and an input vector to a key update module; and 
         [0015]    using said key update module to modify the key based on at least a part of the input vector to derive an updated key 
         [0016]    Using a key in this manner reduces or removes the need for attack countermeasures in the underlying encryption module and also prevents detailed side-channel investigations. Because of the key update techniques used, the updated key cannot be used to derive the original, master key by a side-channel attack. The transitions applied by the key update module require knowledge of the original master key because they use the output of the encryption module derived from the input vector and the key. Furthermore, because the (plaintext) input to the encryption module is constant, there is only a single power trace obtainable. This provides security against side-channel attacks such as DPA that attempt to apply statistical analysis to the power management traces of cryptographic processes and algorithms. 
         [0017]    In embodiments of the present disclosure, the method further comprises the steps of providing the updated key and the constant input to the encryption module; and deriving an updated output using the encryption module. 
         [0018]    Such embodiments improve the security of the updated key by supplying an updated output that has been derived from the updated key and a supplied input vector. Because the updated output has been encrypted with the updated key, rather than the original master key, the security of the original master key is preserved. 
         [0019]    Furthermore, the method can further comprise the steps of: providing the updated output, the updated key and the input vector to the key update module; and using said key update module to modify the updated key based on at least a second part of the input vector. By further modifying the updated key, this step moves the further updated key away from the master key. 
         [0020]    The input vector can comprise two or more parts. Accordingly, such method steps can be repeated for each part of the input vector. In particular, the steps of providing the updated key and the constant input to the encryption module; and deriving an updated output using the encryption module and providing the updated output, the updated key and the input vector to the key update module; and updating the updated key using the key update module can be iterated a number of times equal to the number of parts of the input vector. 
         [0021]    In other words, the input vector can be provided chunk-wise (i.e. in chunks, such as bytes or bits). For example, for an input vector of 128 bit length, the input vector may be considered to comprise 64 parts or chunks, each part being 2 bits long. A pseudo-random output may then be derived by means of the pseudo-random function. Accordingly, the key update module may be considered as acting as a step of a pseudo-random function, processing the input vector and the key to derive a pseudo-random output, such as an updated key, based on values of at least part of the input vector. In this consideration, the input vector and the key are inputs to the pseudo-random function. 
         [0022]    In embodiments, one or more additional input vectors may be provided. A pseudo-random output may then be derived for each additional input vector using the pseudo-random function. Each pseudo-random output may then be concatenated to form a larger pseudo-random output. 
         [0023]    The parts of the input vector can comprise the values of at least a string of bits. Additionally or alternatively, the parts of the input vector can be the values of at least one bit of the input vector. Accordingly, the key update module can derive the updated key based on the value of a bit of the input vector. The key update module can act to apply a defined key update protocol to modify the key or the updated key dependent upon the value of a bit or bits of the input vector. For example, a bit value of 0 for bit  0  may instruct the key update function to rotate selected bits of the key to the right by 1 bit position. Conversely, a bit value of 1 for bit  0  may instruct the key update function to rotate the same or other bits of the key to the right by 2 bit positions. Other permutations are available depending upon the algorithms available to the update function. 
         [0024]    As noted above, based on the value of a bit of the input vector, the key update module can transform or modify the key or the previous updated key using one or more of compression, expansion or permutation operations. 
         [0025]    Utilising iterations increases the complexity of the dependency between the originally obtained key, known as the master key, and the updated key, thus making it more difficult to derive a key higher up in the key tree. This in turn counteracts key recovery by means of differential fault analysis, in particular for the originally obtained master key. Furthermore, because each key only uses the same input, i.e. the input provided to each encryption module is constant, the power trace for each key iteration is the same and therefore the power measurement of each key is resilient to differential power analysis attacks as described above. 
         [0026]    In some examples, the key update module can rotate the value of output or the updated output by a number of bits. For example, the number of bits may be dependent on the value of at least a part of the input vector. 
         [0027]    Alternatively or additionally, the updated key can be a concatenation of at least part of the key or the previous updated key and at least part of the updated output. As noted above, the output of the encryption module is provided to the key update module with the key and the input vector. Accordingly, to generate an updated key of sufficient length, the previous key can be compressed or split into separate parts, such as left and right (based on the number of bits) and combined with the output or updated output to generate the updated key. Complete replacement of the key by the output may also be used, if the output length/key length ratio allows this, before processing part of the input and thus updating the updated key. It can be appreciated that alternative techniques to generate the updated key may also be used, such as the use of salts to pad some or all of one or more of the output or updated output and the previous key to generate the updated key. 
         [0028]    The described aspect provides a leakage resilient type scheme that does not rely on key agreement between parties. This allows reproduction and/or verification of previous transactions or message authentication codes. Additionally, the current approach only utilizes an interim or updated key once—there is no session key per se, instead an updated key is generated for every instance by either progressing further along the values of the input vector or by providing a new input vector. 
         [0029]    In a second aspect, there is provided a method of providing a secure communication of data between a client device and a host device, said method comprising: 
         [0030]    providing a client device with a client microprocessor and client memory wherein the client device comprises a key stored within the client memory; 
         [0031]    providing a host device with a host microprocessor and host memory; 
         [0032]    establishing a secure connection between the host device and the client device; 
         [0033]    supplying at least one input vector to the client device from the host device; 
         [0034]    deriving at least one updated key and at least one updated output based on the input vector using at least part of the methods of the first aspect; and 
         [0035]    using said updated ouput(s) for encrypting communication between the client device and the host device by using the output as a keystream. 
         [0036]    Such aspect may be beneficial in communication protocol between proximity coupled devices and proximity integrated circuit chips. Smartcards are one example of such chips, together with RFID devices. Such devices require authentication between a host device and a client device. Additionally, such devices can allow a client device to supply evidence of the possession of a key to the host device based on an input vector supplied by the host device. 
         [0037]    In the above described aspects, the encryption module can be a block cipher according to any encryption algorithm. Such encryption algorithms include the PRESENT algorithm, or the Advanced Encryption Standard algorithm. Utilising existing block ciphers that may also provide alternative functionality on the device allow the gate equivalent (ge) footprint of the described cryptographic key generation to be kept to a minimum. This allows a low cost to the device. 
         [0038]    In another related aspect, there is provided a method of encrypting data, said method comprising: 
         [0039]    providing a cryptographic device with a microprocessor and memory wherein the device comprises a key stored within the memory and an encryption module; 
         [0040]    supplying an input vector to the device; 
         [0041]    deriving an updated key, based on the input vector and a pseudo-random output, using the method of at least part of the first aspect; 
         [0042]    supplying data to be encrypted; and 
         [0043]    encrypting the data using the updated key. 
         [0044]    In other embodiments, the encryption module could be utilised for authentication protocol such that the protocol is not vulnerable to DPA attacks. This improves the security of such authentication protocols. 
         [0045]    One further aspect may be directed towards an integrated circuit for a cryptographic device comprising a microprocessor and memory, wherein the device comprises a key stored within the memory, an encryption module and a key update module, whereby the integrated circuit is configured to perform the method of any preceding aspect. 
         [0046]    This aspect provides security for a cryptographic device against implementation attacks, such as side-channel attacks. 
         [0047]    In a further aspect, there is provided a method of message authentication code generation, said method comprising: 
         [0048]    providing a cryptographic device with an integrated circuit according to the integrated circuit aspect described above; 
         [0049]    supplying an input vector and a constant input to the device; 
         [0050]    deriving an updated key and an updated output, based on the input vector, using the method of at least part of the first aspect; and 
         [0051]    using the updated output as a message authentication code. 
         [0052]    Additionally, the input vector can be concatenated with a counter to produce several inputs and therefore a longer output. 
         [0053]    In embodiments, the encryption module may be a decryption module or an encryption and decryption module. 
         [0054]    Using a standard encryption module, such as a symmetric block cipher, with the method as outlined above provides encryption keys that make implementation attacks like differential power analysis and fault attacks, etc. impossible without any special countermeasures, except for simple power analysis (SPA) resistance by e.g. parallelism, within the block cipher implementation itself. By repeatedly executing the block cipher while the data input is held constant (e.g. all 0, all 1), the key is modified based on the input vector starting from the original cipher key. This allows having “a secure by design” approach without expensive countermeasures and the need for detailed side-channel analysis. The disclosure can replace a standard block cipher within, for instance, an authentication protocol. 
         [0055]    There may be provided a computer program, which when run on a computer, causes the computer to configure any apparatus, including a circuit, controller, sensor, filter, or device disclosed herein or perform any method disclosed herein. The computer program may be a software implementation, and the computer may be considered as any appropriate hardware, including a digital signal processor, a microcontroller, and an implementation in read only memory (ROM), erasable programmable read only memory (EPROM) or electronically erasable programmable read only memory (EEPROM), as non-limiting examples. The software implementation may be an assembly program. 
         [0056]    The computer program may be provided on a computer readable medium, which may be a physical computer readable medium, such as a disc or a memory device, or may be embodied as a transient signal. Such a transient signal may be a network download, including an internet download. 
     
    
     
       BRIEF DESCRIPTION OF DRAWINGS 
         [0057]    The disclosure will now be described with reference to the following figures in which like reference numerals are used to denote like elements: 
           [0058]      FIG. 1  is a block diagram of a prior art security service; 
           [0059]      FIG. 2  is a block diagram of communication between a host device and a client device; 
           [0060]      FIG. 3  is a cryptographic primitive according to the present invention; 
           [0061]      FIG. 4  is a flow diagram of the cryptographic primitive of  FIG. 3 ; and 
           [0062]      FIG. 5  is an alternative flow diagram of the cryptographic primitive of  FIG. 3 . 
           [0063]    It should be noted that the Figures are diagrammatic and not drawn to scale. Relative dimensions and proportions of parts of these Figures have been shown exaggerated or reduced in size, for the sake of clarity and convenience in the drawings. The same reference signs are generally used to refer to corresponding or similar feature in modified and different embodiments. 
       
    
    
     DETAILED DESCRIPTION 
       [0064]      FIG. 1  shows a prior art security service  10  with an input IV (input vector)  20 , key (K)  30 , block cipher  40  and output  50 . The operation of such a prior art security service is that the input vector  20  is encrypted using the key  30  to provide an encrypted cipher text or output  50 . The block cipher  40  provides instructions of how to encrypt the input using the key. 
         [0065]    An attack method is to examine the internal code, e.g. the S-box, of the block cipher. One method for doing this is using side-channel attacks. For example, by analysing the electromagnetic power consumption and utilising statistics, it is possible to determine the structure of the S-box. Such attacks are often called differential power analysis attacks. 
         [0066]    Security services such as the one shown in  FIG. 1  may be employed on servers or hosts, for example a computer or a proximity coupling device, that is used to read and communicate with passive devices such as radio-frequency identification (RFID) tags. 
         [0067]      FIG. 2  shows an example of a host  120  and a client passive device  140 . In the example shown, the host  120  may be a proximity coupling device (PCD), and the client device  140  may be a proximity integrated circuit chip (PICC), such as a RFID tag or a smartcard  140  suitable for use in the key distribution protocol in accordance with the present disclosure. The host  120  in this embodiment is a computer which includes a processor  130 , a memory  132  and a card interface  134 . The smartcard  140  includes an input/output interface  142 , a processor  144  and a memory  146 . The host  120  communicates with the smartcard  140  via the card interface  134  and the input/output interface  142 . The processor  144  may be a microprocessor or a finite state machine configured to provide cryptographic processing operations as described in greater detail below. The memory  146  of card  140  may be an electronic static or dynamic random access memory (RAM), a magnetic memory or other suitable arrangement of information storage elements. The card interface  134  and input/output interface  142  may be in conformance with a standard card interface such as the personal computer memory card interface adaptor (PCMCIA) standard or a contactless communication interface like ISO 14443. 
         [0068]    In an exemplary embodiment of the disclosure as shown in  FIG. 2 , the card  140  is used to generate a key stream. A process operating on host  120  then provides an encrypted data input to the card for decryption. The card  140  then performs decryption using the key stream. This allows the card  140  to be implemented as a device with relatively limited computational power and low input/output bandwidth. The card  140  in this example will be assumed to operate as a stateless device, such that the current output depends only on the current input and not on any prior inputs. For a given input n, the card  140  will thus output a function with a value determined by the input n, the secret key K stored in memory  146 , and a random or pseudo-random bit sequence generated in card  140  or supplied to card  140  via host  120 . This assumption recognizes that many currently available smart cards include limited memory, processing and input/output capabilities. 
         [0069]    The present disclosure utilises a single constant, the key, which is combined with a known input to generate a pseudo-random output. As noted, in order to prevent an attack using side-channel attacks like differential power analysis attacks, one technique is to change the key on a frequent basis or to build the hardware to prevent attack. 
         [0070]      FIG. 3  describes the process of securing a cryptographic process against implementation attacks, such as side-channel attacks. In a similar manner to that shown in  FIG. 1 , an encryption module, such as a block cipher  240 , is configured to produce an output  250  based on a constant input  210  and a key  230 . In the example shown, the input  210  is n bits long, key  230  is m bits long and the corresponding output  250  is n bits long. In example shown, the input  210  has a 0 value (i.e. the value of all n bits are 0). It can be appreciated that the inputs and outputs may be of arbitrary length. Typically, the key is 128 bits long. 
         [0071]    The output  250  is fed into a key update module  260  together with the value of the key  230 . An input vector  270  is also provided to the key update module  260 . The input vector is fed into the key update module chunk-wise (i.e. in chunks, such as byte by byte). In  FIG. 3 , the input vector  270  is k*j bits long and fed into the key update module  260  in chunks of j bits. The first iteration feeds in bits [0 . . . j−1], the second [j . . . 2j−1] bits until the final chunk of [(k−1)j . . . kj−1]. This divides the input vector  270  into a number of parts  270   0 ,  270   a  . . .  270   k . The key update module  260  contains a key update function (see  FIG. 4 ) that provides (in the first iteration) an updated key  230   a . One part  270   0  of the input vector  270  can also be provided to the key update module  260  (i.e. the input vector is provided bitwise, a single bit at a time). The value of the single bit or chunk provided by the input vector  270   0  to the key update module  260  determines how the key  230  is updated. Based on the value of the single bit or chunk provided by the input vector  270   0  (or  270   a , . . .  270   k ) , the output  250   0  (or  250   a , . . .  250   k ), the value of the key  230   0  (or  230   a  . . .  230   k ) and the key update function within the key update module  260 , an updated key  230   a  (or  230   b , . . .  230   k ) is provided by the key update module  260 . 
         [0072]    The process described above is repeated for every part or bit of the input vector  270 . Accordingly, as shown in  FIG. 4 , the updated key  230   a  is provided to the block cipher  240  together with an input  210  (again, in the example shown, the input  210  has a 0 value). Given that the value of the key  230   a  has changed, the output value  250   a  is also different from the output  250  of the 1 st  iteration. Again, the output  250   a  and the updated key  230   a  are provided to the key update module  260  together with the next bit of the input vector  270   a . Based on the value of the next bit of the input vector  270   a , the updated output  250   a  and updated key  230   a , the key update function of the key update module  260  provides a 2 nd  updated key  230   b . 
         [0073]    The above described process is iteratively repeated for all bits of the input vector  270  until a (final iteration) updated key  230   k  is provided. This updated key  230   k  can then be combined with the input  210   k  and supplied to the block cipher  240  to provide an output value  250   k . The output  250   k  can be used as a keystream. The output  250   k  can be also used to feed a keystream generation function. The output  250   k  can be used as a message authentication code for the input. The output  250   k  can be also used to feed a message authentication code generation function. 
         [0074]      FIG. 4  details the cryptographic primitive, and in particular the key update function within the key update module  260 , as shown in  FIG. 3 . In  FIG. 4 , the key  230  comprises a left half  232   0  and a right half  234   0 . Each half of the key  230  contains half the bits of the key, so for a 128 bit key, the left half contains bits  127 : 64  and the right half contains bits  63 : 0 . The key  230  is provided to an encryption module  240  such as a block cipher, together with an input  210 . The output  250   0  is the ciphertext (C0)  252  output by the encryption module  240 . In addition to the key, encryption module and input, an input vector  270   0  is provided, which is analysed bitwise, such that the value  274  of each bit  272  of the input vector  270   0  is determined. Dependent upon the value  274  of the bit  272  of the input vector  270   0 , the key  230   a  is derived using a concatenation of the ciphertext output  252  and the original key  230 . In the example shown, both values of the input vector specify that the output  252  is concatenated with the right hand side  234   0  of the original key  230 . The left hand side  232   0  of the original key is discarded. Dependent upon the value  274  of the selected bit  272  of the input vector  270   0 , an operation may be performed on the right hand side  234   0  of the original key. For example, as shown in  FIG. 4 , a value  274  of 0 for bit  272  results in a first rotation of the right hand side of the key  234   0  by a value of 1 bit (i.e. the position of the output  252  C0 in relation to the right hand side of the key  234   0 ). Conversely, a value  274  of 1 for bit  272  results in a different rotation of the key, in the example shown a 2 bit rotation, and a different position of the output  252  relative to the right hand side of the key  234   0 . In both cases, this forms an updated key  230   a   1  or  230   a   2 . 
         [0075]    It can be seen that if a 128 bit original key is used with a 64 bit input, the output value can be 64 bits long. Concatenating this output value with half the original key provides a 128 bit updated key. The form of the concatenation may depend on the value  274  of the bit  272  of the input vector  270 . The form of the concatenation may also take alternative forms, such as the use of salts, constants, counters, nonces or other cryptographic constructs. 
         [0076]    It can be appreciated that other functions may be performed on the key in addition to or as an alternative to concatenations. For example, the right hand side  234  of the key may be rotated by several bits. The example shown in  FIG. 4  utilises a simple compression of the original key to provide the updated key. Expansion and other permutations may also be used. 
         [0077]    It can also be appreciated that the functions performed on the key may depend on more than one bit of the input vector  270 . One such example is shown in  FIG. 5 .  FIG. 5  shows an alternative construction of the single iteration of the primitive shown in  FIG. 4 . In this variant, the value of two bits of the input vector  270  are considered. It can be appreciated that any part (i.e. 1 or more bits) of the input vector  270  may be applied. 
         [0078]    For example, input vector  270   a  provides alternative tree paths  270   a   1 ,  270   a   2 ,  270   a   3 ,  270   a   4  for updating the key. The path  270   a   1 ,  270   a   2 ,  270   a   3 ,  270   a   4  chosen depends upon the value of bits ab of the input vector. In the example shown, a value of 00 for bits ab is path  270   a   1 , which leads to a concatenation of the right hand side of the key  234   a  with the output  252   a , with a rotation of the key to the right by 1 bit. Path  270   a   2 , bit value 01, leads to an alternative concatenation between the right hand side of the key  234   a  and the output  252   a  with a 2 bit rotation applied to the key. Bit values of 10 leads to path  270   a   3  and a concatenation of right hand side of the key  234   a  and output  252   a  with a 3 bit rotation and finally value 11 to path  270   a   4  and alternative concatenation of path  270   a   3  with 4 bit rotation. 
         [0079]    Dependent upon the determined value of the input vector bits, an updated key  230   b  is derived based on the value of the original key and the output. The updated key may then be further modified by analyzing the bit values of bits cd of the next chunk of the input vector  270   b , leading to concatenation of the left  232   b  and right  234   b  hand sides (only right hand side  234   b  shown in  FIG. 5 ) of the updated key  230   b  (again with a rotation applied dependent upon the value of the bits cd) with an updated output value  252   b . Alternative paths  270   b   1 ,  270   b   2 ,  270   b   3 ,  270   b   4  are possibilities depending upon the value of the bits cd of the input vector  270  for the second iteration. 
         [0080]    The size of the part of the input vector  270  may allow a greater number of possible transformations or updates of the key dependent upon the value of the part of the input vector. For example, using an 8 bit part of the input vector provides a multitude of paths for the key update function. Using a larger bit value for the part of the input vector also allows a shorter process. 
         [0081]    The present disclosure reduces the need for key randomness. It allows encryption based upon any constant. By varying the value of the input vector, the final updated key  230   k  is also varied. Additionally, for every key there is only one input and therefore only a single power measurement. Because of this, statistical side-channel attacks like differential power attacks are ineffective. 
         [0082]    The present disclosure describes processing the input in a bit wise manner. Accordingly the output for an arbitrary length input would be a n-bit output. In general, the constant is encrypted using a key. In the present example a value of 0 is used, however the input can be of arbitrary length and value. After the encryption of the constant using the key, the input factor is subdivided and used to modify the key in a stepwise manner. This creates a treelike structure for the key. This also creates a pseudo-random function. 
         [0083]    The key update function of the key update module  260  may be applied to any encryption protocol. By only producing a single power trace per key, side-channel attacks are prevented. Additionally, there is no randomness that is uncontrollable from the outside. Every transaction can be identically replayed. Provided the same input vector  270  is provided, the final updated key  230   k  will be the same. 
         [0084]    Unlike other encryption rekeying methods there is no session key. Instead, for each iteration of the bit value of the input vector, the previous key is overwritten. Accordingly, it is not possible to determine or recreate the previous key from the session key and therefore the master key is not vulnerable. 
         [0085]    Another application of the present disclosure may be in authentication. Referring to  FIG. 2 , the proximity integrated circuit chip is able to store a master key  230  within the client memory  146 . Upon contact between the client device  140  and the host device  120 , a standard authentication protocol may be used to determine that both the host and client are mutually trustworthy. The client device  140  can apply the pseudo-random function described above using a received input vector from the host device  120  to generate an output. This output can at this stage be seen as a message authentication code (MAC) and can then be transferred to the host device via the I/O and card interfaces  134 ,  142 . 
         [0086]    From reading the present disclosure, other variations and modifications will be apparent to the skilled person. Such variations and modifications may involve equivalent and other features which are already known in the art of cryptography and which may be used instead of, or in addition to, features already described herein. 
         [0087]    Although the appended claims are directed to particular combinations of features, it should be understood that the scope of the disclosure of the present invention also includes any novel feature or any novel combination of features disclosed herein either explicitly or implicitly or any generalisation thereof, whether or not it relates to the same invention as presently claimed in any claim and whether or not it mitigates any or all of the same technical problems as does the present invention. 
         [0088]    Features which are described in the context of separate embodiments may also be provided in combination in a single embodiment. Conversely, various features which are, for brevity, described in the context of a single embodiment, may also be provided separately or in any suitable sub-combination. The applicant hereby gives notice that new claims may be formulated to such features and/or combinations of such features during the prosecution of the present application or of any further application derived therefrom. 
         [0000]    For the sake of completeness it is also stated that the term “comprising” does not exclude other elements or steps, the term “a” or “an” does not exclude a plurality, a single processor or other unit may fulfil the functions of several means recited in the claims and reference signs in the claims shall not be construed as limiting the scope of the claims.