Abstract:
The invention relates to a method of authentication of a contactless communication circuit, PICC, by a contactless communication terminal, PCD. Within the PICC, a first number is generated by encryption of a second random number, and the first number is sent to the PCD. Within the PCD, a third number is generated by decryption of the first number. Also within the PCD, a fourth number is determined and encrypted to generate a fifth number. The fifth number has first and second portions. Back within the PICC, a sixth number is determined, which is used in the determination of a seventh number. The seventh number is determined by encryption by a cipher block chaining operating mode of the sixth number with an initialization vector equal to the first portion. If the seventh number is different from the second portion, the authentication is interrupted.

Description:
BACKGROUND 
     Technical Field 
       [0001]    The present disclosure generally relates to electronic circuits and, more specifically, to contactless communication circuits. The present disclosure more specifically aims at the authentication of a contactless communication circuit by a contactless communication terminal. 
       Description of the Related Art 
       [0002]    The communication over a contactless link between a proximity coupling device (PCD), for example, a contactless terminal (Contactless Reader), and a contactless device (Proximity Device—PD), particularly a contactless integrated circuit (Proximity Integrated Circuit—PIC) or a contactless integrated circuit card (Proximity Integrated Circuit Card—PICC), generally starts by an operation of mutual authentication of the proximity device and the proximity coupling device. 
         [0003]    The authentication operation comprises a succession of steps of data exchange between the proximity coupling device and the proximity device and of steps of calculation by the proximity coupling device and the proximity device. Some of these steps may be vulnerable to attacks aiming, in particular, at recovering information relative to the encryption method implemented by the proximity device. 
       BRIEF SUMMARY 
       [0004]    It would be desirable to better protect the steps of an operation of authentication of a proximity device by a proximity coupling device. 
         [0005]    Thus, an embodiment provides a method of authentication of a contactless communication circuit by a contactless communication terminal, successively comprising:
       a first phase comprising the determination by the contactless communication circuit of a first number, the first phase ending with the transmission of the first number by the contactless communication circuit to the contactless communication terminal;   a second phase comprising the determination by the contactless communication terminal of a second number, by decryption of the first number by using a first key, the determination by the contactless communication terminal of a third number based on the second number and the determination by the contactless communication terminal of a fourth number by encryption of the third number by using the first key, the second phase ending with the transmission of the fourth number by the contactless communication terminal to the contactless communication circuit; and   a third phase comprising the decryption by the contactless communication circuit of the fourth number by using the first key to obtain the third number and the interruption by the contactless communication circuit of the authentication if a sixth number obtained from the third number is different from a seventh number,   wherein the first phase comprises no encryption operation using the first key.       
 
         [0010]    According to an embodiment, the seventh number is determined by the contactless communication circuit based on an eighth number obtained by decryption by the contactless communication circuit of the first number by using the first key. 
         [0011]    According to an embodiment, the method comprises, at the first phase, determining a ninth number, the ninth number being random, with no operation of encryption by the contactless communication circuit. 
         [0012]    According to an embodiment, in the first phase, the first number is equal to the ninth number. 
         [0013]    According to an embodiment, in the first phase, the first number is obtained by encryption by the contactless communication circuit of the ninth number by using a second key different from the first key, the second key having the same size as the first key, the encryption algorithm using the second key being the same as the encryption algorithm using the first key. 
         [0014]    According to an embodiment, in the first phase, the first number is obtained by encryption by the contactless communication circuit of a tenth non-random number by using a third key which is random, the third key having the same size as the first key, the encryption algorithm using the third key being the same as the encryption algorithm using the first key. 
         [0015]    According to an embodiment, in the first phase, the contactless communication circuit randomly carries out the steps of: 
         [0016]    a) determining the first number as being equal to the result of the encryption of the ninth number with the first key; 
         [0017]    b) determining the first number as being equal to the eighth number. 
         [0018]    According to an embodiment, the method further comprises, at step a), determining the eighth number as being equal to the ninth number and, at step b), performing an encryption operation using a fourth key different from the first key, the fourth key having the same size as the first key, the encryption algorithm using the fourth key being the same as the encryption algorithm using the first key. 
         [0019]    According to an embodiment, the method further comprises, in the third phase, the carrying out of a step c) by the contactless communication circuit, step c) comprising, when step a) is carried out, performing a decryption operation using a fifth key different from the first key, the fifth key having the same size as the first key, the decryption algorithm using the fifth key being the same as the encryption algorithm using the first key and step c) comprising, when step b) is carried out, determining the eighth number by decryption by the contactless communication circuit of the first number by using the first key. 
         [0020]    According to an embodiment, the method successively comprises in the first phase, if a Boolean variable is true, the determination by the contactless communication circuit of the first number as being equal to the result of the encryption of the ninth number with the first key and, if the Boolean variable is false, the reuse by the contactless communication circuit of the last determined value of the first number and comprising setting the Boolean variable to the false state. 
         [0021]    According to an embodiment, the method further comprises, in the third phase, the setting by the contactless communication circuit of the Boolean variable to the true state if the sixth number obtained from the fourth number is equal to the seventh number. 
         [0022]    According to an embodiment, the method comprises, in the second phase, the determination by the contactless communication terminal of a eleventh number, the eleventh number being random, and the determination by the contactless communication terminal of an twelfth number based on the second number, the third number corresponding to the juxtaposition of the eleventh number and of the twelfth number. 
         [0023]    According to an embodiment, the method further comprises, in the third phase, the determination by the contactless communication circuit of an thirteenth number based on the third number, the determination of a fourteenth number by encryption of the thirteenth number with the first key, the third phase ending with the transmission of the fourteenth number by the contactless communication circuit to the contactless communication terminal. 
         [0024]    Another embodiment provides a method of authentication of a contactless communication circuit by a contactless communication terminal, successively comprising:
       a first phase comprising the determination by the contactless communication circuit of a first number equal to the result of the encryption of a second number with a first key, the second number being a random number, the first phase ending with the transmission of the first number by the contactless communication circuit to the contactless communication terminal;   a second phase comprising the determination by the contactless communication terminal of a third number by decryption of the first number by using the first key, the determination by the contactless communication terminal of a fourth number based on the third number and the determination by the contactless communication terminal of a fifth number by encryption of the fourth number by using the first key, the fifth number comprising at least first and second juxtaposed portions, the second phase ending with the transmission of the fifth number by the contactless communication terminal to the contactless communication circuit; and   a third phase comprising the determination of a sixth number by the contactless communication circuit based on the second number, the determination of a seventh number by encryption by a cipher block chaining operating mode of the sixth number by using the first key and an initialization vector equal to the first portion of the fifth number, and the interruption by the contactless communication circuit of the authentication if the seventh number is different from the second portion of the fifth number.       
 
         [0028]    According to an embodiment, the method further comprises, in the third phase, the decryption by the contactless communication circuit of the fifth number by using the first key to provide the fourth number. 
         [0029]    According to an embodiment, the method further comprises, in the third phase, the determination by the contactless communication circuit of an eighth number based on the fourth number, the determination of a ninth number by encryption of the eighth number with the first key, the third phase ending with the transmission of the ninth number by the contactless communication circuit to the contactless communication terminal. 
         [0030]    According to an embodiment, each encryption operation performed by the contactless communication circuit comprises providing at least one first message block and one second message block, providing a first encrypted message block by encryption by means of the first key of the result of the XOR function applied between the first message block and an initialization vector, and providing a second encrypted message block by encryption by means of the first key of the result of the XOR function applied between the second message block and the first encrypted message block. 
         [0031]    According to an embodiment, the method comprises, in the second phase, the determination by the contactless communication terminal of a tenth number, the tenth number being random, and the determination by the contactless communication terminal of an eleventh number based on the third number, the fourth number corresponding to the juxtaposition of the tenth number and of the eleventh number. 
         [0032]    According to an embodiment, the first phase comprises no encryption operation using the first key. 
         [0033]    Another embodiment provides a contactless communication circuit comprising a microprocessor programmed to implement the method previously defined. 
         [0034]    Another embodiment provides a microcircuit card comprising a circuit programmed to implement the method previously defined. 
     
    
     
       BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWINGS 
         [0035]    Non-limiting and non-exhaustive embodiments are described with reference to the following drawings, wherein like labels refer to like parts throughout the various views unless otherwise specified. One or more embodiments are described hereinafter with reference to the accompanying drawings. The foregoing and other features and advantages will be discussed in detail in the following non-limiting description of specific embodiments in connection with the accompanying drawings, among which: 
           [0036]      FIG. 1  very schematically shows an embodiment of a proximity communication system; 
           [0037]      FIG. 2  is a simplified block diagram of a usual example of a method of mutual authentication of a proximity device and a proximity coupling device; 
           [0038]      FIGS. 3 to 5  are simplified block diagrams of embodiments of a method of mutual authentication of a proximity device and a proximity coupling device; 
           [0039]      FIGS. 6 to 8  are simplified block diagrams of encryption circuits capable of implementing an encryption operation according to a block chaining operating mode; and 
           [0040]      FIG. 9  is a simplified block diagram of another embodiment of a method of mutual authentication of a proximity device and a proximity coupling device. 
       
    
    
     DETAILED DESCRIPTION 
       [0041]    The same elements have been designated with the same reference numerals in the different drawings. For clarity, only those elements which are useful to the understanding of the described embodiments have been shown and are detailed. In particular, the exchanges between the proximity coupling device and a proximity integrated circuit once the authentication operation has been performed have not been detailed, the described embodiments being compatible with usual exchanges. Unless otherwise specified, expressions “approximately”, “substantially”, and “in the order of” mean to within 10%, preferably to within 5%. 
         [0042]    Embodiments have been described by taking as an example a contactless card forming a proximity integrated circuit card (PICC) and a contactless reader forming a proximity coupling device (PCD). They however more generally apply to any device used as a proximity coupling device and to any contactless communication integrated circuit where similar problems are posed. 
         [0043]      FIG. 1  very schematically shows an example of a contactless communication system of the type to which the described embodiments apply. 
         [0044]    A contactless communication terminal  10  or proximity reader (READER) generates an electromagnetic field. A contactless card  12  (CARD) located within the range of the reader detects the field and is then capable of exchanging information with reader  10 . 
         [0045]    Card  12  may host one or a plurality of applications. As an example, these applications may use a technology known as MIFARE. The application to be executed by the card may depend on the reader with which it communicates. Indeed, a reader is generally dedicated to an application (for example, bank, transport, access control, etc.) and the activation of a card in the field of the reader depends on the protocol accepted by the card. 
         [0046]    The MIFARE® technology has different variations, particularly the MIFARE® DESFIRE® or MIFARE PLUS® variations. MIFARE®, MIFARE® DESFIRE® and MIFARE PLUS® are registered trademarks of NXP B.V. in the USA. Such variations differ, in particular, by the implemented encryption methods. According to an example, the encryption method corresponds to a symmetrical encryption algorithm, for example, the AES algorithm (Advanced Encryption Standard) or the DES algorithm (Data Encryption Standard) using one key, two keys, or three keys for the encryption. 
         [0047]      FIG. 2  is a simplified block diagram of a usual example of a method of mutual authentication of a reader and a contactless chip card implementing the MIFARE DESFIRE or MIFARE PLUS technology. 
         [0048]    The method of authenticating the PICC card starts when the reader has detected the presence of the card and wants to authenticate the card. Other commands can be sent before the beginning of the authentication. The authentication method comprises successive phases S 1 , S 2 , S 3 , and S 4 , each comprising successive steps. 
         [0049]    The PCD and PD share the knowledge of a number of key values. At phase S 1 , the reader (PCD) selects a key (step  20 ) and transmits its identifier Id k  to the card (PICC) with an authentication control signal. The length of key k especially depends on the implemented encryption algorithm. As an example, the length of the key may be 8, 16, or 24 bits. 
         [0050]    The card generates a random number R b  of length RL (step  22 ). Length RL of random number R b  depends on the implemented encryption algorithm. As an example, length RL may be 8 or 16 bits. The card then determines an encrypted message A 1  by encryption of random number R b  by using key k with identifier Id k  (step  24 ) and transmits encrypted message A 1  to the reader. 
         [0051]    At phase S 2 , the reader decrypts encrypted message A 1  by using the same key k and obtains a random number R b   _   pcd . (step  26 ). The reader then determines a random number R′ b   _   pcd  (step  28 ) based on random number R b   _   pcd  by left rotating, in binary representation, the bits of random number R b   _   pcd  by a plurality of bits, for example, 8 bits. The reader generates a new random number R a   _   pcd  of length RL (step  30 ). The reader determines a message R a   _   pcd ∥R′ b   _   pcd  by concatenation of random number R a   _   pcd  and of random number R′ b   _   pcd  and determines an encrypted message B 1  by encryption of message R a   _   pcd ∥R′ b   _   pcd  by using key k (step  32 ) and transmits encrypted message B 1  to the card. 
         [0052]    At phase S 3 , the card decrypts encrypted message B 1  by using key k to obtain message R a   _   pcd ∥R′ b   _   pcd  (step  36 ). The card then determines a random number R′ b  (step  38 ) based on random number R b  by left rotating, in binary representation, the bits of random number R b  by a plurality of bits, for example, 8 bits. The card compares random numbers R′ b   _   pcd  and R′ b  (step  40 ). If the two random numbers R′ b   _   pcd  and R′ b  are not identical, the card interrupts the authentication operation, which fails (step  42 ). This corresponds to the authentication of the PCD by the PICC. If the two random numbers R′ b   _   pcd  and R′ b  are identical, the card then determines a random number R′ a  (step  44 ) based on random number R a   _   pcd  by left rotating the bits of random number R a   _   pcd  by a plurality of bits, for example, by 8 bits. The card determines an encrypted message A 2  by encryption of random number R′ a  by using key k (step  46 ) and transmits encrypted message A 2  to the reader. 
         [0053]    At phase S 4 , the method may comprise additional steps (step  48 ), particularly the authentication of the PICC by the PCD by verification of the A 2  message, determination of a session key used for subsequent operations of encryption and decryption by the reader and the card. The session key may be obtained from random number R a  and R b . 
         [0054]    For methods of card authentication by contact reading, it is known to provide the counting by the card of the number of unsuccessful authentication attempts and to stop the authentication operation when the number of unsuccessful attempts exceeds a threshold. However, the counting by the card of the number of unsuccessful attempts, which is a time-consuming operation, is generally not provided during a contactless card authentication method. Indeed, a person holding a fraudulent PCD close to the PICC could send invalid authentications until the card is blocked. For technologies that do not provide an unblocking mechanism, that leads to a permanent destruction of the card. Moreover, since data exchanges between the card and the reader only occur during the short time for which the card is close to the reader, the authentication operation should be as fast as possible. An attacker may thus carry out as many authentication attempts as he/she wants. 
         [0055]    A weakness of the previously-described authentication method is that an attacker can repeat the previously-described steps carried out by the card at phase S 1  of the same key k. Each time, a new random number R b  and a new encrypted message A 1  are determined. The analysis of a limited number of side channel attack traces and the obtained encrypted messages A 1  enables to considerably reduce the key space of possible keys k without then requiring to execute for each repetition the other phases of the authentication method. The fact that the PD generates new random numbers provides the attacker with an interesting distribution of traces. The attacker may then carry out a brute force attack on the reduced key space. The attacker knows that the attack has succeeded when the comparison performed by the card at step  40  of phase S 3  does not result in a failure. 
         [0056]    Another weakness of the previously-described authentication method is that the encrypted message B 1  used by the card at phase S 3  may be imposed by the attacker. An attacker can thus repeat decryption step  36  as many times as desired imposing an encrypted message B 1  of its choice, taking side channel attack traces. However, an attack using this weakness takes more time since the steps of phases S 1  and S 2  have to be carried out before each attempt. 
         [0057]    Embodiments of an authentication method will be described where the steps executed at phase S 1  by the card are modified to prevent an attacker from using these steps to obtain sufficient information relative to key k. The previously-described weakness relative to the steps carried out by the card at phase S 1  can then no longer be used by an attacker. 
         [0058]      FIG. 3  is a simplified block diagram of an embodiment of a method of authentication of a PICC card by a PCD reader. The present embodiment of the authentication method comprises the steps of the authentication method previously described in relation with  FIG. 2 , with the difference that steps  22  and  24  are replaced with a step  50  where number A 1  is directly obtained by generation of a random number of length RL. The present embodiment further comprises, at phase S 3 , before step  36 , a step  52  of determining random number R b  by decryption of number A 1  by using key k by the card. 
         [0059]    According to a variation, the present embodiment previously-described step  50  is replaced with a step of determining encrypted message A 1  by encryption of the random number by using a dummy key different from key k. 
         [0060]    According to another variation, at step  50 , encrypted message A 1  is obtained by encryption of a given number, for example, 0, with a key equal to a random number of length RL. 
         [0061]    The previously-described weakness relative to the steps carried out by the card at phase S 1  can no longer be used by an attacker since these steps no longer comprise an encryption step using key k. 
         [0062]      FIG. 4  is a simplified block diagram of another embodiment of a method of card authentication by a reader. In the present embodiment, the method previously described in relation with  FIG. 2  or the method previously described in relation with  FIG. 3  is randomly implemented. 
         [0063]    More specifically, the embodiment of the authentication method comprises the steps of the authentication method previously described in relation with  FIG. 2  with the difference that steps  22  and  24  are replaced with steps  60 ,  62 ,  64 , and  66  described hereafter. The card generates a random number R 1  of length RL (step  60 ). The card determines a random bit c (step  62 ) and compares it with “0” (step  64 ). If bit c is equal to “0”, the card determines encrypted message A 1  by encryption of random number R 1  by using key k (step  66 ) and transmits encrypted message A 1  to the reader. The random number R b  used at phase S 3  is then equal to random number R 1 . If bit c is equal to “1”, number A 1  transmitted by the card to the reader is equal to R 1  and the card performs an encryption operation by assigning to number R b  the result of the encryption of random number R 1  by using a dummy key different from key k (step  68 ). The result of this encryption is not used, but assures that using a side channel attack, the case in which c is equal to “1” provides the same trace as the case in which c is equal to “0”. 
         [0064]    The present embodiment of the authentication method further comprises, at phase S 3 , before step  36 , the additional steps  70 ,  72 , and  74  described hereafter. The card compares random bit c with “0” (step  70 ). If bit c is equal to “0”, that is, when step  66  has been executed at phase S 1 , the card executes a decryption operation by assigning to A 1  the result of a decryption of random number R 1  by using a dummy key different from key k (step  72 ). The result of this decryption is not used, but assures that using a side channel attack, the case in which c is equal to “1” provides the same trace as the case in which c is equal to “0”. 
         [0065]    If bit c is equal to “0”, that is, when step  68  has been executed at phase S 1 , the card determines random number R b  by decryption of number A 1  by using key k (step  74 ). 
         [0066]    The above-described weakness relative to the steps carried out by the card at phase S 1  can no longer be used by an attacker since these steps no longer comprise an encryption step using key k. Further, an encryption step is always performed at phase S 1  and a decryption step is always performed at phase S 2 , even if these steps are not necessarily useful according to the value of bit c. This enables to prevent a side channel attack since an attacker cannot tell useful encryption/decryption steps from non-useful ones. 
         [0067]      FIG. 5  is a simplified block diagram of another embodiment of a method of card authentication by a reader. In the present embodiment, the card carries out previously-described steps  22  and  24  only if the last authentication procedure has occurred correctly. When the last authentication procedure has not occurred correctly, the random number R b  and the encrypted message A 1  used in the last authentication procedure which has occurred correctly are used again. 
         [0068]    More specifically, the present embodiment of the authentication method comprises the steps of the authentication method previously described in relation with  FIG. 2  and further comprises a step  80  at which the card determines whether a Boolean variable ok is true, variable ok being initialized to the true value at the first card authentication attempt. If variable ok is in the true state, steps  22  and  24  are executed by the card. If variable ok is in the false state, the card uses again the values R b  and A 1  determined at the previous authentication procedure (step  82 ). After having executed steps  22  and  24  or step  82 , the card sets variable ok to the false state (step  84 ). The present embodiment further comprises, after steps  36  to  46 , a step  86  at which the card sets variable ok to the true state. 
         [0069]    With the present embodiment, an encryption step at phase S 1  can only be performed by the card if the previous authentication procedure has occurred correctly. An attack where phase S 1  would be repeated without however resulting in a successful authentication, particularly to determine information relative to key k, would not cause, each time phase S 1  is repeated, the carrying out of a new encryption step, which limits the useful information that the attacker may expect to recover. 
         [0070]    An encryption/decryption operation is made by using at least one encryption/decryption module. An encryption/decryption module has a cipher block length, BL, and is able to encrypt/decrypt messages of the same length as the cipher block length. For example, for the DES algorithm, BL can be 8 bits and for the AES algorithm, BL can be 16 bits. For messages that are longer than BL and corresponds to a multiple of BL, the encryption/decryption operation can be made by cipher block chaining (CBC). —Another embodiment will now be described, which is adapted to the case where the encryption or decryption method used to determine encrypted messages A 1  and B 1  implements an operating mode by cipher block chaining (CBC). 
         [0071]      FIG. 6  is a block diagram of an encryption circuit  90  illustrating the principle of an encryption operation according to a CBC operating mode. Circuit  90  comprises encryption modules MOD 1 , MOD 2 , MOD 3 , three modules being shown in  FIG. 6 . Each encryption module MOD 1 , MOD 2 , MOD 3  can make an encryption operation with the same key k. Circuit  90  receives, for each module MOD 1 , MOD 2 , MOD 3 , a message block to be encrypted E 1 , E 2 , E 3  and provides, for each module MOD 1 , MOD 2 , MOD 3 , an encrypted message block O 1 , O 2  and O 3 . Each module MOD 1 , MOD 2 , MOD 3  receives a number IN 1 , IN 2 , IN 3  and provides an encrypted message block O 1 , O 2 , O 3  by encryption of number IN 1 , IN 2 , IN 3  by using a key which is the same for all modules MOD 1 , MOD 2 , MOD 3 . 
         [0072]    The operating mode is called block chaining mode since each number which is encrypted by a module corresponds to the result of the XOR function applied between the input number of the module and the encrypted message block provided by the previous module. As shown in  FIG. 6 , number IN 3  is the result of the XOR function applied between numbers E 3  and O 2  and number IN 2  is the result of the XOR function applied between numbers E 2  and O 1 . For first module MOD 1 , number IN 1  is obtained by binary addition of number E 1  and of a number IV called initialization vector. 
         [0073]      FIG. 7  is a block diagram of an encryption circuit  92  of the type shown in  FIG. 6  capable of being implemented in the previously-described embodiments in the case where the encryption method corresponds to the AES algorithm or to the DES algorithm using one key or two keys. The length of each random number used by the reader or the card is then equal to the length of the number which can be encrypted by an encryption module, that is to say the cipher block length. 
         [0074]      FIG. 7  shows, as an example, the encryption operation to obtain encrypted message B 1  based on random numbers R a   _   pcd  and R b   _   pcd . Encrypted message B 1  has twice length RL and divides into two juxtaposed blocks, a first block B 1,1  and a second block B 1,2 , each having a length RL. Module MOD 1  receives the result of the XOR function applied between random number R a   _   pcd  and initialization vector IV and provides the first block B 1,1  of encrypted message B 1 . Module MOD 2  receives the result of the XOR function applied between random number R b   _   pcd  and encrypted message block B 1,1  and provides the second block B 1,2  of encrypted message B 1 . At the first encryption operation, initialization vector IV is, for example, equal to “0”. Second block B 1,2  is used, for example, as an initialization vector IV at the next encryption operation. As a variation, IV is set equal to “0” for each encryption operation. 
         [0075]      FIG. 8  is a block diagram of an encryption circuit  94  of the type shown in  FIG. 6  capable of being implemented in the previously-described embodiments in the case where the encryption method corresponds to the DES algorithm using three keys. Length RL, in binary representation, of each random number used by the reader or the card is then equal to twice the length BL. 
         [0076]      FIG. 8  shows, as an example, the encryption operation to obtain encrypted message B 1  based on random numbers R a   _   pcd  and R b   _   pcd . Encrypted message B 1  has four times length BL and divides into four juxtaposed blocks B 1,1a , B 1,1b , B 1,2a , and B 1,2b  of length BL. Random number R a   _   pcd  divides in two juxtaposed blocks R a   _   pcd,1  and R a   _   pcd,2  of length BL and random number R b   _   pcd  divides in two juxtaposed blocks R b   _   pcd,1  and R b   _   pcd,2  of length BL. Module MOD 1  receives the result of the XOR function applied between block R a   _   pcd,1  and initialization vector IV and provides the first block B 1,1a  of encrypted message B 1 . Module MOD 2  receives the result of the XOR function applied between block R a   _   pcd,2  and encrypted message block B 1,1a  and provides the second block B 1,1b  of encrypted message B 1 . Module MOD 3  receives the result of the XOR function applied between random number R b   _   pcd,1  and encrypted message block B 1,1b  and provides the third block B 1,2a  of encrypted message B 1 . Module MOD 4  receives the result of the XOR function applied between block R b   _   pcd,2  and block B 1,2a  and provides the fourth block B 1,2b  of encrypted message B 1 . Fourth block B 1,2b  is used, as example, as an initialization vector IV at the next encryption operation. The first and second juxtaposed blocks B 1,1a  and B 1,1b  form a first block B 1,1  of length RL of encryption message B 1  and the third and fourth juxtaposed blocks B 1,2a  and B 1,2b  form a second block B 1,2  of length RL of encrypted message B 1 . 
         [0077]      FIG. 9  is a simplified block diagram of an embodiment of a method of authentication of a card by a reader. 
         [0078]    In the present embodiment, at phase S 3 , additional steps are provided so that an attacker can no longer control the number used for an encryption or decryption operation. 
         [0079]    More specifically, the embodiment of the authentication method comprises the steps of the authentication method previously described in relation with  FIG. 2  with the difference that, at phase S 3 , step  38  is not present and that the card carries out at phase S 3  additional steps  100 ,  102 ,  104 , and  106  before step  36 , described hereafter. The card determines random number R′ b  (step  100 ) based on random number R b  by left rotating, in binary representation, the bits of random number R b  by a plurality of bits, for example, 8 bits. The card implements the encryption method (step  102 ) by using key k and the random number R′ b  which is supplied, according to its length, to the first module or to the first modules of the encryption circuit. For the example of encryption method illustrated in  FIG. 7  where each encryption module can receive a number having the same length RL as random number R′ b , random number R′ b  is supplied to the first encryption module. For the example of encryption method illustrated in  FIG. 8  where each encryption module can receive a number having half length RL of random number R′ b , the first block of random number R′ b  is supplied to the first encryption module and the second block of random number R′ b  is supplied to the second encryption module. Further, the encryption method is carried out by using as an initial vector IV the last block of encrypted message B 1  which is associated with random number R a   _   pcd , that is, block B 1,1  of encrypted message B 1  for the example of encryption method illustrated in  FIG. 7  and block B 1,1b  of encrypted message B 1  for the example of encryption method illustrated in  FIG. 8 . The first module or the first modules of the encryption circuit then provide an encrypted message block B 1,2   _   picc  of length RL. The card then compares second block B 1,2  of encrypted message B 1  with encrypted message block B 1,2   _   picc  (step  104 ). If the second block of encrypted message B 1  is different from number B 1,2   _   picc , the card interrupts the authentication phase (step  106 ). If the two numbers are identical, the card carries on at previously described step  36 . 
         [0080]    As a variation, it is possible for steps  40  and  42  not to be present. 
         [0081]    An attacker who desired to perform an attack at phase S 3  may impose the encrypted message B 1  used by the card at phase S 3 . However, the attacker does not have access to random number R′ b . Since a XOR function is applied between random number R′ b  and a block of encrypted message B 1 , the attacker does not control the number used by the encryption modules during the encryption operation. 
         [0082]    The previously-described embodiments are implemented on the card side and are transparent for the reader. They require no modification on the reader side. The cards thus formed (programmed) are thus compatible with existing readers. 
         [0083]    Various embodiments have been described. Various alterations and modifications will occur to those skilled in the art. In particular, although the embodiments have been described in relation with a microcircuit card, they are compatible with a forming in any proximity communication device where similar problems are posed, for example, a cell phone equipped with a NFC router operating in card mode. Further, although the embodiments have been more specifically described in relation with an example of application to MIFARE transactions, they transpose to other applications where similar problems are posed. Further, the practical implementation of the described embodiments is within the abilities of those skilled in the art based on the functional indications given hereabove and by using or by programming circuits usual per se. In particular, a contactless integrated communication circuit to which these embodiments apply generally comprises at least one microprocessor, one or a plurality of volatile and non-volatile memory units, a proximity communication interface and, often, other circuits according to the hosted applications. 
         [0084]    Various embodiments with different variations have been described hereabove. It should be noted that those skilled in the art may combine various elements of these various embodiments and variations without showing any inventive step. In particular, the embodiment previously described in relation with  FIG. 9  may be implemented with any of the embodiments previously described in relation with  FIGS. 3, 4 and 5 . 
         [0085]    The various embodiments described above can be combined to provide further embodiments. These and other changes can be made to the embodiments in light of the above-detailed description. In general, in the following claims, the terms used should not be construed to limit the claims to the specific embodiments disclosed in the specification and the claims, but should be construed to include all possible embodiments along with the full scope of equivalents to which such claims are entitled. Accordingly, the claims are not limited by the disclosure.