METHOD OF ENCRYPTING, TRANSMITTING AND DECRYPTING OF INFORMATION IN PUBLIC NETWORKS

Abstract: Invention relates to a cryptographic method with the improved speed, in which the ecryption operations are performed with use of asymmetrical keys. A method for confidential transmitting messages includes preliminary encryption of message in such as manner that two independent parts are formed. The method is fast because only the short essential part of information is additionally encrypted by means of the public key. The stability of such encryption is much higher as compared with the use of separately taken methods because the core part, being encrypted by asymmetrical keys, is not subject to decrypting, since it has no semantic criterion.

Description: METHOD OF ENCRYPTING, TRANSMITTING AND DECRYPTING OF INFORMATION IN PUBLIC NETWORKS 5 TECHNICAL FIELD This invention relates to cryptographic systems, computers, and to methods, implemented by means of computers and communication facilities, for encryption and transmission of information with further decryption thereof. More particularly, this invention relates to a cryptographic method with the improved speed, in which the 0 decryption operations are performed with the use of asymmetrical keys. BACKGROUND Public key cryptography is a widely used approach for confidential transmitting messages over public communications channel. Public-key cryptography employs 5 asymmetric key pairs. An "asymmetric" cryptographic key pair consists of two separate keys, a first key to manipulate data in one way and a second key to convert the manipulated data back to its original form. The keys are based upon a mathematical relationship, in which one key cannot be calculated (at least in any reasonable amount of time) from the other key. 0 Cryptographic key pairs can be used for different functions, such as encryption, decryption, digital signing, signature verification, and authentication. As an example, encryption and decryption using an asymmetric key pair can be represented as follows: Eκ P ub (M) =C 5 D K pri (C) =M where " Eκ put> " is an encryption function using a public encryption key "Kpub" to encrypt a plaintext message "M" into ciphertext "C", and " D Kpπ " is a decryption function using a private decryption key "Kpri". The inverse is also true in that a message can be "signed" using the private key and the signature can be verified 0 using the public key. In a public key system, the public key is distributed to other parties and the private key is maintained in confidence. The asymmetric public and private keys ensure two results. First, only the holder of the private key can decrypt a message that is encrypted with the corresponding public key. Second, if another party decrypts 5 a message using the public key, that party can be assured that the message was encrypted by the private key and thus originated with presumably the holder of the private key. One of the best known and most widely used asymmetric ciphers is the RSA cryptographic cipher named for its creators Rivest, Shamir, and Adleman. The original RSA cryptography system is described in U.S. Pat. No. 4,405,829, entitled "Cryptographic Communications System and Method", which issued Sep. 20, 1983, in the names of Rivest, Shamir, and Adleman. This patent is incorporated by reference as background information. The RSA cipher for encryption and decryption is given as follows: RSA Encryption: C=M e mod n RSA Decryption: M=C 1/e mod (p1 "1) (p2 _1) mod n where pi and p 2 are prime numbers, n is a composite number of the form n=p p 2 , and e is a number relatively prime to (p -1) (P 2 -1). The operation "mod" is a "modular reduction" operation, or simply "modulo" operation, which is a common operation for large integer arithmetic. The modulo operation is an arithmetic operation whose result is the remainder of a division operation. It is expressed as "A mod B," where A is a number written in some base and B is the "modulus." The result of A mod B is the remainder of the number A divided by the modulus B. As a simple example, the modulo operation 17 mod 3 yields a result of 2, because 17 divided by 3 yields a remainder of 2. Because it produces a remainder, the modulo operation is often alternately referred to as the "division remainder" operation. With the conventional RSA cryptography, decryption is significantly slower than encryption. This discrepancy is due to the fact that the RSA cipher requires more computations to decrypt a message than are needed to encrypt the same message. The discrepancy can be disadvantageous in certain environments. For example, in the client server context, clients and servers often exchange encrypted messages to one another. Individual clients often enjoy plentiful time and resources to encrypt a message. Unfortunately, the server does not experience such luxury and may on occasions be limited in its ability to rapidly decrypt incoming messages, especially during times of high client request volume. Besides the increasing efficiency facilities of computers allow the well equipped unauthorized persons to decrypt the intercepted messages within acceptable time limits. Accordingly, there is a need to improve the speed of the decryption in the RSA algorithm.. A method that improves the decryption speed in the RSA cipher is known from US 6,081,598. In one embodiment the integer "e" is set as two, so that a new family of trapdoor permutations was based on exponentiation in subgroups of Z n *. One of the drawbacks of the cryptography scheme is that the encryption process is slower than the traditional RSA encrypting, because the coder computes the number x as the function of g, a random element of Zf- Deriving the number x requires additional computations that are not present in the traditional RSA encryption. One way to increase the speed at the encryption phase consists in computing the number x once and then use the old number x to generate a new number x for the next encryption. In particularly, the improvement involves changing the number x for each new encryption operation in a manner, which is less computationally intensive in respect of computation than recomputing g R mod n for each new encryption. One approach to generating a new number x from the old number x is as follows: x xk exp (i) , where " k exp (i) " is expressed as k'. The encoder computes the number x (i.e., x=g R mod n) and stores the number x in memory or a register for subsequent use. For each subsequent encryption, the encoder changes x by computing ^ exp w , and choosing a value "i" such that the value V remains the same, when x changes. The coder then sends value i along with value V to the decoder for use in recovering value x. The process of amortizing the value x over several encryptions reduces the number of computations during each encoding procedure. The cryptography system preserves forward-secrecy for the encoder so that if the number x is leaked, past messages are not compromised, but future messages may be compromised. The encoder may fully recompute the number x at any interval or at any time it deems necessary. The above cryptography system can also be used to improve decryption speed in batch RSA, a well-known variation of RSA. The cryptography system is similar to that described above, but differs in that the random numbers ne r 2 used to derive prime numbers p-i, and p 2 are further constrained to not be divisible by the first b primes, where b is the decryption batch size. For the batch RSA, the number x is still derived as follows: x=g R mod n The value V is then calculated as follows: V=x θ mod n where e = (i+1 )-th odd prime e i is from Zb On the decryption side, the value x is recovered as: χ=v (1/e) mod q1q2 mod n The above modification to batch RSA enables quicker decryption because during the batch inverse operation, the exponents can be reduced modulo q-ιq 2 . Nevertheless, the speed of the above-described system is anyhow low. Moreover, crypto stability of the system is insufficient. A method of encryption [WO 00/65767, Mischenko et al.], is known which allows to transform any machine text (any file) into two encrypted files (the residual file or core and flags), each of which has no meaning, unlike the existing encryption algorithms. The characteristic feature of such representation is that one of files (the core file) can have a small size (settled by the user). Unlike the hash-function operation, here the initial text (file) can be restored from a residual file with the help of another file (flags) and a special confidential key information. According to this method, transformation of a message is performed by cycling. Transformation in each cycle is made in such a manner, as a result of which is formed a message (Ci) transformed in the given cycle of transformation, which message that is smaller in the length than the initial message, and the accessory information for the given cycle (Fi): - the number (n) of transformation cycles of the initial message is selected from a preset criterion (for example, the size of the finally transformed message), • The method further consists in forming an encrypted message consisting of two parts, one of which contains the finally transformed message (Cn - core) that is smaller in the length than the initial message, and the second part contains a set of accessory information (F = {F1 , F2, ..., Fn} - flags). This method of encryption allows both parts of the encrypted message to be independent. In this case the initial text can not be restored by using any of these parts separately. The drawback of this method is that when the both parts of the message are transmitted through one channel, they can be eavesdropped and restored illegally. Besides, this method is not recognized as a means for a digital signature. The aim of the present invention is to improve the speed of encryption with the use of the advantages of asymmetrical keys and to improve the resistance of encryption means. The set aim is realized in the following manner. The method of confidential transmission of information includes the following sequence of steps - first encrypting of the sender's information the in such a manner that two independent parts of information are formed: the informative part ( a core) and the accessory part (flags), each of which separately can not reproduce the initial information even in its separate parts. » - additional encrypting of the core part by means of individual public keys of the recipient. • - transmitting the encrypted parts of information to the recipient. One further improvement consists in that the main encryption is performed in such a manner that the size of the core part of information becomes much smaller than the size of the accessory part thereof. Such transformation can be termed as transformation with compression of the core part of information. It is most preferable that the main encryption is performed in such a manner that the core part has a fixed size, (for example 1 kilobyte), which is substantially smaller that the size of the accessory part. The method for decryption of the initial information includes the following steps: • additional decrypting the core part by means of individual keys of the user and the algorithm for additional decryption; • restoring the initial information by performing the process of the main decryption with interaction of the accessory part of information that comprises the information about transformation and the core part that was pre-recovered in receiving apparatus. • Hence, the claimed method uses the advantages of the methods for encryption with asymmetric keys allowing at the same time to substantially improve the speed of decryption through encrypting only the short part of information. At the same time, decryption of the accessory part of information is not possible as it has no notional connection with the contents of the initial text. The stability of such encryption is much higher as compared with the use of separately taken methods because the core part, being encrypted by asymmetrical keys, is not subject to decrypting, since it has no semantic criterion. At the same time, the keys and the algorithm of the main encryption can be also transferred through public channels. In this case the resistance of encryption will be determined by the resistance of the encryption under RSA. Embodiments of invention It is preferable to use the method of encrypting information including the following steps: • preliminary generating data about encryption/decryption ratio that connect the values of all initial symbols, which can be used in the given kind of information, with the encrypted symbols. • determining the number (n) of transformation cycles for each specific initial information; performing the transformation cycle, comprising: • generating the feature (R,) determining the rule that is used for transforming the information in the current transformation cycle; • transforming information with the use of the selected rule; • repeating the transformation cycles for a particular number of times • while in this case • transformation of information in each cycle is performed in such a manner that it results in forming the information transformed in the said cycle (C,) and the accessory information for the said cycle (F,); • the number (n) for the transformation cycles of the initial information is selected from the preset criterion, • formation of encrypted information consisting of two parts, one of which includes the finally transformed information (core - C n ), and the second part includes the bunch of the accessory information (F = {F 1f F 2 ,...,F n }). - In particular, the method of information encryption can be characterized by the following features: • transformation of information in each cycle is performed in such a manner as a result of which is formed a transformed in the given cycle information (C,) that is smaller in the length or equal to the initial information, and the accessory information for the given cycle (F|); • the number (n) of the cycles for transformation of the initial information is selected from the preset criterion determining the size of the finally transformed information, • formation of encrypted information consisting of two parts, one of which includes the finally transformed information (C n ) that is shorter in the length than the initial information, and the second part includes the bunch (group) of the accessory information (F = {F-i, F 2 ,...,F n }). • • Further the information (C n ) finally transformed at the given step is additionally transformed under the RSA method with the use of a public key of the asymmetric key pair of the recipient. • The finally transformed parts of information are transmitted through one or several channels. • Transmission of the finally encrypted parts in a separate manner or through different communication channels reduces the possibility for tapping or matching the parts and, consequently, improves the resistance of the system for transmitting information, since each part per se has no sense. • When such level of data secrecy is not required, the both parts of encrypted information can be transmitted together. Moreover, the algorithm and the keys for the preliminary encryption can be also transmitted over open channels. In this case the resistance of the system will be determined by the resistance of the algorithm and by the length of RCA keys. However, this system is considerably faster as compared with the traditional RSA system. Additionally, the resistance of the preliminary encryption algorithm is rather high even in case of using public keys because it is determined by the length of the compressed part, which can be large enough, e.g. 1 kilo byte. • The method for decryption of the encrypted information includes the following steps: • Preliminary decrypting, with the use of the RSA algorithm and the closed key taken from the asymmetric key pair of the recipient, of the core part of the encrypted message, that was additionally encrypted by the sender with the use of the public key taken from the asymmetric key pair of the recipient ; • Generating the keys according to the rules used at the preliminary encoding; • Extracting from the encrypted information of the data (Rj) that determine the rule used in the current transformation cycle, which rule connects the values of the encrypted information with the specific symbols of the transformed information of the current transformation cycle; • Selecting the rule connecting the values of the encrypted information with the specific symbols of the transformed information of the current transformation cycle; • Extracting from the accessory information (F) of the accessory information for the given transformation cycle (Fj); • Transforming the transformed hformation (Cj) with the use of the selected rule and the accessory information for the given transformation cycle (Fj); • Making decision about transition to the subsequent cycle or about termination of transformation; • while in this case • the accessory information for the given transformation cycle (Fj) is selected from set of the accessory information (F); • the transformed in the respective cycle information (Cj) is restorered with the use of the selected rule and the accessory information for the given transformation cycle n (Fi); • the decision is made about transition to the subsequent cycle or about termination of transformation; • the respective part of the accessory information is additionally used in each transformation cycle; a restored in the respective cycle information is formed as a result of transformation with the use of the selected rule. Accordingly, the cycles are repeated up to full restoration of the initial information. According to the claimed method the encryption resistance can be specified by both the number of transformation cycles and the key length as well as by the resistance of the RSA algorithm. The traditional and the claimed methods were compared by testing on the computer Processor Pentium II 400Mhz with RAM 64 It is obvious that the claimed method allows encrypting with the use of all advantages of public keys. Moreover, the method is fast because only a short essential part of information is encrypted. At the same time the resistance of such an algorithm is substantially improved since an any part of the initially encrypted information taken alone has no sense. Consequently, all efforts to recover the said part or to open the additional encryption by a public key will be unsuccessful as it is impossible to understand the resulting information. Moreover, the method allows to use encryption according to RSA algorithm for long files, which was not applied before because decryption of a long file consumed too much time.

Claims: Claims 1. A method for confidential transmitting messages including the steps of: • encrypting messages in such a manner that two independent parts are formed, i.e. the core part being a transformed information and the accessory part containing information about transformations, each part separately being unable to reproduce the initial information even in some parts thereof, • transmitting the encrypted parts of the message to the recipient; • characterized in that the additional encryption of the core part of the message is made by means of the public key of the recipient taken from the asymmetric key pair of the recipient. 2. A method of claim 1 , characterized in that the main encryption is performed in such a manner that the size of the core part of the message becomes substantially smaller than the size of the accessory part. 3. A method of claims 1 -2, characterized in that the main encryption is performed in such a manner that the size of the core part of the message is developed to a preset size that is substantially smaller than the size of the accessory part . 4. A method for decryption of a message encrypted according to the method of claim 1 , characterized in that the process of decryption comprises: » preliminary decrypting the core part by means of a secret key of the recipient taken from the asymmetric key pair of the recipient; restoring the initial message by performing the process of decryption during the operation of the reverse transformation of the preliminary recovered core part of the message with the use of the accessory part of the message containing information about transformation.

Inventors: MICHTCHENKO VALENTIN ALEXANDRO, MICHTCHENKO, VALENTIN ALEXANDROVICH
Applicants: MICHTCHENKO VALENTIN ALEXANDRO, MICHTCHENKO, VALENTIN ALEXANDROVICH
Application year: 2001
Main classification: H04L9
IPC codes: H04L9