Abstract:
The present invention provides a symmetric-key cryptographic technique capable of realizing both high-speed cryptographic processing having a high degree of parallelism, and alteration detection. The present invention performs the steps of: dividing plaintext composed of redundancy data and a message to generate a plurality of plaintext blocks each having a predetermined length; generating a random number sequence based on a secret key; generating a random number block corresponding to one of said plurality of plaintext blocks from said random number sequence; outputting a feedback value obtained as a result of operation on said one of the plurality of plaintext blocks and said random number block, said feedback value being fed back to another one of the plurality of plaintext blocks; and performing an encryption operation using said one of the plurality of plaintext blocks, said random number block, and a feedback value obtained as a result of operation on still another one of the plurality of plaintext blocks to produce a ciphertext block.

Description:
CROSS REFERENCE TO RELATED APPLICATIONS  
         [0001]    This application claims priority from Japanese Patent Application Reference No. 2000-070994, filed Mar. 9, 2000, and No. 2000-210690, filed Jul. 6, 2000, the entire contents of which are hereby incorporated by reference.  
           [0002]    This application is related to U.S. Ser. No. 09/572,790, filed May 17, 2000 entitled “CRYPTOGRAPHIC APPARATUS AND METHOD”, having Soichi Furuya and Michael Roe listed as inventors, the entire contents of which are hereby incorporated by reference.  
         BACKGROUND OF THE INVENTION  
         [0003]    The present invention relates to a technique for ensuring security of confidential information.  
           [0004]    Cryptographic processing apparatuses proposed so far employ a block cipher or a stream cipher for concealing data. Various types of block ciphers have been proposed including DES and IDEA. DES and IDEA are described in the following reference.  
           [0005]    Reference 1: Menezes, van Oorschot, Vanstone, Handbook of Applied Cryptography, CRC Press, 1996, pp. 250-259, pp. 263-266.  
           [0006]    The security of the total cryptographic process of each block cipher and its characteristics are discussed based on a block-cipher operation mode employed, such as ECB, CBC, CFB, OFB, or the counter mode. However, only the iaPCBC mode is known to be capable of performing both cryptographic processing and detection of an alteration at the same time, and other modes cannot detect alterations by themselves. Block-cipher operation modes are described in the following reference.  
           [0007]    Reference 2: Schneider, Applied Cryptography, Second Edition, John Wiley &amp; Sons, Inc., 1996, pp. 189-209.  
           [0008]    The iaPCBC mode is described in the following reference.  
           [0009]    Reference 3: Gligor, Donescu, “Integrity-Aware PCBC Encryption Schemes,” Preproceedings in Secure Protocol Workshop, Cambridge, 1999, to appear in Lecture Notes in Computer Science series, Springer-Verlag.  
           [0010]    The iaPCBC mode is an operation mode which uses a block cipher. Regarding encryption, the iaPCBC mode can perform neither parallel processing nor preprocessing, which makes it very difficult to implement the iaPCBC mode in the environment in which processing at extremely high speed is required.  
           [0011]    On the other hand, there is a system which generates a cryptographic checksum called a “message authentication code” (hereinafter referred to as “MAC”) in order to detect alterations. By implementing a MAC generation process as an independent mechanism, and executing the process during cryptographic processing in one of the above block-cipher operation modes, it is possible to perform both cryptographic processing and detection of an alteration at the same time. In this case, however, it is necessary to share two completely independent cryptographic keys, one for encryption and the other for alteration detection, and, furthermore, data to be encrypted must be processed twice, that is, for encryption and for MAC generation. As a result, a realized cryptographic system may be complicated or may not be suitable for processing data having an extended length. In addition, the processing speed of the block cipher is slower than the current communication speed, which means that it is difficult to apply any technique using a combination of the block cipher and MAC to processing of the order of gigabit-per-second or terabit-per-second. MAC is described in the following reference.  
           [0012]    Reference 4: Menezes, van Oorschot, Vanstone, Handbook of Applied Cryptography, CRC Press, 1996, pp. 352-368.  
           [0013]    In contrast with the block cipher, a stream cipher is an encryption mechanism which uses one of various proposed cryptographic pseudorandom number generators. The stream cipher was not able to detect alerations by itself regardless of security or characteristics of each implementation. Well-known stream ciphers, or pseudorandom number generators used for stream ciphers include SEAL, a linear feedback shift register using a nonlinear combination generator, a linear feedback shift register using a nonlinear filter, and a clock-controlled linear feedback shift register. SEAL is described in the following reference.  
           [0014]    Reference 5: Schneider, Applied Cryptography, Second Edition, John Wiley &amp; Sons, Inc., 1996, pp. 398-400.  
           [0015]    On the other hand, systems based on the above feedback shift registers are described in the following reference.  
           [0016]    Reference 6: Menezes, van Oorschot, Vanstone, Handbook of Applied Cryptography, CRC Press, 1996, pp. 203-212.  
           [0017]    A technique using a combination of a stream cipher and a MAC can also perform both cryptographic processing and detection of an alteration at the same time, and, furthermore, processing of a stream cipher is 2 to 20 times faster than that of a block cipher. However, as is the case with the combination of a block cipher and MAC, every MAC generation system (meaning every combination of a stream cipher and MAC) requires sharing of two different keys, and processing of a message twice. When considered in detail, the MAC generation system requires a particular mechanism in addition to that necessary for the stream cipher itself, and considerable computational complexity. For example, MAC generation systems such as HMAC and UMAC require a safe hash function having guaranteed cryptographically-collision-free one-way characteristics. This means that it is necessary to implement the above safe function in addition to a stream cipher. HMAC is described in the above Reference 4 (pp. 355, Example 9.67) while UMAC is described in the following reference.  
           [0018]    Reference 7: Black, Halevi, Krawczyk, Krovetz, Rogaway, “UMAC: Fast and Secure Message Authentication,” Advances in Cryptology,—CRYPTO &#39;99 Lecture Notes in Computer Science, Vol. 1666, Springer-Verlag, 1999.  
           [0019]    Generally, however, hash functions such as SHA-1 and MD5 are very complicated, and are not easy to implement. These hash functions are described in the following reference.  
           [0020]    Reference 8: Menezes, van Oorschot, Vanstone, Handbook of Applied Cryptography, CRC Press, 1996, pp. 347-349.  
           [0021]    The security of hash functions has not yet been studied adequately in contrast with study of the security of block ciphers. Therefore, a user may not be able to incorporate a hash function because the user cannot rely on the hash function. Of MAC generation systems, MMH uses only a pseudorandom number generator, and requires a very small amount of additional resources such as circuits and programs to add an alteration detection function to the cryptographic process. However, MMH requires a pseudorandom number sequence whose length is as long as that of the message, taking long time to generate necessary random numbers. MMH is described in the following reference.  
           [0022]    Reference 9: Halevi, Krawczyk, “MMH: Software Message Authentication in the Gbit/Second Rates,” Fast Software Encryption, 4 th  International Workshop, FSE &#39;97, Lecture Notes in Computer Science, Vol. 1267, Springer-Verlag, 1997.  
           [0023]    As described above, the prior art techniques are unsatisfactory in terms of ensuring of security and high-speed processing, and therefore it is required to develop a safer and faster cryptographic processing technique.  
         SUMMARY OF THE INVENTION  
         [0024]    The present invention provides a safer and faster symmetric-key cryptographic processing technique.  
           [0025]    The present invention provides a symmetric-key cryptographic method which is capable of performing alteration detection and decryption at the same time, and whose safety for data confidentiality and data alteration protection is provable.  
           [0026]    The present invention provides a symmetric-key cryptographic method which advantageously has preprocessing and parallel processing functions, and which is capable of processing at high speed, capitalizing on the high-speed processing characteristics of the pseudorandom number generator.  
           [0027]    The present invention provides a symmetric-key cryptographic method whose processing speed is not only faster than that of the conventional block cipher, but can be made still faster as the amount of resources employed is increased, and which can attain a high level of parallel operation for high-speed processing.  
           [0028]    The present invention provides a symmetric-key cryptographic method whose processing speed does not drop even when a very short message is processed.  
           [0029]    The present invention provides a symmetric-key cryptographic method which can be implemented by adding a very small circuit or program to stream cipher equipment.  
           [0030]    The present invention provides a symmetric-key cryptographic method capable of processing each block using a pseudorandom number sequence as a key stream, and detecting an alteration at the same time.  
           [0031]    A symmetric-key cryptographic method according to a first aspect of the present invention generates ciphertext C, using plaintext P, a key stream S, redundancy data (hereinafter simply referred to as a redundancy) R, and an initial value V, where the length of the key stream S is longer than that of the ciphertext C.  
           [0032]    Specifically, when the length of the redundancy R is b bits and the length of the plaintext P is L=n*b+t bits (t is an integer equal to or larger than 0 and smaller than b, and n is an integer equal to or larger than 0), this method adds ((b−t) mod b) number of “0” bits and then the redundancy R to the end of the plaintext P to produce a character string having a length of L+((b−t) mod b)+b bits. This length is a multiple of the length b.  
           [0033]    This character string is divided into blocks P i (1≦i≦m) each having b bits. The expression “Xi (1≦i≦n)” denotes a string of variables Xi having n elements from 1 to n. In the above case, the key stream must have a length of 2*m*b bits.  
           [0034]    This key stream is either shared secretly between the encryption side apparatus and the decryption side apparatus beforehand, or generated from a secret key shared beforehand (this secret key corresponds to an input to a pseudorandom number generator, for example).  
           [0035]    The key stream of the above length is divided into two block series, A i  and B i  (1≦i≦m, each block has b bits).  
           [0036]    Letting the feedback initial value F 0 =V, ciphertext blocks C i  are calculated by the following formula. (This initial value V is also shared but it is not necessary to keep it secret).  
             F   i   =P   i ^ A i   , C   i =( F   i   *B   i )^  F   i−1 (1≦i≦m).  
           [0037]    The obtained cipher blocks C i  are concatenated to produce a character string, which is output as ciphertext C. Here, the operators “*” and “^ ” denote multiplication and addition, respectively, in the finite field F2 b .  
           [0038]    The corresponding decryption is performed as follows.  
           [0039]    If the length of ciphertext C′ is not a multiple of b bits, a rejection indication is output. If it is a multiple of b bits, on the other hand, the ciphertext C′ is divided into blocks C′ i (1≦i≦m′) each having b bits.  
           [0040]    By setting key stream blocks A i  and B i  (1≦i≦m′), and letting the feedback value F′ 0 =V, the following processing is performed.  
             F′   i =( C′   i   ^ F′   i−1 )/ B   i   , P′   i   =A   i   ^ F′   i  (1≦i≦m′).  
           [0041]    The obtained results P′ i  are concatenated to produce a character string, which is stored as decryption results P′. The operator “/” denotes division in the finite field F2 b .  
           [0042]    The redundancy R must be restored as the b-bit character string P′ m  if no alteration has been made. It is guaranteed that the probability that an attacker who does not know the keys might successfully make an alteration to the ciphertext without changing the redundancy R, which is restored as the character string P′ m , is at most ½ b . Based on the above fact, it is possible to detect alterations by checking whether the character string P′ m  is identical to the redundancy R when b is sufficiently large (32 or more).  
           [0043]    The symmetric-key cryptographic method of the first aspect is characterized in that influence of an alteration made to a cipher block is propagated to the last block when the ciphertext has been decrypted, whichever cipher block has been altered. Accordingly, even if an attacker makes an alteration without directly changing the redundancy R, it is possible to detect the alteration.  
           [0044]    More specifically, after a feedback value for the next block is generated and stored, encryption operation on the current block is performed using a feedback value generated as a result of encryption operation on the previous block. That is, when generated intermediate values are denoted by X t  (t=1 . . . n), that is, X 1 , X 2 , . . . X n , in the order of generation, and the feedback value F i  for the next block is indicated by the intermediate value X i , and furthermore, the intermediate value to which the feedback value F i−1  generated as a result of operation on the previous block is applied is indicated by X j , the arguments i and j have the relationship i≦j (a necessary condition).  
           [0045]    According to the first aspect of the present invention, the probability that an alteration made to ciphertext might pass the alteration detection check is ½ b . However, the method requires division operation in a finite field in decryption, and uses random-number data whose size is twice the size of the plaintext.  
           [0046]    Description will be made of a symmetric-key cryptographic method according to a second aspect of the present invention, which does not ensure cryptographic security as high as that provided by the symmetric-key cryptographic method of the first aspect, but can provide more efficient processing, instead.  
           [0047]    The symmetric-key cryptographic method of the second aspect processes a message and a redundancy in the same way as they are processed in the symmetric-key cryptographic method of the first aspect. When plaintext with a redundancy has m blocks, a key stream having a length of b*(m+1) bits is required. This key stream is divided into blocks A i  (1≦i≦m) and B (B≠0).  
           [0048]    Letting the feedback initial value F 0 =V, cipher blocks C i  are obtained by the following formula.  
             F   i   =P   i   ^ A   i   , C   i =( F   i   *B )^  F   i−1  (1≦i≦m).  
           [0049]    The obtained cipher blocks C i  are concatenated to produce a character string, which is output as ciphertext C.  
           [0050]    The corresponding decryption is performed as follows.  
           [0051]    If the length of ciphertext C′ is not a multiple of b bits, a rejection indication is output. If it is a multiple of b bits, on the other hand, the ciphertext C′ is divided into blocks C′ i (1≦i≦m′) each having b bits.  
           [0052]    As in the encryption, by setting key stream blocks A i  (1≦i≦m′) and B, and letting the feedback value F′ 0 =V, the following processing is performed.  
             F′   i =( C′   i   ^ F′   i−1 )/ B, P′   i   =A   i   ^ F′   i  (1≦i≦m′).  
           [0053]    The redundancy portion is extracted from the obtained series of blocks P′ i , and checked whether it is identical to the predetermined redundancy (the encrypted redundancy R). If the redundancy portion is identical to the predetermined redundancy, the remaining blocks of the series of blocks P′ i  are output as a message; otherwise a rejection indication is output.  
           [0054]    The redundancy (the encrypted redundancy R) must be restored as the b-bit character string P′ m  if no alteration has been made.  
           [0055]    The symmetric-key cryptographic method of the second aspect uses a plurality of key streams (each obtained from a different pseudorandom number sequence) during encryption/decryption of blocks (plaintext or ciphertext blocks) Of the plurality of key streams, one is changed for each iteration of the processing while the others are left unchanged, that is, the same key streams are used for all the iterations. More specifically, when two pseudorandom number sequences (key streams) supplied for encryption/decryption of the i-th block are denoted as A i  and B i , the key stream A i  is changed each time a block is processed, whereas B i  is not changed during processing of all the blocks.  
           [0056]    According to the second aspect of the present invention, the probability that an alteration made to ciphertext by an attacker who does not know the keys might not be detected in the subsequent alteration detection process is (m−1)/2 b . Generally, the alteration success rate is preferably ½ 32  or less. Since the data length m is set to about 232 at maximum for actual implementation, b is preferably equal to 64 or more. In such a case, multiplication operation in the finite field F2 64  is performed for both encryption and decryption. This operation is implemented by means of hardware at very high speed and low cost. In the case of software implementation, however, high-speed operation may be provided using a symmetric-key cryptographic method according to a third aspect of the present invention as described below.  
           [0057]    The symmetric-key cryptographic method according to the third aspect of the present invention uses a longer redundancy. To begin with, the redundancy is set to have b*d bits, assuming that the subsequent processing is carried out in units of b bits. The message and the redundancy are processed in the same way as they are processed in the symmetric-key cryptographic methods of the first and second aspects to produce a series of blocks P i  (1≦i≦m,m≦d) composed of the message and the redundancy, each block having b bits. The key stream is set to have a length of b*(m+d) bits, and is divided into two block series A i  (1≦i≦m) and B i  (≠0,1≦i≦d).  
           [0058]    Letting the feedback initial value F (i)   0 =V i  (1≦i≦d), cipher blocks C i  are calculated by the following formula.  
             F   (1)   i   =P   i   ^ A   i ,  
             F   (j+1)   i =( F   (j)   i   *B   j )^  F   (j)   i−1  (1≦j≦d),  
             C   i   =F   (d+1)   i  (1≦i≦m).  
           [0059]    The obtained cipher blocks C i  are concatenated to produce a character string, which is output as ciphertext C.  
           [0060]    The corresponding decryption is performed as follows.  
           [0061]    If the length of ciphertext C′ is not a multiple of b bits, a rejection indication is output. If it is a multiple of b bits, on the other hand, the ciphertext C′ is divided into blocks C′ i  (1≦i≦m′) each having b bits.  
           [0062]    As in the encryption, by setting key stream blocks A i  (1≦i≦m′) and B i  (≈0,1≦i≦d), and letting the feedback initial value F (i)   0 =V i  (1≦i≦d), the following processing is performed.  
             F′   (d+1)   i   =C′   i ,  
             F′   (j)   i =( F′   (j+1)   i   ^ F′   (j)   i−1 )/ B   j  (1≦j≦d),  
             P′   i   =A   i   ^ F′   (1)   i  (1≦i≦m).  
           [0063]    The redundancy portion is extracted from the obtained blocks P′ i , and checked whether it is identical to the predetermined redundancy (the encrypted redundancy). If the extracted redundancy is identical to the predetermined redundancy, the remaining blocks of the blocks P′ i  are output as a message; otherwise a rejection indication is output.  
           [0064]    In the symmetric-key cryptographic method of the third aspect, although a redundancy having a length of b*d bits is used, operations necessary for encryption and decryption are carried out in the finite field F2 b . Multiplication in the finite field F2 b  requires a computational amount (computational complexity) only 1/d 2  of that required by multiplication in the finite field F2 b*d  However, since the number of required multiplication operations increases by a factor of d, this high-speed processing method possibly takes time about 1/d of the time taken by the conventional method to complete the multiplication operations using a redundancy of the same length.  
           [0065]    A symmetric-key cryptographic method according to a fourth aspect of the present invention incorporates the multiplication in the finite field F2 b  employed by the symmetric-key cryptographic methods of the first through third aspects into the 3-round Feistel structure. Specifically, the operation A*B is replaced by a function which calculates  
             M   1   =A   L ^ ( A   R   *B   L ),  M   2   =A   R ^ ( M   1   *B   R ),  M   3   =M   1 ^ ( M   2   *B   L ),  
           [0066]    and outputs M 3 ∥M 2  (B L  and B R  can be switched around, as A L  and A R , or M 2  and M 3 ). These operations are self-invertible, and therefore the same operations can be used for the corresponding decryption.  
           [0067]    A fifth aspect of the present invention relates to a method of dividing a message for processing. Specifically, plaintext P is divided into a predetermined number t of character strings P i  (1≦i≦t). The predetermined number t is decided according to a rule on which both the transmitter and the receiver have agreed. Each character string is combined with a different redundancy R i  (1≦i≦t) and then encrypted to produce ciphertext C i  using a symmetric-key cryptographic method according to one of the above aspects of the present invention. Separately from the above process, all redundancies R i  are concatenated to produce plaintext (R 1 ∥R 2 ∥R 3 ∥ . . . ∥R t ), which is then encrypted using a redundancy R shared between the transmitter and the receiver to obtain ciphertext C t+1 . The above pieces of ciphertext (a series of ciphertext blocks) are concatenated (that is, C 1 ∥C 2 ∥C 3 ∥ . . . ∥C t+1 ) to produce the final ciphertext C.  
           [0068]    In the corresponding decryption, the ciphertext is divided into t number of character strings according to a predetermined rule, and the character strings are each decrypted separately. If each decryption result is not a reject, and all the redundancies R i  are included in the redundancy plaintext (encrypted using the redundancy R in the encryption process, and now obtained as a result of decryption), the decryption results are accepted, and each piece of plaintext obtained as a result of decryption is concatenated in the order of the corresponding redundancy. If any one of the decryption results is a reject, the entire decryption results are rejected.  
           [0069]    According to a sixth aspect of the present invention, multiplication in the finite field F2 b  in the above five aspects of the present invention is replaced with multiplication in the finite field Fp, where p is a prime number which can be expressed as “2 k +1” using an integer k.  
           [0070]    Specifically, the operation a*(b+1)+1 in the finite field Fp is performed instead of the multiplication a*b in the finite field F2 b . This operation can be accomplished by a combination of one multiplication operation, two addition operations, and one shift operation of a 2 b -bit shift register, making it possible to perform multiplication operations in the finite field F2 b  using a general-purpose processor at high speed.  
           [0071]    The above operation a*(b+1)+1 in the finite field Fp can provide high-speed processing, compared with multiplication in F2 b , which requires b number of exclusive OR operations and b number of shift operations, and compared with multiplication in Fp using a general prime number p, which requires one multiplication operation and one division operation (a division operation requires time a few tens of times longer than that required by an addition operation or a shift operation).  
           [0072]    Since the present invention uses pseudorandom numbers, a user can employ a cryptographic primitive which the user believes is most reliable by selecting one from among block ciphers, hash functions, and stream ciphers as the pseudorandom number generator, which means that the security of the system can be easily attributed to the cryptographic primitive which the user has selected. Furthermore, the pseudorandom number generation can be carried out separately from the plaintext and the ciphertext processing, making it possible to employ parallel processing and preprocessing, resulting in processing at high speed.  
           [0073]    As for implementation cost, the present invention can avoid additional implementation which is difficult to make, such as the additional implementation of a hash function.  
           [0074]    These and other benefits are described throughout the present specification. A further understanding of the nature and advantages of the invention may be realized by reference to the remaining portions of the specification and the attached drawings. 
       
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS  
       [0075]    [0075]FIG. 1 is a system configuration employed in embodiments of the present invention;  
         [0076]    [0076]FIG. 2 is a flowchart of a plaintext preparation subroutine;  
         [0077]    [0077]FIG. 3 is a flowchart of a random number generation subroutine;  
         [0078]    [0078]FIG. 4 is a flowchart of an encryption subroutine;  
         [0079]    [0079]FIG. 5 is a flowchart of the decryption program shown in FIG. 1.  
         [0080]    [0080]FIG. 6 is a flowchart of the ciphertext preparation subroutine shown in FIG. 5;  
         [0081]    [0081]FIG. 7 is a flowchart of the decryption subroutine shown in FIG. 5;  
         [0082]    [0082]FIG. 8 is a flowchart of the plaintext extraction subroutine shown in FIG. 5;  
         [0083]    [0083]FIG. 9 is a flowchart of the redundancy extraction subroutine shown in FIG. 5;  
         [0084]    [0084]FIG. 10 is a diagram showing data blocks in encryption;  
         [0085]    [0085]FIG. 11 is a diagram showing data blocks in the decryption shown in FIG. 7;  
         [0086]    [0086]FIG. 12 is a flowchart of the random number generation 2 subroutine according to a second embodiment of the present invention;  
         [0087]    [0087]FIG. 13 is a flowchart of the encryption  2  subroutine of the second embodiment;  
         [0088]    [0088]FIG. 14 is a flowchart of the decryption program of the second embodiment;  
         [0089]    [0089]FIG. 15 is a flowchart of the decryption  2  subroutine of the second embodiment;  
         [0090]    [0090]FIG. 16 is a diagram showing data blocks in the encryption according to the second embodiment;  
         [0091]    [0091]FIG. 17 is a diagram showing data blocks in the decryption according to the second embodiment;  
         [0092]    [0092]FIG. 18 is a flowchart of the encryption program according to a third embodiment of the present invention;  
         [0093]    [0093]FIG. 19 is a flowchart of the random number generation 3 subroutine of the third embodiment;  
         [0094]    [0094]FIG. 20 is a flowchart of the encryption 3 subroutine of the third embodiment;  
         [0095]    [0095]FIG. 21 is a flowchart of the decryption program of the third embodiment;  
         [0096]    [0096]FIG. 22 is a flowchart of the decryption 3 subroutine of the third embodiment;  
         [0097]    [0097]FIG. 23 is a diagram showing data blocks in the encryption according to the third embodiment;  
         [0098]    [0098]FIG. 24 is a diagram showing data blocks in the decryption according to the third embodiment;  
         [0099]    [0099]FIG. 25 is a flowchart of the parallel encryption program according to a fifth embodiment of the present invention;  
         [0100]    [0100]FIG. 26 is a flowchart of the parallel decryption program of the fifth embodiment;  
         [0101]    [0101]FIG. 27 is a diagram showing data blocks in the encryption according to the fifth embodiment;  
         [0102]    [0102]FIG. 28 is a diagram showing data blocks in the decryption according to the fifth embodiment;  
         [0103]    [0103]FIG. 29 is a flowchart of the random number generation 4 subroutine according to a fourth embodiment of the present invention;  
         [0104]    [0104]FIG. 30 is a flowchart of the plaintext preparation 2 subroutine of the fourth embodiment;  
         [0105]    [0105]FIG. 31 is an explanatory diagram showing a padding operation on a message according to the fourth embodiment;  
         [0106]    [0106]FIG. 32 is a flowchart of the decryption program of the fourth embodiment;  
         [0107]    [0107]FIG. 33 is a flowchart of the plaintext extraction  2  subroutine shown in FIG. 32;  
         [0108]    [0108]FIG. 34 is an explanatory diagram showing an extraction operation on decrypted text according to the fourth embodiment;  
         [0109]    [0109]FIG. 35 is a diagram showing the configuration of a system for cryptocommunications according to a sixth embodiment of the present invention;  
         [0110]    [0110]FIG. 36 is a diagram showing the configuration of an encryption apparatus employed in a cryptocommunication system according to a seventh embodiment of the present invention;  
         [0111]    [0111]FIG. 37 is a diagram showing the configuration of a contents delivery system according to an eighth embodiment of the present invention;  
         [0112]    [0112]FIG. 38 is a diagram showing the configuration of a system according to a ninth embodiment of the present invention; and  
         [0113]    [0113]FIG. 39 is a diagram showing the configuration of an encryption/decryption router according to a tenth embodiment of the present invention.  
     
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS  
       [0114]    (First Embodiment)  
         [0115]    [0115]FIG. 1 shows the configuration of a computer system including a computer A 10002  and a computer B 10003  connected to each other through a network  10001  for cryptocommunications from the computer A 10002  to the computer  10003 . The computer A 10002  has an operation unit (hereinafter referred to as “CPU”)  10004 , a memory unit (volatile or nonvolatile, hereinafter referred to as “RAM”)  10005 , and a network interface  10006  therein, and a display  10007  and a keyboard  10008  externally connected thereto for the user to operate the computer A 10002 . The RAM  10005  stores an encryption program PROG 1 _ 10009 , a random number generation program PROG 2 _ 10010 , a secret key K 10011 , which is secret information shared only between the computers A 10002  and B 10003 , a redundancy R 10012  and an initial value V 10013 , which both are data shared between the computers A 10002  and B 10003 , and encryption-target data  10014  to be transmitted to the computer B 1003 . The computer B 10003  has a CPU  10015 , a RAM  10016 , and a network interface  10017  therein, and a display  10018  and a keyboard  10019  externally connected thereto for the user to operate the computer B 10003 . The RAM  10016  stores a decryption program PROG 3 _ 10020 , a random number generation program PROG 2 _ 10021 , the secret key K 10011 , the redundancy R 10012 , and the initial value V 10013 .  
         [0116]    The computer A 10002  executes the encryption program PROG 1 _ 10009  to generate ciphertext C 10022  from a message M 10014 , and transmits the generated ciphertext C 10022  to the network  10001  through the network interface  10006 . Receiving the ciphertext C 10022  through the network interface  10017 , the computer B 10003  executes the decryption program PROG 3 _ 10020 , and if no alteration is detected, the computer B 10003  stores the decryption results in the RAM  10016 .  
         [0117]    Each program employed can be introduced into each RAM by receiving the program from another computer in the form of a transmission signal, which is a transmission medium on the network  10001 , or by using a portable medium such as a CD or an FD. Each program can be configured so that it runs under control of the operating system (not shown) of each computer.  
         [0118]    The encryption program PROG 1 _ 10009  is read out from the RAM  10005 , and executed by the CPU  10004  in the computer A 10002 . The encryption program PROG 1 _ 10009  internally calls a random number generation program PROG 2 _ 10010  as a subroutine to process the input secret key K 10011 , the redundancy R 10012 , the initial value V 10013 , and the message M 10014  so as to output ciphertext C 10022 .  
         [0119]    The decryption program PROG 3 _ 10020  is read out from the RAM  10016 , and executed by the CPU  10015  in the computer B 10003 . The decryption program PROG 3 _ 10020  internally calls a random number generation program PROG 2 _ 10021  as a subroutine to process the input key  10011 , the redundancy R 10012 , the initial value V 10013 , and the ciphertext C 10022  so as to output a message or an alteration detection alarm.  
         [0120]    Description will be made of the process flow of the encryption program PROG 1 _ 10009 .  
         [0121]    Step  20002  (a data setting subroutine): waits for input of an initial value V, a redundancy R, and a secret key K.  
         [0122]    Step  20003  (a plaintext preparation subroutine): waits for input of plaintext, adds predetermined padding and a redundancy to the given plaintext, and divides the padded plaintext into a series of plaintext blocks P i  (1≦i≦n) each having 64 bits and outputs them.  
         [0123]    Step  20004  (a random number generation subroutine): outputs pseudorandom number sequences A i  and B i  (1≦i≦n) based on the secret key K.  
         [0124]    Step  20005  (an encryption subroutine): uses the pseudorandom number sequences A i  and B i , the series of plaintext blocks P i  (1≦i≦n), and the initial value V to output a series of ciphertext blocks C i  (1≦i≦n).  
         [0125]    Step  20006 : concatenates the series of ciphertext blocks C i  (1≦i≦n) obtained at step  20005  one after another sequentially to output ciphertext C.  
         [0126]    In this specification, the term “padding” used above refers to addition of additional data to main data. In the case of padding of digital data, the additional data is often concatenated to the main data, simply bits to bits.  
         [0127]    Description will be made of the process flow of the plaintext preparation subroutine with reference to FIG. 2.  
         [0128]    Step  20202 : waits for input of an encryption-target message M. The message M is either input from the keyboard  10008  or read out from a RAM, or introduced from another medium.  
         [0129]    Step  20203 : adds padding indicating the length of the message. Specifically, this step adds 64-bit binary data indicating the length of the message M to the head of the message M.  
         [0130]    Step  20204 : adds padding to the message so that the length of the message is a multiple of a predetermined number. Specifically, the padded data is set to have an integer multiple of 64 bits for subsequent processing. When the length of the message M to which the data indicating the length is added at step  20203  is L bits, this step adds (64−L(mod 64)) number of Os to the end of the message M.  
         [0131]    Step  20205  (addition of redundancy data): further adds a redundancy R of 64 bits to the end of the message.  
         [0132]    Step  20206  (division of message data into plaintext blocks): divides the data obtained at step  20205  into blocks P 1 , P 2 , . . . P n , each having 64 bits.  
         [0133]    Description will be made of the process flow of the random number generation subroutine with reference to FIG. 3.  
         [0134]    Step  20302  (input of necessary parameters): obtains the number n of blocks making up the padded message, and the secret key K.  
         [0135]    Step  20303  (generation of a pseudorandom number sequence A): calls the random number generation program PROG 2  to generate a pseudorandom number sequence having 64*n bits and output it as a pseudorandom number sequence A.  
         [0136]    Step  20304  (division of random number sequence A into blocks): divides the pseudorandom number sequence A into blocks A 1 , A 2 , . . . , A n , each having 64 bits.  
         [0137]    Step  20305  (initialization of a counter i): initializes a counter so that i=1.  
         [0138]    Step  20306  (generation of a random number B i ): executes PROG 2  using the secret key K to generate a random number B i  having 64 bits.  
         [0139]    Step  20307 : if the random number B i  generated at step  20306  is 0, returns to step  20306 .  
         [0140]    Step  20308 : if i=n, performs step  20310 .  
         [0141]    Step  20309 : increments the counter i and returns to step  20306 .  
         [0142]    Description will be made of the process flow of the encryption subroutine with reference to FIG. 4.  
         [0143]    Step  20402 : sets an initial value F 0  so that F 0 =V.  
         [0144]    Step  20403 : sets a counter so that i=1.  
         [0145]    Step  20404 : calculates a feedback value F i  by the formula F i =P i ^ A i .  
         [0146]    Step  20405 : calculates a ciphertext block C i  by the formula C i =(F i *B i )^ F i−1 .  
         [0147]    Step  20406 : if i=n, performs step  20408 .  
         [0148]    Step  20407 : increments the counter i and returns to step  20404 .  
         [0149]    Description will be made of the process flow of the decryption program PROG 3 _ 10020  with reference to FIG. 5.  
         [0150]    Step  20502  (a data setting subroutine): waits for input of the initial value V, the redundancy R, and the secret key K.  
         [0151]    Step  20503  (a ciphertext preparation subroutine): waits for input of ciphertext C′, and divides the given ciphertext C′ into a series of ciphertext blocks C′ i  (1≦i≦n) each having 64 bits and outputs them.  
         [0152]    Step  20504  (a random number generation subroutine): outputs pseudorandom number sequences A i  and B i  (1≦i≦n) based on the secret key K.  
         [0153]    Step  20505  (a decryption subroutine): uses the pseudorandom number sequences A i  and B i , the series of ciphertext blocks C′ i  (1≦i≦n), and the initial value V to output a series of plaintext blocks P′ i  (1≦i≦n).  
         [0154]    Step  20506  (a plaintext extraction subroutine): combines the series of plaintext blocks P′ i  into three data strings L′, M′, and Z′.  
         [0155]    Step  20507  (a redundancy extraction subroutine): divides Z′ into R′ and T′.  
         [0156]    Step  20508 : if T=0 and R′=R, proceeds to step  20510 .  
         [0157]    Step  20509 : outputs a rejection indication and proceeds to step  25011 .  
         [0158]    Step  20510 : stores M′ into a RAM.  
         [0159]    At step  20509  or  20510 , the decryption program outputs a result (acceptance/rejection or the encryption result) to the display  10018  as a notification to the user.  
         [0160]    Description will be made of the process flow of the ciphertext preparation subroutine with reference to FIG. 6.  
         [0161]    Step  20602 : waits for input of ciphertext C′.  
         [0162]    Step  20603 : divides the ciphertext C′ into blocks C′ 1 , C′ 2 , . . . C′ n , each having 64 bits.  
         [0163]    Description will be made of the process flow of the decryption subroutine with reference to FIG. 7.  
         [0164]    Step  20702 : sets an initial value F′ 0  so that F′ 0 =V.  
         [0165]    Step  20703 : initializes a counter so that i=1.  
         [0166]    Step  20704 : calculates a feedback value F′ i  by the formula F′ i =(C′ i ^ F′ i−1 )/B i .  
         [0167]    Step  20705 : calculates a plaintext block P′ i  by the formula P′ i =F′ i ^ A i .  
         [0168]    Step  20706 : if i=n, performs step  20708 .  
         [0169]    Step  20707 : increments the counter i and returns to step  20704 .  
         [0170]    Description will be made of the process flow of the plaintext extraction subroutine with reference to FIG. 8.  
         [0171]    Step  20802 : sets L′ to the first 64-bit plaintext block.  
         [0172]    Step  20803 : sets M′ to the L′ number of bits starting from the most significant bit of P′ 2  included in the series of decrypted plaintext blocks.  
         [0173]    Step  20804 : after L′ and M′ are removed from the series of decrypted plaintext blocks, sets Z′ to the remaining decrypted plaintext blocks (data).  
         [0174]    Description will be made of the process flow of the redundancy extraction subroutine with reference to FIG. 9.  
         [0175]    Step  20902 : sets R′ to the lower 64 bits of Z′.  
         [0176]    Step  20903 : after R′ is removed from Z′, sets T′ to the remaining data.  
         [0177]    [0177]FIG. 10 is an explanatory diagram showing the encryption process. The encircled plus “(+)” denotes an exclusive OR logic operation between two pieces of data each having a width of 64 bits, while the encircled X mark “(×)” denotes a multiplication operation between two pieces of data each having a width of 64 bits in the finite field F2 64 .  
         [0178]    The message M 20931  is added with data  20930  indicating the length, appropriate padding  20932 , and a redundancy R 20933  to produce plaintext P 20934 .  
         [0179]    The produced plaintext P 20934  is divided into blocks P 1     —     20935 , P 2     —     20936 , P 3     —     20937 , . . . P n     —     20938 , each having 64 bits.  
         [0180]    P 1     —     20935  and A 1     —     20940  are exclusive-ORed to produce a feedback value F 1     —     20941  which is then multiplied by B 1     —     20942  in a finite field. The result is exclusive-ORed with an initial value F 0     —     20939  to obtain a ciphertext block C 1     —     20943 .  
         [0181]    Similarly, P 2     —     20936  and A 2     —     20946  are exclusive-ORed to produce a feedback value F 2     —     20945  which is then multiplied by B 2     —     20946  in a finite field. The result is exclusive-ORed with the feedback value F 1     —     20941  to obtain a ciphertext block C 2     —     20947 .  
         [0182]    The above procedure is repeated up to P n     —     20938 , obtaining ciphertext blocks C 1     —     20943 , C 2     —     20947 , C 3     —     20951 , . . . , C n     —     20955 . The ciphertext blocks are concatenated one after another in that order to obtain ciphertext C_ 20956 .  
         [0183]    [0183]FIG. 11 is an explanatory diagram showing the decryption process. The encircled slash “(/)” denotes a division operation between two pieces of data each having a width of 64 bits in the finite field F2 64 . In the figure, data introduced to the encircled slash symbol from top is the dividend, while data introduced from left is the divisor.  
         [0184]    Ciphertext C′_ 20960  is divided into blocks C′ 1     —     20962 , C′ 2     —     20963 , C′ 3     —     20964 , . . . , C′ n     —     20965 , each having 64 bits.  
         [0185]    C′ 1  and an initial value F′ 0     —     20961  are exclusive-ORed, and the result is divided by B 1     —     20966 . The division result is set as a feedback value F′ 1     —     20967 . The feedback value F′ 1     —     20967  and A 1     —     20968  are exclusive-ORed to obtain a plaintext block P′ 1     —     20969 .  
         [0186]    The other blocks C′ 2     —     20963 , C′ 3     —     20964 , . . . , C′ n     —     20965  are also processed in the same way as C′ 1     —     20962  to obtain plaintext blocks P′ 1     —     20969 , P′ 2     —     20972 , P′ 3     —     20977 , . . . , P′ n     —     20981 , which are then concatenated one after another to produce plaintext P′_ 20982 . The plaintext P′_ 20982  is divided into L′_ 20983 , M′_ 20984 , and Z′_ 20985 . Furthermore, Z∝_ 20985  is divided into T′_ 20988  and R′_ 20989  so as to check the redundancy R′_ 20989 .  
         [0187]    The first embodiment uses a pseudorandom number sequence whose length is about twice as long as that of the message for cryptographic processes. Even though pseudorandom-number processing is faster than block-cipher processing, it is highest in computational complexity in these cryptographic processes. Therefore, it is desirable to reduce the number of random numbers to use.  
         [0188]    (Second Embodiment)  
         [0189]    As describe below, a second embodiment of the present invention employs a function different from that used by the first embodiment. By employing this function, the second embodiment can reduce the number of random numbers necessary to use, and use the same divisor for each iteration in its decryption process, which makes it possible to perform the division operation at substantially the same speed as that of a multiplication operation if the reciprocal is calculated beforehand, resulting in very efficient processing.  
         [0190]    The second embodiment employs an encryption program PROG 1 A and a decryption program PROG 3 A instead of the encryption program PROG 1  and the decryption PROG 3 , respectively.  
         [0191]    The encryption program PROG 1 A replaces the random number generation subroutine  20004  and the encryption subroutine  20005  employed in the encryption program PROG 1 _ 10009  in FIG. 1 by a random number generation 2 subroutine  21004  and an encryption 2 subroutine  21005 , respectively.  
         [0192]    Description will be made of the process flow of the random number generation 2 subroutine  21004  with reference to FIG. 12.  
         [0193]    Step  21102  (input of necessary parameters): obtains the number n of message blocks making up a padded message, and a secret key K.  
         [0194]    Step  21103  (generation of pseudorandom number sequence A): calls the random number generation program PROG 2  to generate a pseudorandom number sequence having 64*n bits and output it as a pseudorandom number sequence A.  
         [0195]    Step  21104  (division of pseudorandom number sequence A into blocks): divides the pseudorandom number sequence A into blocks A 1 , A 2 , . . . , A n , each having 64 bits.  
         [0196]    Step  21105  (generation of random number B): executes PROG 2  using the secret key K to generate a random number B having 64 bits.  
         [0197]    Step  21106 : if the value of B generated at step  21105  is 0, returns to step  21105 .  
         [0198]    Description will be made of the process flow of the encryption 2 subroutine  21005  with reference to FIG. 13.  
         [0199]    Step  21202 : sets an initial value F 0  so that F0=V.  
         [0200]    Step  21203 : sets a counter so that i=1.  
         [0201]    Step  21204 : calculates a feedback value F i  by the formula F i =P i ^ A i .  
         [0202]    Step  21205 : calculates a ciphertext block C i  by the formula C i =(F i *B)^ F i−1 .  
         [0203]    Step  21206 : if i=n, performs step  21208 .  
         [0204]    Step  21207 : increments the counter i and returns to step  21204 .  
         [0205]    Description will be made of the process flow of the decryption program PROG 3 A corresponding to PROG 1 A with reference to FIG. 14.  
         [0206]    The decryption program PROG 3 A replaces the random number generation subroutine  20504  and the decryption subroutine  20505  employed in the decryption program PROG 3 _ 10020  by a random number generation 2 subroutine  21304  and a decryption 2 subroutine  21305 , respectively.  
         [0207]    Step  21302  (a data setting subroutine): waits for input of the initial value V, the redundancy R, and the secret key K.  
         [0208]    Step  21303  (a ciphertext preparation subroutine): waits for input of ciphertext C′, and divides the given ciphertext C′ into a series of ciphertext blocks C′ i  (1≦i≦n) each having 64 bits and outputs them.  
         [0209]    Step  21304  (a random number generation subroutine): outputs pseudorandom number sequences A i  (1≦i≦n) and B in response to the secret key K.  
         [0210]    Step  21305  (a decryption subroutine): uses the pseudorandom number sequences A i  and B, the series of ciphertext blocks C′ i  (1≦i≦n), and the initial value V to output a series of plaintext blocks P′i (1≦i≦n).  
         [0211]    Step  21306  (a plaintext extraction subroutine): combines the series of plaintext blocks P′ i  into three data strings L′, M′, and Z′.  
         [0212]    Step  21307  (a redundancy extraction subroutine): divides Z′ into R′ and T′.  
         [0213]    Step  21308 : if T=0 and R′=R, proceeds to step  21310 .  
         [0214]    Step  21309 : outputs a rejection indication and proceeds to step  21311 .  
         [0215]    Step  21310 : stores M′ into a RAM.  
         [0216]    Description will be made of the process flow of the decryption 2 subroutine  21305  in FIG. 14 with reference to FIG. 15.  
         [0217]    Step  21402 : sets an initial value F′ 0  so that F′ 0 =V.  
         [0218]    Step  21403 : calculates 1/B beforehand.  
         [0219]    Step  21404 : initializes a counter so that i=1.  
         [0220]    Step  21405 : calculates a feedback value F′ i  by the formula F′ 1 =(C′ i ^ F′ i−1 )*(1/B).  
         [0221]    Step  21406 : calculates a plaintext block P′ i  by the formula P′ i =F′ i ^ A i .  
         [0222]    Step  21407 : if i=n, performs step  21409 .  
         [0223]    Step  21408 : increments the counter i and returns to step  21405 .  
         [0224]    [0224]FIG. 16 is an explanatory diagram showing the encryption process employed by the above method of increasing the processing speed.  
         [0225]    The message M 21421  is added with data  21420  indicating the length, appropriate padding  21422 , and a redundancy R 21423  to produce plaintext P 21424 .  
         [0226]    The produced plaintext is divided into blocks P 1     —     21425 , P 2     —     21426 , P 3     —     21427 , . . . , P n     —     21428 , each having 64 bits.  
         [0227]    P   —     21425  and A 1     —     21431  are exclusive-ORed to produce a feedback value F 1     —     21432  which is then multiplied by B_ 21429  in a finite field. The result is exclusive-ORed with an initial value F 0     —     21430  to obtain a ciphertext block C 1     —     21433 .  
         [0228]    Similarly, P 2     —     21426  and A 2     —     21434  are exclusive-ORed to produce a feedback value F 2     —     21435  which is then multiplied by B_ 21429  in a finite field. The result is exclusive-ORed with the feedback value F 1     —     21432  to obtain a ciphertext block C 2     —     21436 .  
         [0229]    The above procedure is repeated up to P n     —     21428 , obtaining ciphertext blocks C 1     —     21433 , C 2     —     21436 , C 3     —     21439 , . . . , C n     —     21442 . The ciphertext blocks are concatenated one after another in that order to obtain ciphertext C_ 21443 .  
         [0230]    [0230]FIG. 17 is an explanatory diagram showing the corresponding decryption process.  
         [0231]    Ciphertext C′_ 21450  is divided into blocks C′ 1     —     21453 , C′ 2     —     21454 , C′ 3     —     21455 , . . . , C′ n     —     21456 , each having 64 bits.  
         [0232]    C′ 1  and an initial value F′ 0     —     21451  are exclusive-ORed, and the result is multiplied by 1/B_ 21452 . The multiplication result is set as a feedback value F′ 1     —     21457 . The feedback value F′ 1     —     21457  and A 1     —     21458  are exclusive-ORed to obtain a plaintext block P′ 1     —     21459 .  
         [0233]    The other blocks C′ 2     —     21454 , C′ 3     —     21455 , . . . , C′ n     —     21456  are also processed in the same way as C′ 1     —     21453  to obtain plaintext blocks P′ 1     —     21459 , P′ 2     —     21462 , P′ 3     —     21465 , . . . P′ n     —     21468 , which are then concatenated one after another to produce plaintext P′_ 21476 . The plaintext P′_ 21476  is divided into L′_ 21469 , M′_ 21470 , and Z′_ 21471 . Furthermore, Z′_ 21471  is divided into T′_ 21474  and R′_ 21475  so as to check the redundancy R′_ 21475 .  
         [0234]    The second embodiment uses a 64-bit redundancy, and therefore employs addition and multiplication in the finite field F2 64 .  
         [0235]    With enhanced efficiency provided by this embodiment, it is possible to realize high-speed cryptographic processing. An implementation example written in the C programming language achieved a processing speed of 202 Mbit/sec in encryption processing using a 64-bit processor with a clock frequency of 600 MHz. On the other hand, a processing speed of 207 Mbit/sec was observed in decryption processing.  
         [0236]    The above implementation uses such operations as pseudorandom number generation, exclusive OR, and multiplication in the finite field F2 64  which are efficiently implemented especially by hardware. For example, it is estimated that with a gate array fabricated in a 0.35-μm process, the above operations can be implemented by adding an additional circuit having 3 k gates for the pseudorandom number generator. Furthermore, the pseudorandom number generator can be implemented using parallel processing, making it easy to realize a parallel processing device (including the pseudorandom number generator) having a processing speed as high as required. Thus, it is possible to realize a processing speed of 9.6 Gbit/sec at maximum by adding a circuit having about 36 k gates to a parallel pseudorandom number generator.  
         [0237]    (Third Embodiment)  
         [0238]    As described below, a third embodiment of the present invention uses another high-speed processing function to provide processing at higher speed with the same security level as those of the first and the second embodiments. In another aspect, the third embodiment can provide higher security equivalent to F2 128  if operations in the finite field F2 64  employed in the first and second embodiments are also used.  
         [0239]    In the aspect of providing processing at higher speed described above, the third embodiment uses an operation in the finite field F2 32  twice. Since multiplication in the field F2 64  generally requires a computational amount (computational complexity) four times as much as that for the finite field F2 32 , the third embodiment requires only half ((¼)*2) of the computational amount (computational complexity) required by an operation in the finite field F2 64 , actually doubling the processing speed.  
         [0240]    In the aspect of enhancing security, the third embodiment can use both an operation in the finite field F2 64  and a 64-bit feedback value twice to reduce the alteration success rate from 2 −64  of the above method to 2 −128 .  
         [0241]    The third embodiment employs an encryption program PROG 1 B and a decryption program PROG 3 B instead of the encryption program PROG 1  and the decryption program PROG 3 .  
         [0242]    The encryption program PROG 1 B replaces the random number generation subroutine (step  20004 ) and the encryption subroutine (step  20005 ) employed in the encryption program PROG 1 _ 10009  in FIG. 1 by a random number generation 3 subroutine  21504  and an encryption 3 subroutine  21505 . Description will be made of the process flow of the encryption program PROG 1 B with reference to FIG. 18.  
         [0243]    Step  21502  (a data setting subroutine): waits for input of an initial value V, a redundancy R, and a secret key K.  
         [0244]    Step  21503  (a plaintext preparation subroutine): waits for input of plaintext, adds predetermined padding and a redundancy to the given plaintext, and divides the padded plaintext into a series of plaintext blocks P i  (1≦i≦n) each having 32 bits and outputs them.  
         [0245]    Step  21504  (random number generation 3 subroutine): outputs pseudorandom number sequences A i  (1≦i≦n), Ba, and Bb based on the secret key K.  
         [0246]    Step  21505  (encryption 3 subroutine): uses the pseudorandom number sequences A i , Ba, and Bb, the series of plaintext blocks P i  (1≦i≦n), and the initial value V to output a series of ciphertext blocks C i  (1≦i≦n).  
         [0247]    Step  21506 : concatenates the series of ciphertext blocks C i  (1≦i≦n) obtained at step  21505  one after another sequentially to output ciphertext C.  
         [0248]    Description will be made of the process flow of the random number generation 3 subroutine  21504  with reference to FIG. 19.  
         [0249]    Step  21602  (input of necessary parameters): obtains the number n of message blocks making up the padded message and the secret key K.  
         [0250]    Step  21603  (generation of pseudorandom number sequence A): calls the random number generation program PROG 2  to generate a pseudorandom number sequence having 32*n bits and output it as a pseudorandom number sequence A.  
         [0251]    Step  21604  (division of random number sequence A into blocks): divides the pseudorandom number sequence A into blocks A 1 , A 2 , . . . , A n , each having 32 bits.  
         [0252]    Step  21605  (generation of random number Ba): executes PROG 2  using the secret key K to generate a random number Ba having 32 bits.  
         [0253]    Step  21606 : if the value of the random number Ba generated at step  21605  is 0, returns to step  21605 .  
         [0254]    Step  21607  (generation of random number Bb): executes PROG 2  using the secret key K to generate a random number Bb having 32 bits.  
         [0255]    Step  21608 : if the value of the random number Bb generated at step  21607  is 0, returns to step  21607 .  
         [0256]    Description will be made of the process flow of the encryption 3 subroutine  21505  with reference to FIG. 20. The symbols “*” and “^ ” denote multiplication and addition, respectively, in the finite field F2 32 .  
         [0257]    Step  21702 : sets initial values FA 0  and FB 0  so that FA 0 =FB 0 =V.  
         [0258]    Step  21703 : initializes a counter so that i=1.  
         [0259]    Step  21704 : calculates a feedback value FA i  by the formula FA i =P i ^ A i .  
         [0260]    Step  21705 : calculates a feedback value FB i  by the formula FB i =(FA i *Ba)^ FA i−1 .  
         [0261]    Step  21706 : calculates a ciphertext block C i  by the formula C i =(FB i *Bb)^ FB i−1 .  
         [0262]    Step  21707 : if i=n, performs step  21709 .  
         [0263]    Step  21708 : increments the counter i and returns to step  21704 .  
         [0264]    Description will be made of the process flow of the decryption program PROG 3 B with reference to FIG. 21. The decryption program PROG 3 B replaces the random number generation subroutine  20504  and the decryption subroutine  20505  employed in the decryption program PROG 3 _ 10020  by a random number generation 3 subroutine  21804  and a decryption 3 subroutine  21805 , respectively.  
         [0265]    Step  21802  (a data setting subroutine): waits for input of the initial value V, the redundancy R, and the secret key K.  
         [0266]    Step  21803  (a ciphertext preparation subroutine): waits for input of ciphertext C′, and divides the given ciphertext C′ into a series of ciphertext blocks C′ i  (1≦i≦n) each having 32 bits and outputs them.  
         [0267]    Step  21804  (a random number generation subroutine): outputs pseudorandom number sequences A i  (1≦i≦n), Ba, and Bb based on the secret key K.  
         [0268]    Step  21805  (a decryption subroutine): uses the pseudorandom number sequences A i , Ba, Bb, the series of ciphertext blocks C′ i  (1≦i≦n), and the initial value V to output a series of plaintext blocks P′ i  (1≦i≦n).  
         [0269]    Step  21806  (a plaintext extraction subroutine): combines the series of plaintext blocks P′ i  into three data strings L′, M′, Z′.  
         [0270]    Step  21807  (a redundancy extraction subroutine): divides Z′ into R′ and T′.  
         [0271]    Step  21808 : if T=0 and R=R′, proceeds to step  21810 .  
         [0272]    Step  21809 : outputs a rejection indication and proceeds to step  21811 .  
         [0273]    Step  21810 : stores M′ into a RAM.  
         [0274]    Description will be made of the process flow of the decryption 3 subroutine  21805  in FIG. 21 with reference to FIG. 22. The symbol “/” denotes division in the finite field F2 32 .  
         [0275]    Step  21902 : sets initial values FA′ 0  and FB′ 0  so that FA′ 0 =FB′ 0 =V.  
         [0276]    Step  21903 : calculates 1/Ba and 1/Bb beforehand.  
         [0277]    Step  21904 : initializes a counter so that i=1.  
         [0278]    Step  21905 : calculates a feedback value FB′ i  by the formula FB′ i =(C′ i ^ FB i−1 )*(1/Bb).  
         [0279]    Step  21906 : calculates a feedback value FA′ i  by the formula FA′ i =(FB′ i ^ FA′ i−1 )*(1/Ba).  
         [0280]    Step  21907 : calculates a plaintext block P′ i  by the formula P′ i =FA′ i ^ A i .  
         [0281]    Step  21908 : if i=n, performs step  21910 .  
         [0282]    Step  21909 : increments the counter i and returns to step  21905 .  
         [0283]    [0283]FIG. 23 is an explanatory diagram showing the encryption process employed by the above method of increasing the processing speed.  
         [0284]    The message M 21921  is added with data L 21920  indicating the length, appropriate padding  21922 , and a redundancy R 21923  to produce plaintext P 21924 .  
         [0285]    The produced plaintext P 21924  is divided into blocks P 1     —     21925 , P 2     —     21926 , P 3     —     21927 , . . . , P n_21928, each having 32 bits.    
         [0286]    P 1     —     21925  and A 1     —     21933  are exclusive-ORed to produce a feedback value FA 1     —     21934  which is then multiplied by Ba_ 21929  in a finite field. The result is exclusive-ORed with an initial value FA 0     —     21930  to obtain a feedback value FB 1     —     21935 . The obtained feedback value FB 1     —     21935  is multiplied by Bb_ 21931  in a finite field, and the multiplication result is exclusive-ORed with an initial value FB 0     —     21932  to obtain a ciphertext block C 1     —     21936 .  
         [0287]    Similarly, P 2     —     21926  and A 2     —     21937  are exclusive-ORed to produce a feedback value FA 2     —     21938  which is then multiplied by Ba_ 21929  in a finite field. The result is exclusive-ORed with the feedback value FA 1     —     21934  to obtain an feedback value FB 2     —     21939 . The obtained FB 2     —     21939  is multiplied by Bb_ 21931  in a finite field, and the multiplication result is exclusive-ORed with the feedback value FB 1     —     21935  to obtain a ciphertext block C 2     —     21940 .  
         [0288]    The above procedure is repeated up to P n     —     21928 , obtaining ciphertext blocks C 1     —     21936 , C 2     —     21940 , C 3     —     21944 , . . . , C n_21950. The ciphertext blocks are concatenated one after another in that order to obtain ciphertext C_21951.    
         [0289]    [0289]FIG. 24 is an explanatory diagram showing the corresponding decryption process.  
         [0290]    Ciphertext C′_ 21960  is divided into blocks C′ 1     —     21961 , C′ 2     —     21962 , C′ 3     —     21963 , . . . , C′ n_21964, each having  32 bits.  
         [0291]    C′ 1  and an initial value FB′   —     21965  are exclusive-ORed, and the result is multiplied by 1/Bb_ 21966 . The multiplication result is set as a feedback value FB′ 1     —     21969 . The feedback value FB′ 1     —     21969  is exclusive-ORed with an initial value FA′ 0     —     21967 , and the result is multiplied by 1/Ba_ 21968  to generate a feedback value FA′ 1     —     21970 . The feedback value FA′ 1     —     21970  is exclusive-ORed with A 1     —     21971  to obtain a plaintext block P′ 1     —     21972 .  
         [0292]    The other blocks C′ 2     —     21962 , C′ 3     —     21963 , . . . , C′ n     —     21964  are also processed in the same way as C′ 1     —     21961  to obtain plaintext blocks P′ 1     —     21972 , P′ 2     —     21976 , P′ 3     —     21980 , P n_21985, which are then concatenated one after another to produce plaintext P′_21986. The plaintext P′_21986 is divided into L′_21897, M′_21988, and Z∝_21989. Furthermore, Z′_21989 is divided into T′_21992 and P′_21993 so as to check the redundancy R′_21993.    
         [0293]    (Fourth Embodiment)  
         [0294]    As described below, a fourth embodiment of the present invention provides a cryptographic method capable of properly starting encryption/decryption processing without using information on the length of a message to be processed. Accordingly, the fourth embodiment makes it possible to perform cryptographic processing of data (message) of a stream type, whose entire length is not known beforehand.  
         [0295]    The fourth embodiment replaces the random number generation 2 subroutine and the plaintext preparation subroutine in the encryption program PROG 1 A, and the decryption program PROG 3 A employed in the second embodiment by a random number generation 4 subroutine, a plaintext preparation 2 subroutine, and a decryption program PROG 6 , respectively.  
         [0296]    Description will be made of the process flow of the random number generation 4 subroutine with reference to FIG. 29.  
         [0297]    Step  40212  (input of necessary parameters): obtains the number n of message blocks making up a padded message, and a secret key K.  
         [0298]    Step  40213  (generation of pseudorandom number sequence A): calls the random number generation program PROG 2  to generate a pseudorandom number sequence having 64*n bits and output it as a pseudorandom number sequence A.  
         [0299]    Step  40214  (division of pseudorandom number sequence A into blocks): divides the pseudorandom number sequence A into blocks A 1 , A 2 , . . . A n , each having 64 bits.  
         [0300]    Step  40215  (generation of random number B): executes PROG 2  using the secret key K to generate a random number B having 64 bits.  
         [0301]    Step  40216 : if the value of B generated at step  40215  is 0, returns to step  40215 .  
         [0302]    Step  40217  (generation of random number Q): executes PROG 2  using the secret key K to generate a random number Q having 64 bits.  
         [0303]    Next, description will be made of the process flow of the plaintext preparation 2 subroutine with reference to FIGS. 30 and 31.  
         [0304]    Step  40202 : waits for input of an encryption-target message M 40300 . The message is either input from the keyboard  10008  or read out from a RAM, or introduced from another medium.  
         [0305]    Step  40203 : adds padding to the message so that the length of the message is a multiple of a predetermined number. Specifically, the padded data (message) is set to have an integer multiple of 64 bits for subsequent processing. When the length of the message M 40300  is L bits, this step adds (64−L(mod 64)) number of Os to the end of the message M 40300 .  
         [0306]    Step  40204  (addition of secret data): further adds 64-bit secret data Q 40302  to the end of the message M 40300 . The secret data Q 40302  can be known by only a person who holds or has obtained its key (or the key data). The secret data may be a random number generated from the secret key K. The above step  40217  performs this process of generating secret data.  
         [0307]    Step  40205  (addition of redundancy data): still further adds a redundancy R 40303  of 64 bits to the end of the message M 40300 .  
         [0308]    Step  40206  (division of message data into plaintext blocks): divides the data P 40304  (the padded message) obtained at step  40205  into blocks P 1 , P 2 , . . . , P n , each having 64 bits.  
         [0309]    Description will be made of the process flow of the decryption program PROG 6  with reference to FIGS. 32 and 34.  
         [0310]    Step  40402  (a data setting subroutine): waits for input of the initial value V, the redundancy R, and the secret key K.  
         [0311]    Step  40403  (a ciphertext preparation subroutine): waits for input of ciphertext C′, and divides the given ciphertext C′ into a series of ciphertext blocks C′ i  (1≦i≦n) each having 32 bits and output them.  
         [0312]    Step  40404  (random number generation 4 subroutine): outputs pseudorandom number sequences A i  (1≦i≦n) and B based on the secret key K.  
         [0313]    Step  40405  (decryption 3 subroutine): uses the pseudorandom number sequences A i , B, and Q, the series of the ciphertext blocks C′ i  (1≦i≦n), and the initial value V to output a series of plaintext blocks P′ i  (1≦i≦n).  
         [0314]    Step  40406  (plaintext extraction 2 subroutine): combines the series of plaintext blocks P′ i   40601  into three data strings M′ 40602 , Q′ 40603 , and R′ 40604 .  
         [0315]    Step  40407 : if Q′ 40603 =Q 40302  and R′ 40604 =R 40303 , proceeds to step  40409 .  
         [0316]    Step  40408 : outputs a rejection indication and proceeds to step  40410 .  
         [0317]    Step  40409 : stores M′ into a RAM.  
         [0318]    Step  40410 : ends the process.  
         [0319]    Next, description will be made of the process flow of the plaintext extraction 2 subroutine with reference to FIG. 33.  
         [0320]    Step  40502 : removes the last 128 bits of the decrypted plaintext, and sets a plaintext block M′ to the remaining decrypted text.  
         [0321]    Step  40503 : sets Q′ to the upper 64 bits of the removed last 128 bits obtained at step  40502 .  
         [0322]    Step  40504 : sets R′ to the lower 64 bits of the removed last 128 bits.  
         [0323]    (Fifth Embodiment)  
         [0324]    The above first through fourth embodiments of the present invention have a single-processor configuration, that is, they do not employ parallel processing. A fifth embodiment of the present invention, however, shows that the present invention can be easily applied to parallel processing.  
         [0325]    The system configuration (not shown) of the fifth embodiment is different from that shown in FIG. 1 in that the computer A 10002  employs both a CPU  1 _ 30004  and a CPU  2 _ 30005  instead of the CPU  10004 , and the RAM  10005  stores a parallel encryption program PROG 4 _ 30016  in addition to the components shown in FIG. 1. Furthermore, the computer B 10003  employs both a CPU  1 _ 30017  and a CPU  2 _ 30018  instead of the CPU  10015 , and the RAM  10016  stores a parallel decryption program PROG 5 _ 30025  in addition to the components shown in FIG. 1.  
         [0326]    The computer A 10002  executes the parallel encryption program PROG 4 _ 30016  to generate ciphertext C 10022  from a message M 10014  and transmit the generated ciphertext C 10022 . Receiving the ciphertext C 10022 , the computer B 10003  executes the parallel decryption program PROG 5 _ 30025 , and if no alteration is detected, the computer B 10003  stores the decryption results into the RAM  10016 .  
         [0327]    The CPUs  1 _ 30004  and  2 _ 30005  implement the parallel encryption program PROG 4 _ 30016  by executing the program read out from the RAM  10005  in the computer A 10002 . The parallel encryption program PROG 4 _ 30016  internally calls and executes the encryption program PROG 1 _ 10009  and the random number generation program PROG 2 _ 10010  as its subroutines.  
         [0328]    The CPUs  1 _ 30017  and  2 _ 30018  executes the parallel decryption program PROG 5 _ 30025  read out from the RAM  10016  in the computer B 10003 . The parallel decryption program PROG 5 _ 30025  calls and executes the decryption program PROG 3 _ 10020  and the random number generation program PROG 2 _ 10021  as its subroutines.  
         [0329]    The other configurations and operations of the system are the same as those shown in FIG. 1.  
         [0330]    Description will be made of the process flow of the parallel encryption program PROG 4 _ 30016  with reference to FIG. 25. The expression “A∥B” denotes concatenation of two bit-strings A and B.  
         [0331]    Step  40002 : divides a message M into two parts, M 1  and M 2 , in message processing performed by the CPU  1 .  
         [0332]    Step  40003 : uses an initial value V+1, a redundancy R+1, a secret key K, and the plaintext M 1  to output ciphertext C 1  in encryption processing by the encryption program PROG 1 _ 10009  executed by CPU  1 .  
         [0333]    Step  40004 : uses an initial value V+2, a redundancy R+2, the secret key K, and the plaintext M 2  to output ciphertext C 2  in encryption processing by the encryption program PROG 1 _ 10009  executed by CPU  2 .  
         [0334]    Step  40005 : uses an initial value V, a redundancy R, the secret key K, and plaintext (R 1 ∥R 2 ) to output ciphertext C 3  in encryption processing by the encryption program PROG 1 _ 10009  executed by CPU  1 .  
         [0335]    Step  40006 : generates ciphertext C (C=C 1 ∥C 2 ∥C 3 ).  
         [0336]    Step  40007 : stores the ciphertext C into a memory.  
         [0337]    Description will be made of the process flow of the parallel decryption program PROG 5 _ 30025  with reference to FIG. 26.  
         [0338]    Step  40102 : divides ciphertext C′ into three parts, C′ 1 , C′ 2 , and C′ 3 . C′ 3  has 192 bits, and C′ 1  and C′ 2  has the same length, where C′=C′ 1 ∥C′ 2 ∥C′ 3 .  
         [0339]    Step  40103 : uses the initial value V+1 and the secret key K to decrypt the ciphertext block C′ 1  into a message block M′ 1  and the redundancy R+1 in decryption processing by the decryption program PROG 3 _ 10020  executed by the CPU  1 , and stores the message block M′ 1  and the redundancy R+1.  
         [0340]    Step  40104 : uses the initial value V+2 and the secret key K to decrypt the ciphertext block C′ 2  into a message block M′ 2  and the redundancy R+2 in decryption processing by the decryption program PROG 3 _ 10020  executed by CPU  2 , and stores the message block M′ 2  and the redundancy R+2.  
         [0341]    Step  40105 : if at least one of the decryption results obtained at steps  40103  and  40104  is a reject, performs step  40111 .  
         [0342]    Step  40106 : uses the initial value V and the secret key K to decrypt the ciphertext block C′ 3  into a block and the redundancy R in decryption processing by the decryption program PROG 3 _ 10020  executed by the CPU 1 , and stores the decryption result (the decrypted block) and the redundancy R.  
         [0343]    Step  40107 : if the decryption results obtained at step  40106  is a reject, performs step  40111 .  
         [0344]    Step  40108 : if the decrypted block obtained at step  40106  is not equal to (R+1)∥(R+2), performs step  40111 .  
         [0345]    Step  40109 : lets M′=M′ 1 ∥M′ 2  (M′: decryption result).  
         [0346]    Step  40110 : stores M′ into a memory and performs step  40112 .  
         [0347]    Step  40111 : outputs a rejection indication.  
         [0348]    As described above, the fifth embodiment can provide parallel cryptographic processing using two separate processors.  
         [0349]    [0349]FIG. 27 is an explanatory diagram showing the encryption process employed by the above parallel cryptographic processing method.  
         [0350]    M 1     —     40141  and M 2     —     40142  obtained as a result of dividing a message M 40140  are added with redundancies R+1 and R+2, respectively, and denoted as blocks  40143  and  40144 . The blocks  40143  and  40144  are encrypted by use of encryption processes  40146  and  40147  to obtain ciphertext blocks C 1     —     40149  and C 2     —     40150 , respectively. Further, a combination of the redundancies R+1 and R+2, which is set as a message, and another redundancy R are encrypted to obtain a ciphertext block C 3     —     40151 .  
         [0351]    The ciphertext blocks C 1     —     40149 , C 2     —     40150 , and C 3     —     40151  are concatenated one after another to output ciphertext C 40152 .  
         [0352]    [0352]FIG. 28 is an explanatory diagram showing the corresponding parallel decryption process.  
         [0353]    Ciphertext C′ 40160  is divided into three blocks, C′ 1     —     40161 , C′ 2     —     40162 , and C′ 3     —     40163 .  
         [0354]    The obtained blocks C′ 1     —     40161 , C′ 2     —     40162 , and C′ 3     —     40163  are decrypted by decryption processes  40164 ,  40165 , and  40166  to obtain plaintext blocks  40167 ,  40168 , and  40169 , respectively.  
         [0355]    If the obtained plaintext blocks are accepted, and the redundancies included in the plaintext blocks  40167  and  40168  are identical to the message portions of the plaintext block  40169 , and furthermore the redundancy included in the plaintext block  40169  is equal to the one shared beforehand, the message portions M′ 1     —     40170  and M′ 2     —     40171  are extracted from the plaintext blocks  40167  and  40168 , respectively, and concatenated to obtain a message M′ 40172 .  
         [0356]    Any CPU capable of executing a program can be used for the above embodiments whether it is a general-purpose CPU or a dedicated one. Even though the above embodiments are each implemented by execution of programs by a CPU (or CPUs), dedicated hardware can be used for each process employed, providing high speed and low cost.  
         [0357]    Any of known pseudorandom number generators can be applied to the above embodiments. The known pseudorandom number generators include a pseudorandom generator using a linear feedback shift register (LFSR) with a nonlinear filter, a nonlinear feedback shift register, a combining generator, a shrinking generator, a clock-controlled pseudorandom number generator, a Geffe generator, an alternating step generator, RC4, SEAL, PANAMA, the OFB mode of the block cipher, the counter mode of the block cipher, and other pseudorandom number generators using hash functions.  
         [0358]    (Sixth Embodiment)  
         [0359]    The above first through fifth embodiments each provides a cryptographic processing method. A sixth embodiment of the present invention, on the other hand, shows that the present invention can be applied to various information systems.  
         [0360]    [0360]FIG. 35 is a diagram showing the configuration of a system in which computers A 50016  and B 50017  are connected through a network  50009  for cryptocommunications from the computer A 50016  to the computer B 50017 . The computer A 50016  has a CPU  50007 , a RAM  50001 , and a network interface device  50008  therein. The RAM  50001  stores key-exchange protocol software  50002  for executing a key-exchange protocol, a public key  50004  of the authentication center, a secret-key generation program  50003 , an encryption program  50006 , and communication data  50005  (corresponding to the message M in each embodiment described above) to be transmitted using cryptocommunications. The computer B 50017  has a CPU  50014 , a RAM  50010 , and a network interface device  50015  therein. The RAM  50010  stores key-exchange protocol software  50011  and a decryption program  50013 .  
         [0361]    The computer A executes the secret-key generation program  50003  to generate a secret key used for cryptocommunications with the computer B 50017 . The computers A 50016  and B 50017  executes the key-exchange protocol software  50002  and  50011 , respectively, to share the secret key generated by the computer A.  
         [0362]    After sharing the secret key, the computer A 50016  executes the encryption program  50006  of the present invention to encrypt the communication data  50005  at high speed. The computer A 50016  then transmits the encryption results to the computer B 50017  through the network  50009  using the network interface device  50008 .  
         [0363]    The computer B 50017  executes the decryption program  50013  of the present invention to decrypt received ciphertext at high speed to restore the communication data.  
         [0364]    This embodiment shows that the present invention can provide high-speed and safe cryptocommunications even when available hardware resources are limited. That is, the present invention is capable of realizing a highly safe cryptocommunication system which is faster than the conventional cryptographic method, and provides confidentiality as well as a mathematically proven alteration detection function.  
         [0365]    (Seventh Embodiment)  
         [0366]    The above sixth embodiment performs cryptographic processing by use of software. A seventh embodiment of the present invention, on the other hand, shows that the present invention can be realized by hardware implementation.  
         [0367]    [0367]FIG. 36 is a diagram showing the configuration of an encryption apparatus employed in a crytocommunication system using a network. The computer  50110  has a RAM  50101 , a CPU  50104 , and a network interface device  50105  therein, and is connected to a network  50106 . The RAM  50101  stores communication data  50103  (corresponding to the message M in each embodiment described above) to be encrypted and a communication program  50102 , and the CPU  50104  executes the communication program  50102  to output the communication data  50103  to the network interface device  50105 . The network interface device  50105  includes a secret-key generation circuit  50107 , an encryption circuit  50109 , and a key-exchange protocol circuit  50108 , and has a public key  50110  of the authentication center stored in its memory area. According to the execution of the communication program  50102 , the network interface device  50105  generates a secret key by use of the secret-key generation circuit  50107 , and exchanges the generated secret key with another device on the network using the key-exchange protocol circuit  50108  so as to share the generated secret key with the communication destination device. The encryption circuit  50109  in the network interface device  50105  encrypts the input communication data  50103  at high speed using the generated and then shared secret key to generate ciphertext, which is then output to the network  50106 .  
         [0368]    This embodiment shows that the present invention can provide safe and fast cryptocommunications using limited hardware resources. Particularly, if this embodiment is combined with the cryptographic processing method of the second embodiment, more efficient and safe cryptocommunications can be realized. This is because addition and multiplication in the finite field F2 64  employed in the second embodiment are suitable for hardware implementation. The decryption process can also be implemented by hardware in the same way.  
         [0369]    As shown by this embodiment, the present invention can provide a cryptographic method whose hardware implementation requires a small number of gates or performs very high-speed processing.  
         [0370]    (Eighth Embodiment)  
         [0371]    By using a computer capable of performing cryptographic processing employed in the sixth or seventh embodiment, it is possible to easily realize a contents delivery protected by encryption. An eighth embodiment of the present invention shows an example of a contents delivery.  
         [0372]    As shown in FIG. 37, a storage device (whose medium is not limited to a specific type, that is, it is possible to use a semiconductor storage device, a hard disk, a magnetic storage device such as one using tape, or an optical storage device such as a DVD or an MO) storing contents  50201  as digital information is connected to a computer  50202  capable of performing encryption processing according to the present invention. An information reproduction device  50205  (an MPEG reproduction device, a digital TV, a personal computer, etc.) which is to reproduce contents and may be located in a physically remote place is connected to an external coding device  50204  capable of performing decryption processing according to the present invention. The computer  50202  and the external coding device are connected to each other through a network  50203 .  
         [0373]    The contents  50201  is encrypted by the computer  50202  capable of encryption, and then transmitted to the network  50203 . The external coding device  50204  capable of decryption decrypts the encrypted contents, and outputs the decryption results to the information reproduction device  50205 . The information reproduction device  50205  stores and reproduces input information.  
         [0374]    The contents  50201  handled by the information reproduction device  50205  include not only electronic files but also multimedia data such as computer software, sound, and image. Contents which require real-time processing, such as sound and movie, can be encrypted or decrypted at high speed by applying the present invention, making it possible to secure smooth real-time transmission. Furthermore, the receiving device can detect data corruption due to alteration or noise during the transmission, ensuring communications free of transmission errors.  
         [0375]    (Ninth Embodiment)  
         [0376]    The eighth embodiment delivers contents by transmission through a network. When it is necessary to deliver a very large amount of information, however, it is more efficient to deliver ciphertext on a DVD, etc. beforehand, and then transmit the decryption key at the time of permitting the decryption of the ciphertext. Such a system is provided by a ninth embodiment.  
         [0377]    As shown in FIG. 38, contents are distributed to the consumer as ciphertext, using a medium such as a DVD-ROM  50307 , beforehand. The consumer enters information  50306  (money transfer information) on payment for contents using a contents-key exchange program  50305  running on the consumer&#39;s personal computer  50304 . The contents-key exchange program  50305  then obtains a key from a contents-key table in a key server  50302  through a network  50303 . A decryption program  50308  decrypts the ciphertext contents recorded on the DVD-ROM  50307  using the obtained key. The decryption results are output to the information reproduction device  50309  which then reproduces the contents.  
         [0378]    This embodiment may be configured such that the contents are not output to the information reproduction device  50309 , and the personal computer  50304  itself reproduces them. In a typical example, the contents is a program to be executed on a personal computer. The above reproduction method of using a personal computer is efficient in such a case. When ciphertext contents recorded on a DVD-ROM can be divided into several parts, and each part is encrypted using a different key, it is possible to control keys transmitted to the contents-key acquisition program  50305  so as to limit contents which can be decrypted by the consumer.  
         [0379]    The ninth embodiment was described assuming that data recorded on the DVD-ROM  50307  is to be read out. Generally, a very large amount (a few tens of megabytes to a few hundreds of megabytes) of data is stored on the DVD-ROM  50307 , and therefore a fast cryptographic processing method is required for processing such data. Since the present invention can provide high-speed decryption, the present invention is suitably applied to distribution of charged contents using a DVD medium.  
         [0380]    (Tenth Embodiment)  
         [0381]    In a tenth embodiment of the present invention, the present invention is applied to a router which controls packet transfer on a network. This router encrypts packets differently depending on the destination router of each packet at the time of their transmission to the network.  
         [0382]    [0382]FIG. 39 is a diagram showing the configuration of a cryptographic router. The network router  50401  has a routing table  50402 , a packet exchanger  50403 , network interfaces A 50404 , B 50405 , and C 50406 , and an internal parallel encryption/decryption device  50410  therein. The network interfaces A 50404 , B 50405 , and C 50406  are connected to external networks A 50407 , B 50408 , and C 50409 , respectively.  
         [0383]    The internal parallel encryption/decryption device  50410  has a secret-key table  50411 , a router-key storage area  50412 , and a parallel encryption/decryption circuit  50413  therein.  
         [0384]    A packet sent from the network A 50407  is transmitted to the internal parallel encryption/decryption device  50410  through the network interface A 50404 . After recognizing that the received packet is originated from the network A 50407 , the internal parallel encryption/decryption device  50410  refers to the secret-key table  50411  to obtain the secret key corresponding to the network A 50407 , stores the obtained secret key in the router-key storage area  50412 , and decrypts the packet using the parallel encryption/decryption circuit  50413 . The internal parallel encryption/decryption device  50410  then transmits the s decryption results to the packet exchanger  50403 .  
         [0385]    The following description assumes that this decrypted packet should be transmitted to the network B. The packet exchanger  50403  transfers the packet to the internal parallel encryption/decryption device  50410 . The internal parallel encryption/decryption device  50410  refers to the secret-key table  50411  to obtain the secret key corresponding to the network B 50408 , stores the obtained secret key in the router-key storage area  50412 , and encrypts the packet using the parallel encryption/decryption circuit  50413 . The internal parallel encryption/decryption device  50410  then transmits the encryption results to the network interface B 50405  which, in turn, transmits the received encrypted packet to the network B 50408 .  
         [0386]    This embodiment is applied to an application used in an environment in which a large quantity of hardware resources are available and which requires cryptocommunications at very high speed. In the CBC mode of the block cipher in which parallel processing is difficult to employ, it is difficult to enhance its processing speed even when a large quantity of hardware resources are available. In contrast, parallel processing is very easy to employ in the present invention (providing a high level of parallel operation) since the pseudorandom number generation process is independent from the plaintext and ciphertext processing. That is, the present invention can attain a higher communication speed in the environment in which a large quantity of hardware resources suitable for parallel processing are available.