Patent Publication Number: US-2021165914-A1

Title: Cryptographic method for verifying data

Description:
TEHNICAL FIELD 
     The present invention relates to digital cryptography and to the security of computational and electronic devices, and in particular to digital signatures. 
     BACKGROUND 
     Computers and electronic apparatuses are often connected to a network, physically, wirelessly, by RFID, or by any other secure or unsecure means, and sometimes need to know the identity of the apparatus that has sent them certain data, for example in order to ensure that these data have not been transmitted by another apparatus, which intercepted them and modified them before sending them on to the legitimate recipient, or quite simply to identify beyond a shadow of a doubt the identity of the sender of the data, which is for example an automobile on a road network or an RFID tag worn by a competitor during a sporting event, or for any other reason why the identity of the sender of the data is important to the recipient. 
     The transmitted data may be sent entirely encrypted with a key attributed to the sender. However, the encryption of all of the data makes the use of single-use keys (one-time pads) difficult. Specifically, the encryption of all of the data is a method that uses keys that are as long as the data that they encrypt, and these keys must be renewed after use. 
     It is therefore necessary for computers or other electronic devices entering into communication, for example via the exchange of text, identifiers, numbers, computer programs, images or video or audio codes, to verify the identity of the sending device using the encryption of an amount of data smaller than the amount of data sent. It is for this reason that an electronic signature consisting in encrypting a hash of the data is used. The term “hash” is used to refer to the result of a hash function that, on the basis of an initial datum provided as input, computes a fingerprint that serves to rapidly, though incompletely, identify the initial datum. It is common to send, with the data, an encrypted hash that will then be decrypted by the recipient, then compared to the hash of the received data. MD5, SHA1 and SHA256 are algorithms conventionally used for such hashing operations. However, data hashes are generally much smaller in size than the original data, and it may be possible to create other data, similar but slightly different to the original data, having a hash equal to the hash of the original data. These data could therefore be substituted for the original data, without being rejected lay the procedure for verifying the hash. Any type of data may be substituted, but the detectability by the user of the substitution decreases as the complexity of the data increases (a long text, an audio file, a photo or a video). To make the substitution, it is not even necessary to decrypt the encrypted hash. It is enough to simply compute the hash of the original data. Furthermore, hash functions such as MD5 and SHA1 are hash functions that are at the present time relatively easy to bypass. 
     The quantum computers that are in the process of being developed should soon be capable of bypassing the security provided by hash functions, since they are capable of optimizing the start files so that they have a preset hash. 
     Methods for improving the security of systems using hashing techniques are known in the prior art. 
     Patent application CN101547184 uses a plurality of auxiliary authentication values that are exchanged between a server and users. 
     In the method proposed in patent application US2011/0246433, a hash of the data to be sent is generated and concatenated with the data chunk to be sent and a random number tag. 
     Patent application EP 1 421 548 describes a method for transmitting information, in which a message to be sent is concatenated with a random number then hashed. The result of the hashing is sent unencrypted to the other party. The message is sometimes transmitted as such or encrypted. The random number is always transmitted signed, and optionally encrypted, to the other party. The fact of not encrypting the hash when the message is itself not encrypted makes the transmission vulnerable to very powerful or quantum computers that are able to compute random numbers compatible with the unencrypted message and the result of the hash. Moreover, encrypting the entire message has the drawback, if such an encryption uses one-time pads, which are supposed to be uncrackable, of requiring both the two corresponding parties to have access to such shared keys. 
     SUMMARY 
     There is a need to further improve the security of hashing techniques, decreasing the probability of error in the verification of data, and, where appropriate, allowing a more reliable authentication of the sender of these data. 
     The invention in particular aims to meet this need, and it achieves this aim by virtue of a method, implemented by a least one apparatus, for comparing a first dataset and second dataset, in particular with a view to determining whether these two datasets are identical, this method comprising the following steps:
         a) mixing a number, called the mixer number, with the first dataset, using a mixing function, in order to obtain mixed data,   b) hashing the mixed data using a hash function, and   c) comparing the hash thus obtained in step b) with a third dataset assumed to be the hash of the second dataset mixed with the same mixer number as that used in step a) and with the same mixing function.       

     By virtue of the invention, and in particular of the mixing of the first dataset with a mixer number prior to the hashing, it becomes very improbable to be able to create data similar to this first dataset that, after having been mixed with the same mixing number, will have the same hash is the mixed first dataset. 
     Preferably, the method according to the invention does not require two datasets to be simultaneously present in the apparatus. 
     Preferably, the mixer number is generated randomly. 
     The mixer number is preferably generated by the apparatus. As a variant, the mixer number is generated by another trusted apparatus. 
     The generation of the mixer number may be based on a pair of input values that are physical quantities at least one of which varies continuously, such as for example the temperature and the time, or on a quantum phenomenon. For example, such a generation may be based on which of two Young&#39;s slits a photon chooses to use to pass through a plate. 
     Preferably, the mixing operation in step a) is carried out by the apparatus. As a variant, the mixing is carried out by another trusted apparatus. 
     The mixing function combines the first dataset and the mixer number. It is, preferably, an XOR logic function that adds the bits of the first dataset and those of the mixer number, one by one. Since the size of the mixer number is generally smaller than the size of the first dataset, it is possible to add via an XOR the bits of the mixer number to the first or last bits of the first dataset. 
     The mixer number may have the same size as the first dataset. In this case, the addition via the XOR function is carried out on all the bits, one by one. 
     Alternatively, the mixing function consists in adding the mixer number to the end of the first dataset. 
     The mixing function may even be an encrypting function using the mixer number as encryption key to encrypt the first dataset. 
     Preferably, the data in step b) are hashed by the apparatus. As a variant, the hashing is carried out by another trusted apparatus. 
     Preferably, the hash function is chosen among SHA1, SHA2, SHA256 and MD5 and the Jenkins function. 
     A first variant of the method according to the invention is a method for verifying with the apparatus the integrity of a message originating from a sender, the method comprising:
         i. the apparatus receiving the message and an identifier of the message, said message forming the first dataset,   ii. generating the mixer number,   iii. implementing steps a) and b), in which the message is mixed with the mixer number then hashed,   iv. optionally encrypting the mixer number,   v. the apparatus sending the identifier of the message and the optionally encrypted mixer number to the sender of the message,   vi. the apparatus receiving the encrypted third dataset, preferably with the identifier of the message, originating from the sender,   vii. decrypting the third dataset, and   viii. implementing step c), the integrity of the message being ensured if the third dataset decrypted in step vii and the hash obtained in step b) are identical.       

     By “integrity” of the message, what must be understood is its non-alteration, for example by a malicious third-party that intercepted it during its transmission. 
     The identifier of the message may be a sequence of alphanumeric characters and/or signs able to be converted into a digital word via an ASCII code inter alia. 
     The identifier of the message may contain the identifier of the sender and an order number of the message. 
     The authentication of the sender is in particular ensured by the decrypting operation in step vii. 
     This first variant of the invention makes it possible to ensure both the integrity of the received message and of the identity of the sender of the message. 
     The steps relating to sending and receiving the data may be carried out using the same communication protocol, or using different communication protocols. For example, the data received in step i are received via Wi-Fi, the data sent in step v are sent via 4G and the data received in step vi are received via WiMAX. 
     In step i, the apparatus may also receive an identifier of the sender. This identifier is useful if the apparatus is able to receive messages from various senders, such an identifier allowing it to choose the encryption keys to be used to encrypt or decrypt the information exchanged with the sender during the encrypting and decrypting operations described in this first variant of the invention. 
     Preferably, the method according to this first variant comprises, between steps v and vi:
         the sender receiving the identifier of the message and the optionally encrypted mixer number,   optionally decrypting the mixer number,   identifying, using the identifier of the message, the message sent to the apparatus,   mixing the message with the optionally decrypted mixer number using the mixing function,   hashing the data resulting from the preceding step using the hash function,   encrypting the hash resulting from the preceding step, and   sending to the apparatus the encrypted hash preferably with the identifier of the message.       

     The optional encryption of the mixer number in step iv is preferably carried out by the apparatus. 
     The optional encryption of the mixer number makes it possible to prevent this number from being intercepted and altered by a malicious third-party. 
     Preferably, the optional encryption of the mixer number is carried out using a single-use key of a size at least equal to that of the number. Since the key is single-use, a new key is used each time a mixer number is sent. 
     The encryption may also be carried out using a symmetric key. The symmetric encryption key is kept secret between the sender and the apparatus, and is preferably renewed after a certain number of transmissions. 
     Alternatively, the optional encryption of the mixer number is asymmetric, being carried out either using a public key of the sender known to the apparatus, so as to allow the decryption by the sender using its associated private key, or using a private key of the apparatus the public key of which is known to the sender. 
     Thus, a third party is prevented from learning or altering the mixer number. 
     Preferably, the decryption in step vii is carried out by the apparatus. 
     Preferably, the decryption in step vii is carried out using a symmetric key, if the encryption in step iv is carried out using a single-use key. 
     Alternatively, the decryption in step vii is carried out using a single-use key, if the encryption in step iv is carried out using a symmetric key. 
     The decryption in step vii may also be carried out using other methods, for example using a public key known to the apparatus, associated with a private key of the sender having served to encrypt the hash received in step vi. Thus, the apparatus is capable of certifying the identity of the sender. 
     The mixer number may have the same size as the symmetric key that serves to encrypt it, if such a symmetric key is used, and also the same size as the hash. 
     Preferably, the private, symmetric and single-use encryption keys and the mixer numbers are unguessable and unobservable by third-party devices, to prevent listening to the data sent by the sender or the apparatus from making it possible to generate and transmit fraudulent second datasets that would cause the integrity of messages received by the apparatus but transmitted by a sender other than that legitimately supposed to hold said keys to be wrongly recognized. 
     If the encryption key X of the mixer number x is known, then the hash of the mixed message may be known, because it is enough to decrypt the encryption of x and to compute the mixture of the message before hashing it. The key Y encrypting the hash may then also be guessed or known to belong to a small universe, the hash of the mixed message and its encryption with Y both being known or observable. The encryption key Y is therefore a function F of the encryption key X, or else the encryption key Y belongs to a universe depending on the encryption key X. The observation of a plurality of transmissions causes a plurality of functions to appear, and the values of the keys X and Y are at the intersection of these functions. It is preferable to avoid this situation. It is therefore recommended either to use, for the key X or the key Y, values that change over the course of the transmissions, or to use encrypting functions such that, for each observation of exchanges of the triplet “message, encrypted number, encrypted hash”, the universe of the keys Y for each possible X is large; this making the universe resulting from the intersection of these universes deducible at each observation large. It is not recommended to take, for the key Y, the randomly generated mixer number x. Specifically, if the mixer number x is used as encryption key Y, or indeed if the key Y is computed depending on the mixer number x using a defined formula, knowing the encrypted value C of the mixer number x encrypted with the key X, the mixer number x, and therefore Y, becomes another function G of the key X; and the keys X and Y would be at the intersection of the function and, of this new function G. Preferably, the key X or the key Y is renewed after each exchange. 
     The apparatus may furthermore comprise a counter of consecutive failed verification attempts that triggers a blockage thereof when a defined number is reached, the apparatus possibly being unblocked during the renewal of the encryption key used to encrypt the mixer number or the encryption key used to encrypt the hash. 
     A second variant of the method according to the invention is a method for verifying with the apparatus the integrity of a message originating from a sender, the method comprising:
         i. the apparatus receiving the message, the encrypted third dataset and the encrypted mixer number,   ii. decrypting the mixer number and the third dataset, and   iii. implementing steps a) to c), the integrity of the message being ensured if the hash obtained in step b) and the third dataset decrypted in step ii are identical.       

     Preferably, the method according to this second variant of the invention comprises, before step i:
         the sender generating the mixer number,   mixing the mixer number with the message, using the mixing function,   hashing the data resulting from the preceding step using the hash function,   encrypting the hash resulting from the preceding step and forming the third dataset,   encrypting the mixer number, and   sending, to the apparatus, the message, the encrypted third dataset and the encrypted mixer number.       

     These steps are carried out by the genuine sender and allow the alteration of the message by an unauthorized third party to be detected. 
     The decryption in step ii of the mixer number and of the third dataset is preferably carried out by the apparatus. 
     Preferably, the encryption of the mixer number is carried out using a single-use key, and the encryption of the third dataset is carried out using a symmetric key, the symmetric key preferably being renewed occasionally. 
     Alternatively, the encryption of the mixer number is carried out using a symmetric key, and the encryption of the third dataset is carried out using a single-use key, the symmetric key preferably being renewed occasionally. 
     The encryption of the mixer number and the encryption of the third dataset may also be of the same type, or of different types, these types of encryption possibly employing symmetric keys, or asymmetric keys. 
     If a pair of asymmetric keys is used for the encryption of the mixer number, the private key of said pair is preferably kept by the apparatus, the corresponding public key then being known to the sender. 
     The encryption of the third dataset is, preferably, carried out using a private key kept by the sender, the corresponding public key then being known to the apparatus. 
     Thus, by decrypting the mixer number and the third dataset, the apparatus is capable of certifying the identity of the sender. 
     The encryption of the mixer number and that of the third dataset may be carried out using the same encrypting function, in particular when the encryption of the mixer number is asymmetric. 
     Alternatively, the encryption of the mixer number and that of the third dataset are carried out by two different encrypting functions. 
     Preferably, the types of encrypting functions to be used form part of the configuration of the sender and of the apparatus, prior to the setup of the communication between the latter two. 
     A third variant of the method according to the invention is a method in which the first dataset is present in the apparatus and the second dataset is present in a second apparatus, the method comprising:
         i. implementing steps a) and b),   ii. encrypting the mixer number,   iii. the apparatus sending, to the second apparatus, the encrypted mixer number,   iv. the apparatus receiving an encrypted hash of the second dataset,   v. decrypting the encrypted hash, and   vi. implementing step c).       

     Preferably, the method according to this third variant of the invention comprises, between steps iii and iv:
         the second apparatus receiving the encrypted mixer number,   decrypting the mixer number,   creating a modified copy of the second dataset using the mixer number and the mixing function,   hashing the modified copy of the second dataset using the hash function,   encrypting the hash resulting from the preceding step and forming the third dataset, and   the second apparatus sending, to the apparatus, the encrypted hash of the second dataset.       

     The encryption of the mixer number in step ii and the decryption of the encrypted hash in step v are preferably carried out by the apparatus. 
     Preferably, the encryption of the mixer number is carried out using a symmetric encryption key shared with the second apparatus. 
     Preferably, the encryption of the hash is carried out using a single-use key and the encryption of the mixer number is carried out using a symmetric key that is renewed occasionally. 
     Alternatively, the encryption of the mixer number is carried out using a single-use key and the encryption of the hash is carried out using a symmetric key that is renewed occasionally. 
     The encryption of the mixer number and the encryption of the hash may also be of the same type, or of different types, these types of encryption possibly employing symmetric keys, in particular single-use keys, or asymmetric keys. 
     A fourth variant of the method according to the invention is a method for verifying that a dataset present in the apparatus has not been modified between two times d 1  and d 2 , this dataset forming, at the time d 1 , the first dataset and, at the time d 2 , the second dataset, the method comprising:
         i. implementing steps a) and b),   ii. the apparatus securely saving the mixer number and the hash obtained in step b),   iii. creating a modified copy of the second dataset using the mi r number and the mixing function,   iv. hashing the modified copy using the hash function to form the third dataset, and   v. implementing step c).       

     Advantageously, the method according to this fourth variant does not require the dataset to be kept securely. 
     Another subject of the invention is a computer-program product containing instructions readable by a processor of an apparatus for implementing the method according to the invention, according to any one of the variants defined above. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The invention will possibly be better understood on reading the following detailed description of nonlimiting examples of implementation thereof, and on examining the appended drawings, in which: 
         FIG. 1  schematically shows the data and functions necessary to implement the invention according to its first or its second variant, 
         FIG. 2  schematically illustrates an example of implementation of the invention according to its first variant, 
         FIG. 3  schematically shows an example of implementation of the invention according to its second variant, 
         FIG. 4  schematically illustrates the data and functions used to implement the invention according to its third variant, 
         FIG. 5  schematically shows an example of implementation of the invention according to its third variant, 
         FIG. 6  illustrates a scheme of implementation of the invention according to its fourth variant, 
         FIG. 7  schematically illustrates the data used to implement the example of  FIG. 8 , 
         FIG. 8  shows a first example of implementation of the invention applied to the verification of software packages, 
         FIG. 9  shows a second example of implementation of the invention applied to the verification of software packages, 
         FIG. 10  schematically illustrates devices and data used to implement the example of  FIG. 11 , 
         FIG. 11  illustrates an example of implementation of the invention applied to increasing the security of Internet browsers, 
         FIG. 12  schematically shows devices and data used to implement the example of  FIG. 13 , and 
         FIG. 13  shows an example of implementation of the invention applied to increasing the security of entails. 
     
    
    
     DETAILED DESCRIPTION 
       FIG. 1  schematically shows data and functions used to implement the invention according to its first or its second variant, in which a message  101  must be sent by a device A to a device B via a data transmission channel  109 , which channel may be secure or unsecure. 
     The device A may be a personal computer or a smartphone, and the device B an email server, the message  101  for example being an email sent by the computer or the phone via the Internet. 
     The device A may also be a server sending an email or a webpage, the device B then being a personal computer or a smartphone receiving said email or web page. 
     The device A may even be a measuring apparatus, for example for measuring the consumption of electricity, of gas or of water, or for measuring the wear of a part in a machine, the message  101  then being the result of such a measurement, and the device B a server that gathers the measurements and communicates with the measuring apparatus via a telecommunications network, for example an Internet of things, a Wi-Fi network or an LTE network. 
     The devices A and B may also be personal computers or smartphones. 
     The device A may be a web browser, the device B a web server and the message  101  a form filled in by the user of the browser A, the reception of the message not needing to be differentiated with respect to its transmission. 
     The devices A and B may each be equipped with a processor for executing the steps of the method according to the invention, and with a memory for saving the data required for this execution. 
     The device B has available to it encryption/decryption data  102 B, such as a private key. 
     The device A has available to it encryption/decryption data  102 A, such as the public key associated with the private key  102 B. 
     The device A also has available to it encryption/decryption data  103 A, such as a private key associated with a public key  103 B present in the device B. 
     The devices A and B possess random-number generators  104 A and  104 B, respectively, a common mixing function  105  and a common hash function  106 . 
     The devices A and B also have encrypting functions  107 A and  107 B, respectively, and decrypting functions  108 A and  108 B, respectively. 
       FIG. 2  illustrates an example of implementation of the method according to the first variant of the invention. 
     In step  201 , a first number, used to identify the message  101 , is generated by the device A. 
     It may optionally be generated using the random-number generator  104 A. 
     In step  202 , the first number is added to the message  101 . This addition may be a concatenation in any order defined by the communication protocol used between the two devices. 
     In step  203 , the device A sends the data resulting from step  202  to the device B via the data transmission channel  109 . 
     In step  204 , on reception of the data, the device B randomly generates a second number using the random-number generator  104 B. 
     In step  205 , the device B makes use of the mixing function  105  to mix the second number with the message  101 . By way of example, this mixing function is an XOR operating between the bits of the second number and the same number of bits of the message  101 . 
     The mixing function  105  is known by the device A. 
     In step  206 , the device B uses the hash function  106  to hash the data obtained in the preceding step. The device B also uses the public encryption key  103 B and the encrypting function  107 B, to encrypt the second number. 
     In step  207 , the device B sends to the device A via the channel  109  the first number and the encrypted second number. 
     In step  208 , on reception of the two numbers, the device A decrypts the second number using the private encryption key  103 A associated with the public key  103 B that was necessarily used for the encryption, and the decryption function  108 A associated with the encryption function  107 B. If the second number was not encrypted by the device B, its decryption will be erroneous. 
     With the first number, the device A is able to identify the message  101 , and to mix, using the mixing function  105 , the decrypted second number with the identified message  101 . 
     In step  209 , the device A uses the hash function  106  to hash the data resulting from the preceding step. 
     In step  210 , the device A uses the private encryption key  103 A and the encrypting function  107 A to encrypt the hash obtained in the preceding step. 
     In step  211 , the device A sends the encrypted hash to the device B via the channel  109 . 
     In step  212 , on reception of the encrypted hash, the device B decrypts it using the public encryption key  103 B associated with the private key  103 A that was necessarily used for the encryption, and the decrypting function  108 B associated with the encrypting function  107 A. 
     In step  213 , the device B compares the decrypted hash obtained in step  212  with the hash computed in step  206 . If the two hashes are identical, the device B concludes that the message  101  has not been altered. 
     Preferably, the second number used in the mixing must be kept secret until the hashes have been compared to carry out the verification, but this mixer number may be revealed before, if it is possible to trust the devices that compute the hashes so that the data are not modified between the moment at which the mixer number is revealed and the comparison of the hashes. 
       FIG. 3  illustrates a second example of implementation of the method according to the second variant of the invention, the message  101  needing to be sent by the device A to the device B. 
     The devices A and B may be personal computers or smartphones, and the message  101  may be an email. 
     The devices A and B may be neighboring automobiles, the exchanged data then being information relating to their movements, and the connection being achieved via a data link between the two vehicles, fur example a 5G link, a Low-Energy Bluetooth link, an ultrahigh frequency RFID link, a Lora link or a Sigfox link. 
     In step  301 , a random number is generated by the device A, using the random number generator  104 A. 
     In step  302 , the device A mixes the message  101  with the random number using the mixing function  105 . 
     In step  303 , the device A hashes the mixed data resulting from the preceding step, using the hash function  106 . 
     In step  304 , the device A encrypts the hash obtained in the preceding step using the encrypting function  107 A and the private encryption key  103 A. 
     In step  305 , the device A encrypts the random number using the encrypting function  107 A and the public encryption key  102 A. 
     In step  306 , the message  101 , the encrypted random number and the encrypted hash are sent to the device B via the transmission channel  109 , using the communication protocol agreed between the two devices. 
     In step  307 , on reception of the data, the device B uses the decrypting function  108 B and the public encryption key  103 B to decrypt the hash, and the private encryption key  102 B to decrypt the random number. 
     The device B is thus able to authenticate the device A. 
     In step  308 , the device B mixes the message  101  with the random number, using the mixing function  105 . 
     In step  309 , the device B hashes the mixed data resulting from the preceding step, using the hash function  106 . 
     In step  310 , the device B compares the hash that it computed with the decrypted hash, and makes a conclusion as regards the integrity of the message  101 . 
     In this example, the device B may forward the data received from device A to a third device. The device B decrypts, using the private key  102 B the random number that it received from the device A before encrypting it again using the public key of the third device. The device B then transmits, to the third device, the encrypted random number and the hash encrypted by the device A. The third device, which has available to it the public key of the device A, will be able to verify that this hash indeed came from the device A, insofar as the device B did not modify the hash encrypted by the device A. A given dataset may therefore be verified as authentic by many users. This option however exposes the security of the certification, a fraudulent device being able to decrypt the random number, and potentially modify the message so that it has the same random hash as the initial hash. This implementation is therefore preferably used to certify the communication between computer systems formed from elements protected against such a fraudulent use. 
       FIG. 4  schematically illustrates the data and functions required to implement the invention according to its third variant, to verify that a file  401 A present on a device A is identical to a file  401 B present on a device B. 
     The devices A and B communicate via a transmission channel  409  that is for example a Wi-Fi network. 
     The device A possesses a random-number generator  404 . 
     The devices A and B have in common a mixing function  405 , a hash function  406  and a symmetric encryption key  410 . 
     The device B has available to it an encrypting function  407 . 
     The device A has available to it a decrypting function  408 . 
       FIG. 5  illustrates a third example of implementation of the method according to the third variant of the invention. 
     In step  501 , a random number is generated in device A using the random-number generator  404 . 
     In step  502 , a modified copy of the file  401 A is created using the mixing function  405  and the random number. 
     In step  503 , the modified copy of the file  401 A is hashed using the hash function  406 . 
     In step  504 , the random number is encrypted using a symmetric encrypting algorithm and the symmetric encryption key  410 , and is sent to the device B via the transmission channel  409 . 
     In step  505 , on reception of the encrypted random number, the device B decrypts it and uses it in a mixing function  405  to create a modified copy of the file  401 B. By decrypting the random number, the device B can verify the identity of the device A. 
     In step  506 , the modified copy of the file  401 B is hashed with the same hash function  406 . 
     In step  507 , the hash of the modified copy is encrypted using the encrypting function  407  and the encryption key  410 . 
     In step  508 , the encrypted hash is sent to the device A. 
     In step  509 , on reception of the encrypted hash, the device A decrypts it using the decrypting function  408  and, the key  410 . 
     In step  510 , the device A compares the decrypted hash to the hash that it calculated in step  503 , and thus is able to verify whether the two files  401 A and  4018  are identical. 
       FIG. 6  illustrates a fourth example of implementation of the method according to the fourth variant of the invention, for verifying that a file has not been modified between two times d 1  and d 2 , while keeping completely secure between the two times a smaller dataset, this set comprising a number that is kept intact and secret and a hash that is kept intact and preferably secret. 
     In step  601 , a random number is generated. 
     In step  602 , at the time d 1 , a modified copy of the file is created using the generated random number and a mixing function, this function for example consisting in adding the random number to the end of the file. 
     In step  603 , a hash of the modified copy is created, for example using the SHA2 function. 
     In step  604 , the random number and the hash are stored securely and secretly, so that they cannot be modified and such that the random number is not disclosed to a third party. 
     In step  605 , at the time d 2 , the person or the device having access to the information stored in step  604  desires to compare the file at the time d 2  with the file used in steps  601  to  604 . To do this, the saved random number is used to create a second modified copy of the file at the time d 2 , using the same mixing function as in step  602 . 
     In step  606 , a hash of the second modified copy is created using the same hash function as in step  603 . 
     In step  607 , the hash created in the preceding step is compared with the stored hash in order to ensure that the file has not been modified between the times d 1  and d 2 . 
       FIG. 7  schematically illustrates the keys necessary to implement a fifth example, shown in  FIG. 8 , of the method according to the invention applied to the verification of software packages. 
     In the rest of the description, the operation of mixing a datum with a random mixer number followed by the hashing operation will be referred to as “random hashing” of this datum. 
     The example shown in the  FIG. 8  is implemented between two devices: a device A called the software distributor and a device B called the client device. 
     Device A possesses two keys  701  and  702 . 
       701  is a key serving to encrypt a hash, and is preferably private. 
       702  is a key serving to encrypt a random number, and is preferably public. 
     The device B possesses two keys  703  and  704 . 
       703  is a key used to decrypt a hash encrypted using the key  701 , and is preferably public. 
       704  is a key that is used to decrypt a random number encrypted using the key  702 , and is preferably private. 
     The pair of keys ( 701 ,  703 ) is what may be called the pair of keys of the software distributor, the latter being able to use it to communicate with all the apparatuses on which one of the software packages that it distributes is installed. 
     The pair of keys ( 704 ,  702 ) is what may be called the pair of keys of the client, the latter being able to use it for all the software packages that it verifies during their download. 
     In step  801 , the software distributor A carries out a random hashing of a software package to be transmitted to client B, in steps  301  to  305  described above with reference to  FIG. 3 . 
     The software distributor A uses the key  702  to encrypt the random number and the key  701  to encrypt the random hash of the software package. 
     In step  802 , the software distributor A sends, to the client B, a dataset containing the software package, the encrypted hash of the software package and the encrypted random number, over a transmission line that may be secure or unsecure. 
     In step  803 , on reception of the data set, the client B decrypts the hash with the key  703  and the random number with the key  704 . The client B then uses the random number to carry out the random hashing of the received software package. 
     In step  804 , if the computed hash is identical to the received hash, the client B permits the execution of the received software package, or replaces the preceding version of the software package with the version that it has just received. 
     In step  805 , for greater security, steps  803  and  804  are re-executed at pre-programmed time intervals in order to verify the authenticity of the software package. 
       FIG. 9  describes another possible implementation of the random hashing, for verifying that the software package in the process of being downloaded is permitted by a software package in the process of being executed on an apparatus. 
     In step  901 , the apparatus uses the method illustrated in  FIG. 2  to verify that a received software package originates from a reliable source. 
     In step  902 , steps  601  to  604  of  FIG. 6  are executed to create, in the apparatus, a secure signature of the software package. 
     In step  903 , before using the software package, steps  605  to  607  of  FIG. 6  are executed to verify that the software package has not been modified since step  902 . 
       FIG. 10  shows the objects necessary to implement the example illustrated in  FIG. 11 , allowing the security of data displayed by web browsers to be increased. 
     A web browser  1001  has available to it a pair of asymmetric keys that consist of a private key  1002   p  and a public key  1002   u.    
     A server  1003   s,  which delivers to the browser the public keys of secure Internet sites  1004   s,  possesses pair of asymmetric keys  1003  consisting of a private key  1003   p  and a public key  1003   u.    
     The Internet site  1004   s  possesses a pair of asymmetric keys  1004  consisting of a private key  1004   p  and a public key  1004   u.    
     It step  1101 , a user enters, into the address bar of the browser  1001  the URL address of the site that he desires to consult. 
     In step  1102 , the browser  1001  uses the pair of keys  1002  and sends, to the server  1003   s,  the following information:
         the URL, address of the site that the user desires to consult,   the public key  1002   u  of the browser, and   the URL address of the browser  1001  so that the server can respond thereto.       

     In step  1103 , the server  1003   s  uses the method according to the invention illustrated in  FIG. 2  to securely send to the browser the public key  1004   u  of the site  1004   s.    
     The public key  1002   u  will be used by the server to decrypt the second number that the navigator sends thereto during the exchanges. 
     In step  1104 , the browser  1001  sends to the site  1004   s  the following information:
         the name of the page of the site that the user desires to consult,   the public key  1002   u  of the browser, and   the U address of the browser so that the site can respond thereto.       

     In step  1105 , the server  1004   s  uses the method according to the invention illustrated in  FIG. 2  to send to the browser securely the requested page. 
       FIG. 12  shows the objects required. to implement the example illustrated in  FIG. 13 , which allows the security of emails to be increased. 
     A first electronic device A, which may possibly be a computer or a smart phone, allows emails  1200  taking the form of electronic files to be sent, received, archived, edited and displayed. 
     This first device A has access to a pair of asymmetric keys  1201   c  consisting of a public key  1201   u  and a private key  1201   p.    
     A second electronic device B allows emails  1200  to be sent, received, archived, edited and displayed. 
     This second device B has access to a pair of asymmetric keys  1202   c  consisting of a public key  1202   u  and a private key  1202   p.    
     A server  1203  gathers the identification numbers and the public keys of electronic devices, such as A and B, certified to preserve the integrity of received emails and the confidentiality of the random numbers associated with the random hashing method according to the invention. 
     The server  1203  has access to a pair of keys  1203   c  consisting of a public key  1203   u  and of a private key  1203   p.  It will be noted that this server may have a plurality of pairs of keys, each pair dedicated to the communication with one clearly defined electronic device. 
     A server  1204  associates the one or more electronic devices with the destination address  1205  of the email. 
     The server  1204  has access to a pair of keys  1204   c  consisting of a public key  1204   u  and of a private key  1204   p.  It will be noted that this server may have a plurality of pairs of keys, each dedicated to communication with one clearly defined electronic device. 
     In step  1301 , a user requests that the first device A send the email  1200  to the destination address  1205 . 
     In step  1302 , the first device A communicates with the server  1204 , the public key of which it knows, using the method according to the invention illustrated in  FIG. 2 , in order to determine the identifier and the public key of the device B associated with the address  1205 . After authentication of the first device A by the server  1204 , the latter sends to the first device A the identifier and the public key of the device B. This is also done using the method illustrated in  FIG. 2 , the server  1204  knowing the public key of the device A and the latter knowing the public key of the server  1204 . This method allows the device A to receive, from the server  1204 , unmodified data. The server  1204  will itself have been able to obtain the public key of the device B from the server  1203  and, at the same time, to verify the public key of the device A. 
     In step  1303 , the first device A communicates its identifier to the device B. 
     In step  1304 , the device B, having received the identifier communicated in step  1303 , communicates with the server  1203  in order to determine the public key of the first device A. This information is sent thereto using the method of  FIG. 2 , which allows the device B to receive unmodified information. The device B informs the device A of the reception of this information by sending thereto a reception acknowledgment. 
     In step  1305 , on reception of the reception acknowledgment sent in step  1304 , the first device A uses the method according to the invention illustrated in  FIG. 2  to send the email  1200  to the device B, which may then be certain that this information was sent by the device A and has been received unaltered. In addition, the device A is certain to have certified this information only with the device B. 
     Since encrypting methods employing asymmetric keys and symmetric keys may be vulnerable to quantum computers, these encrypting methods may be replaced, in the examples described above, with encrypting methods using single-use keys. 
     The invention is not limited to the examples of embodiments described above, nor to the exemplified applications. The invention may in particular be used to increase the security of financial transactions.