Patent Application
20060050872
The present invention relates to a data transformation apparatus, data transformation methods, and storage media in which data transformation methods are recorded, for encryption, decryption, and data diffusion in order to protect digital information on information communications.
As shown in
As shown in
Conventional encryption devices use multiple S-boxes. Since some ciphers are equipped with mutually different tables, memory usage is increased as compared to ones equipped with one S-box. Since, on the other hand, other ciphers use only one S-box, the security of the cipher is decreased.
As shown in
Furthermore, in generating extension keys, complex operations are required in order to generate the extension keys having higher security. There is another problem in case of generating the extension keys that the number of bits of key data to be input as an initial value should be fixed.
The present invention aims to provide systems in which circuits for encryption and decryption are the same, and in which circuit area, program size and memory usage which are used for non-linear transformation computation can be reduced, and furthermore, the extension keys can be generated using a simpler configuration.
A data transformation apparatus of the present invention is characterized by that in the data transformation apparatus having a data processing unit for inputting key data and performing at least one of encryption of data and decryption of data,
the data processing unit divides data to be transformed into first data (L) and second data (R) and performs a data transformation, and
the data processing unit includes:
a normal data transformation unit (FL) for transforming the first data (L); and
an inverse data transformation unit (FL−1) for transforming the second data (R) by performing an inverse transformation of a transformation by the normal data transformation unit (FL).
The above data processing unit includes a first input port, a second input port, a first output port, and a second output port,
the above normal data transformation unit (FL) outputs transformed data to the first input port of the data processing unit, and
the above inverse data transformation unit (FL−1) transforms the data output from the second output port of the data processing unit and outputs transformed data.
The above data processing unit includes a first input port, a second input port, a first output port, and a second output port,
the normal data transformation unit (FL) outputs transformed data to the second input port of the data processing unit, and
the inverse data transformation unit (FL−1) transforms the data output from the first output port of the data processing unit and outputs transformed data.
A data transformation apparatus of the present invention is characterized by that in the having a data processing unit for inputting key data and performing at least one of encryption of data and decryption of data,
the data processing unit includes a non-linear transformation unit for performing a non-linear transformation of data,
the non-linear transformation unit includes:
a first transformation unit (s1) for inputting a part of data to be transformed as first partial data, transforming the first partial data using a transformation table T which inputs data, transforms a value of the data into another value and outputs the data, and outputting transformed data; and
a second transformation unit (s2) for inputting at least another part of the data to be transformed as second partial data, transforming the second partial data by a transformation using the transformation table T and an operation for second part, and outputting transformed data.
The above first transformation unit (s1) inputs data y1 to the transformation table T to output data s1(y1) and outputs the data s1(y1) as data z1=s1(y1), and
the second transformation unit (s2) inputs data y2 to the transformation table T to output data s1(y2), performs rotational shift on s1(y2) to output (rot (s1(y2))), and outputs the data (rot(s1(y2))) as data z2=rot (s1(y2)).
The above data processing unit further includes a third transformation unit (s3) and a fourth transformation unit (s4) for respectively inputting partial data which is different from the first partial data and the second partial data as third partial data and inputting partial data which is different from the first partial data, the second partial data, and the third partial data as fourth partial data, transforming the third partial data and the fourth partial data by the transformation using the transformation table T and an operation for third part and an operation for fourth part, both of which are different from the operation for second part of the second transformation unit (s2), and outputting transformed data.
A data transformation apparatus of the present invention is characterized by that in the data transformation apparatus having a data processing unit for inputting key data and performing at least one of encryption of data and decryption of data,
the data processing unit includes:
a subfield transformation unit for inputting data to be transformed, assuming the data as an element of a field, transforming the data by an inverse element circuit using a subfield of the field, and outputting transformed data; and
an affine transformation unit for vector space GF(2)n on GF(2), provided at at least one of a former round and a latter round of the subfield transformation unit, for assuming data on GF(2)n to be transformed as an element of GF(2)n which corresponds naturally.
The above subfield transformation unit includes only plural N/2-bit operation units for equally dividing data X having N (N: even number) bits into upper 2/N-bit data X1 and lower N/2 bit data X0 so as to be X=X0+βX1 (X0, X1: elements of the subfield, β: an element of the field), and obtaining data Y by respectively operating upper N/2-bit data Y1 and lower N/2-bit data Y0 so as to be Y=Y0+βY1=1/(X0+βX1) (where Y=0, when X=0).
A data transformation apparatus of the present invention is characterized by that in the data transformation apparatus having a data processing unit for inputting key data and performing at least one of encryption of data and decryption of data, and a key generating unit for generating key data to be used by the data processing unit and supplying the key data to the data processing unit,
the data processing unit includes a non-linear transformation unit having cascaded plural rounds, each of the plural rounds inputs an extension key and performs a non-linear transformation,
the key generating unit includes a key shifting unit for inputting at least one of the key data and data generated from the key data and depending on the key data, performing a rotational shift by a predetermined number of bits Z1, Z2, . . . , Zm (where each of i, j, k is one of 1 through m, Zk−Zj=I×(Zi+1−Zi)=I×B (I is an integer, B=Zi+1−Zi)), and generating an extension key for the each of the plural rounds of the non-linear transformation unit from the key data on which the rotational shift is performed, and
the key shifting unit includes:
a rotational shift register for performing a rotational shift by (Zi+1−Zi) bits (B bits) at one operation; and
a controller for operating the rotational shift register 1 time on the key data, on which the rotational shift is performed by Zi bits, to perform the rotational shift by (Zi+1−Zi) bits (B bits), making the rotational shift register to generate the key data which is performed the rotational shift by Zi+1 bits, and
operating the rotational shift register I time(s) on the key data, on which the rotational shift is performed by Zi+1 bits, to perform the rotational shift by I×(Zi+1−Zi) bits (I×B bits), and making the rotational shift register to generate the key data which is performed the rotational shift by Zi+2 bits.
The above rotational shift register is a circuit which performs a rotational shift of Zi+1−Zi bits (B bits) by 1 clock cycle of an operation clock supplied for operating the rotational shift register.
The above rotational shift circuit includes a selector for selecting one of B1=8×J1+1 (J1=an integer greater than 0) bits and B2=8×J2−1 (J2=an integer greater than 1, there is no relation between J1 and J2, namely, J1≠J2 or J1=J2) bits as (Zi+1−Zi) bits (B bits).
A data transformation apparatus of the present invention is characterized by that in the data transformation apparatus having a data processing unit for inputting key data and performing at least one of encryption of data and decryption of data, and a key generating unit for generating key data to be used by the data processing unit and supplying the key data to the data processing unit,
the data processing unit includes a non-linear transformation unit of cascaded plural rounds, each of the plural rounds inputs an extension key and performs a non-linear transformation,
the key generating unit includes a key shifting unit for rotationally shifting key data by a predetermined number of bits (B bits) successively on generating the extension key to be supplied to the each of the plural rounds of the non-linear transformation unit, and generating an extension key used for the each of the plural rounds of the non-linear transformation unit from key data,
the key shifting unit does not generate the extension key by ignoring certain data among the key data being rotationally shifted by B bits successively, and generates the extension key from other remaining data.
A data transformation apparatus of the present invention is characterized by that in the data transformation apparatus having a data processing unit for inputting key data and performing at least one of encryption of data and decryption of data, and a key generating unit for generating key data to be used by the data processing unit and supplying the key data to the data processing unit,
the key generating unit includes:
a first G-bit key transformation unit for inputting G-bit key data having G bits, transforming the G-bit key data, and outputting first G-bit transformed key data having G bits; and
a second G-bit transformation unit for inputting the first G-bit transformed key data output from the first G-bit key transformation unit, transforming the G-bit key data, and outputting second G-bit transformed key data, and
the key generating unit, in case that the key generating unit inputs G-bit key data K, inputs the G-bit key data K to the first G-bit key transformation unit to transform and outputs G-bit transformed key data K: output from the first G-bit key transformation unit as G-bit key data transformed, and
the key generating unit, in case that the key generating unit inputs 2G-bit key data K, generates G-bit key data from the 2G-bit key data K, inputs the G-bit key data generated to the first G-bit key transformation unit to transform, and outputs first G-bit transformed key data K1, inputs the first G-bit transformed key data K1 to the second G-bit transformation unit to transform, and outputs second G-bit transformed key data K2, concatinates the first G-bit transformed key data K1 output from the first G-bit key transformation unit and the second G-bit transformed key data K2 output from the second G-bit transformation unit, and outputs a concatinated result as transformed 2G-bit key data (K1, K2).
The above first G-bit key transformation unit includes:
a non-linear transformation unit having two rounds for performing non-linear transformation on the G-bit key data; and
a logical operation unit for performing a logical operation of a halfway transformed G-bit key data output from a second round of the non-linear transformation unit and the G-bit key data input to the first G-bit key transformation unit.
The above key generating unit further includes a bit length transformation unit for converting Q-bit key data into the 2G-bit key data in case that the Q-bit (G<Q<2G) key data is input.
A data transformation apparatus of the present invention is characterized by that in a data transformation apparatus having:
a data processing unit for inputting key data and performing at least one of encryption of data and decryption of data; and,
a key generating unit for generating key data to be used by the data processing unit and supplying the key data to the data processing unit,
the data transformation apparatus including a non-linear function unit (F) having:
a key function unit for performing a logical operation of data to be transformed and the key data;
an S function unit for converting data to be transformed into other data; and
a P function unit for performing a logical operation among pieces of data to be transformed, and
the key function unit is placed between the S function unit and the P function unit in the non-linear function unit (F).
A data transformation apparatus of the present invention is characterized by that in a data transformation apparatus having:
a data processing unit for inputting key data and performing at least one of encryption of data and decryption of data, and a key generating unit for generating key data to be used by the data processing unit and supplying the key data to the data processing unit,
the data transformation apparatus including a non-linear function unit (F) including:
a key function unit for performing a logical operation of data to be transformed and the key data;
an S function unit for converting data to be transformed into other data; and
a P function unit for performing a logical operation among pieces of data to be transformed, and
the key function unit is placed one of before the S function unit and the P function unit and after the S function unit and the P function unit in the non-linear function unit (F).
The above S function unit includes:
a first transformation unit (s1) for inputting a part of data to be transformed as first partial data, transforming the first partial data using a transformation table T, which inputs data, transforms a value of the data into another value, and outputs the data, and outputting transformed data; and
a second transformation unit (s2) for inputting at least another part of the data to be transformed as second partial data, transforming the second partial data by a transformation using the transformation table T and an operation for the second part, and outputting transformed data.
A data transformation apparatus of the present invention is characterized by that in a data transformation apparatus having a data processing unit for inputting key data and performing at least one of encryption of data and decryption of data, the data transformation apparatus includes
a non-linear function unit (F) including a P function unit which performs a logical operation among pieces of data to be transformed, and
the P function unit inputs eight pieces of 4n-bit data (n is an integer greater than 1) z1, z2, . . . , z8 and includes:
a circuit for performing an XOR operation of at least two of the four pieces of data z1, z2, z3, . . . , z4 to obtain 4n-bit operation result U1;
a circuit for performing an XOR operation of at least two of the four pieces of data z5, z6, z7, . . . , z8 to obtain 4n-bit operation result U2;
a circuit for performing an XOR operation of U1 and U2 to obtain 4n-bit operation result U3;
a rotational circuit for performing a rotational shift on U1; and
a circuit for performing an XOR operation of output from the rotational circuit and U3 to obtain 4n-bit operation result U4, and
the data transformation apparatus divides U3 and U4 into four pieces of data, respectively, and outputs eight pieces of n-bit data z′1, z′2, . . . , z′8.
A data transformation method of the present invention is characterized by that in a data transformation method for executing a data processing process for inputting key data and performing at least one of encryption of data and decryption of data,
the data processing process divides data to be transformed into first data (L) and second data (R) and performs data transformation, and
the data processing process includes:
a normal data transformation process (FL) for transforming the first data (L); and
an inverse data transformation process (FL−1) for transforming the second data (R) by performing an inverse transformation of a transformation of the normal data transformation process (FL).
A data transformation method of the present invention is characterized by that in a data transformation method for executing a data processing process for inputting key data and performing at least one of encryption of data and decryption of data,
the data processing process includes a non-linear transformation process for performing a non-linear transformation of data,
the non-linear transformation process includes:
a first transformation process (s1) for inputting a part of data to be transformed as first partial data, transforming the first partial data using a transformation table T, which inputs data, transforms a value of the data into another value and outputs the data, and outputting transformed data; and
a second transformation process (s2) for inputting at least another part of data to be transformed as second partial data, transforming the second partial data by transformation using the transformation table T and an operation for second part, and outputting transformed data.
A data transformation method of the present invention is characterized by that in a data transformation method for executing a data processing process for inputting key data and performing at least one of encryption of data and decryption of data, the data processing process includes:
a subfield transformation process for inputting data to be transformed, assuming the data as an element of a field, transforming the data by an inverse element circuit using a subfield of the field, and outputting transformed data; and
an affine transformation process for vector space GF(2)n on GF(2), provided at at least one of a former round and a latter round of the subfield transformation unit for assuming data on GF(2)n to be transformed as an element of GF(2)n which corresponds naturally.
A data transformation method of the present invention is characterized by that in a data transformation method for executing a data processing process for performing at least one of encryption of data and decryption of data, and a key generating process for generating key data to be used by the data processing process and supplying the key data to the data processing process,
the data processing process includes a non-linear transformation process having cascaded plural rounds, each of the plural rounds inputs an extension key and performs a non-linear transformation,
the key generating process includes a key shifting process for inputting at least one of the key data and data which is generated from the key data and depending on the key data, performing a rotational shift by a predetermined number of bits Z1, Z2, . . . , Zm (where each of i, j, k is one of 1 through m, Zk−Zj=I×(Zi+1−Zi) (I is an integer, B=Zi+1−Zi)), and generating an extension key for the each of the plural round of the non-linear transformation process from the key data on which the rotational shift is performed, and
the key shifting process includes:
a rotational shifting process; and
a control process for operating the rotational shifting process 1 time on the key data, on which the rotational shift is performed by Zi bits, to perform the rotational shift by (Zi+1−Zi) bits (B bits), making the rotational shifting process to generate the key data which is performed the rotational shift by Zi+1 bits, and operating the rotational shifting process I times on the key data, on which the rotational shift is performed by Zi+1 bits, to perform the rotational shift by I×(Zi+1−Zi) bits (I×B bits), and making the rotational shifting process to generate the key data which is performed the rotational shift by Zi+2 bits.
A data transformation method of the present invention is characterized by that in a data transformation method for executing a data processing process for inputting key data and performing at least one of encryption of data and decryption of data, and a key generating process for generating key data to be used by the data processing process and supplying the key data to the data processing process,
the data processing process includes a non-linear transformation having cascaded plural rounds, each of the plural rounds inputs an extension key and performs a non-linear transformation,
the key generating process includes a key shifting process for rotationally shifting key data by a predetermined number of bits (B bits) successively on generating the extension key to be supplied to the each of the plural rounds of the non-linear transformation process, and generating an extension key used for the each of the plural rounds of the non-linear transformation process from key data being rotationally shifted,
the key shifting process does not generate the extension key by ignoring certain data among the key data being rotationally shifted by B bits successively, and generates the extension key from other remaining data.
A data transformation method of the present invention is characterized by that in a data transformation method for executing a data processing process for inputting key data and performing at least one of encryption of data and decryption of data, and a key generating process for generating key data to be used by the data processing process and supplying the key data to the data processing process,
the key generating process includes:
a first G-bit key transformation process for inputting G-bit key data having G bits, transforming the G-bit key data, and outputting first G-bit transformed key data having G bits; and
a second G-bit transformation process for inputting the first G-bit transformed key data output from the first G-bit key transformation process, transforming the G-bit key data, and outputting second G-bit transformed key data, and
the key generating process, when the key generating unit inputs G-bit key data K, inputs the G-bit key data K to the first G-bit key transformation unit, transforms the G-bit key data K, and outputs G-bit transformed key data K1 output from the first G-bit key transformation process as G-bit key data transformed, and
the key generating process, when the key generating unit inputs 2G-bit key data K, generates G-bit key data from the 2G-bit key data K, inputs the G-bit key data generated to the first G-bit key transformation unit to transform and outputs the first G-bit transformed key data K1, inputs the first G-bit transformed key data K1 to the second G-bit transformation process to transform and outputs second G-bit transformed key data K2, concatenates the first G-bit transformed key data K1 output from the first G-bit key transformation unit and the second G-bit transformed key data K2 output from the second G-bit transformation unit, and outputs a concatenated result as transformed 2G-bit key data (K1, K2).
A data transformation method of the present invention is characterized by that in a data transformation method for executing a data processing process for inputting key data and performing at least one of encryption of data and decryption of data, and a key generating process for generating key data to be used by the data processing process and supplying the key data to the data processing process, the data transformation method including a non-linear function process (F) including:
a key function process for performing a logical operation of data to be transformed and the key data;
an S function process for converting data to be transformed into other data; and
a P function process for performing a logical operation among pieces of data to be transformed, and
the key function process is placed between the S function process and the P function process in the non-linear function process (F).
A data transformation method of the present invention is characterized by that in a data transformation method for executing a data processing process for inputting key data and performing at least one of encryption of data and decryption of data, and a key generating process for generating key data to be used by the data processing process and supplying the key data to the data processing process, the data transformation method including a non-linear function process (F) having:
a key function process for performing a logical operation of data to be transformed and the key data;
an S function process for converting data to be transformed into other data; and
a P function process for performing a logical operation among pieces of data to be transformed, and
the key function process is placed one of before the S function process and the P function process and after the S function process and the P function process in the non-linear function process (F).
A data transformation apparatus of the present invention is characterized by that in a data transformation apparatus having a data processing unit for inputting key data and performing at least one of encryption of data and decryption of data,
the data processing unit includes:
a first input port;
a second input port;
a first output port;
a second output port;
a non-linear transformation unit for performing data encryption and data decryption using same algorithm;
a first input normal data transformation unit for transforming data input to the first input port; and
a second output inverse data transformation unit for inputting data output from the second output port and performing an inverse transformation of a transformation by the first input normal data transformation unit.
The above non-linear transformation unit includes an algorithm that first input data and second output data become identical and second input data and first output data become identical in case of:
inputting first input data from the first input port,
inputting second input data from the second input port,
performing non-linear transformations on the first input data and the second input data using key data for encryption and generates first transformed data and second transformed data,
outputting the first transformed data from the first output port,
outputting the second transformed data from the second output port,
inputting the first transformed data from the second input port,
inputting the second transformed data from the first input port,
performing non-linear transformations on the first transformed data and the second transformed data using key data for decryption, and generates first output data and second output data,
outputting the first output data from the second output port, and
outputting the second output data from the first output port.
The above data processing unit further includes:
a second input normal data transformation unit for transforming data input to the second input port;
a first output inverse data transformation unit for inputting data output from the first output port and performing an inverse transformation of a transformation by the second input normal data transformation unit.
A data transformation apparatus of the present invention is characterized by that in a data transformation apparatus having a data processing unit for inputting key data and performing at least one of encryption of data and decryption of data, and a key generating unit for generating key data to be used by the data processing unit and supplying the key data to the data processing unit,
the data processing unit includes a non-linear function unit (F) for performing a non-linear transformation on data to be transformed, and
the key generating unit processes the key data to be supplied to the non-linear function unit (F), supplies a processed key data to make an operation with data to a part other than the non-linear function unit (F) in the data processing unit.
A data transformation method of the present invention is characterized by that in a data transformation method for executing a data processing process of inputting key data and performing at least one of encryption of data and decryption of data, and a key generating process of generating key data which is used by the data processing process and supplying the key data to the data processing process,
the data processing process includes a non-linear function process (F) for performing a non-linear transformation of data to be transformed, and
the key generating process processes the key data to be supplied to the non-linear function process (F), supplies a processed key data to make calculate data to a part other than the non-linear function process (F) in the data processing process.
A present invention is characterized by a computer-readable storage medium for storing a program for having a computer perform the above data transformation method.
A present invention is characterized by a program for having a computer perform the above data transformation method.
The data transformation unit for encryption 100 is, for example, an encryption device which outputs 128-bit ciphertexts from 128-bit input plaintexts. The data transformation unit for decryption 400 is a decryption device which outputs 128-bit plaintexts from 128-bit input ciphertexts. The data transformation unit for encryption 100 consists of an encryption unit 200 and a key generating unit 300. The encryption unit 200 is a data processing unit for encrypting plaintexts. The key generating unit 300 generates multiple (n) 64-bit or 128-bit extension keys using constants Vi from 128-bit, 192-bit or 256-bit input key data, and supply them to the encryption unit 200. The data transformation unit for decryption 400 consists of a decryption unit 500 and a key generating unit 600. The decryption unit 500 is a data processing unit for decrypting ciphertexts. The key generating unit 600 is the same as or similar to the above key generating unit 300. Furthermore, since the encryption unit 200 and the decryption unit 500 can run the same procedure, they can share one circuit or one program, though the encryption unit 200 and the decryption unit 500 are illustrated separately in the figures. Similarly, the key generating units 300 and 600 can share one circuit or one program. That is, one circuit or one program can be shared by the data transformation unit for encryption 100 and the data transformation unit for decryption 400.
In
The non-linear data transformation unit 210 is equipped with a first non-linear data transformation unit 280 and a second non-linear data transformation unit 281. For arbitrary two pieces of input data, right input data R0 and left input data L0, the former performs the first non-linear transformation on the left input data L0 using a first extension key k1, outputs an XORed result of the output data of the first non-linear transformation and the right input data R0 as the first left intermediate data L1, and outputs the left input data L0 as the first right intermediate data R1. The latter performs the second non-linear transformation on the first left intermediate data R1 using a second extension key k2, outputs an XORed result of the output data of the second non-linear transformation and the first right intermediate data R1 as the second left intermediate data L2, and outputs the first left intermediate data L1 as the second right intermediate data R2. The non-linear data transformation unit 210, in which the first non-linear data transformation unit 280 through the sixth non-linear data transformation unit 285 are cascade, outputs the final right intermediate data R6 and the left intermediate data L6 as the output data after transformation.
The right input data 72 is ORed with an extension key 73 at an OR circuit 74, and then, the ORed data is XORed with the left input data 71 at an XOR circuit 75. Then, the output from the XOR circuit 75 becomes left output data 80, and is ANDed with an extension key 76 at an AND circuit 77. After that, the ANDed result is left rotational shifted by 1 bit at a 1-bit left rotational shifting unit 78, and the shifted data is XORed with the right input data 72 at an XOR circuit 79. The output from the XOR circuit 79 becomes right output data 81.
The normal data transformation unit (FL) 251 shown in
The relationship in which the input data to one unit can be obtained as output data from the other unit by making the output data from the one unit be input data to the other is called a relation between normal and inverse transformations. The normal data transformation unit (FL) 251 and the inverse data transformation unit (FL−) 271 are circuits which realize such relation between normal and inverse transformations.
Both of the 1-bit left rotational shifting unit 55 of
x andn y: (not x) and y
x orn y: (not x) or y
x xorn y: (not x) and y
Some recent CPUs are provided with commands of “and”, “or”, and “xor” including “not”. These commands can be performed at the same cost as “and”, “or”, and “xor”.
The conventional encryption unit 201 is equipped with two normal data transformation units FL. Thus, the decryption unit should be equipped with two inverse data transformation units FL−1 in order to perform inverse operations. Therefore, since the encryption unit generally has a different configuration from the decryption unit, the encryption unit and the decryption unit cannot share the same circuit.
On the other hand, as shown in
As described above, the encryption unit 200 and the decryption unit 500 can be implemented by the same configuration, and the encryption unit 200 and the decryption unit 500 can share the circuit.
In this way, when the normal data transformation unit (FL) 251 and the inverse data transformation unit (FL−1) 271 are located at point symmetry on the non-linear data transformation unit 280, the encryption and the decryption can be performed using the same configuration.
As shown in
In
The 6-round non-linear data transformation unit 210, the 6-round non-linear data transformation unit 220, and the 6-round non-linear data transformation unit 230 are circuits that can be used for encryption and decryption.
Here, a normal/inverse data transformation unit 211 consists of the 6-round non-linear data transformation unit 210, and the normal data transformation unit (FL) 250, and the inverse data transformation unit (FL−1) 271. The normal/inverse data transformation unit is a circuit that can be used for both encryption and decryption. Namely, the normal/inverse data transformation unit is one normal/inverse transformation circuit in which the input data to the unit can be obtained as the output data from the other unit by making the output data from the unit be the input data to the other unit.
A normal/inverse data transformation unit 221 also consists of the 6-round non-linear data transformation unit 220, and the normal data transformation unit (FL) 251, and the inverse data transformation unit (FL−1) 273.
In addition, a normal/inverse data transformation unit 231 consists of the 6-round non-linear data transformation unit 230, and the normal data transformation unit (FL) 253, and the inverse data transformation unit (FL−1) 275.
The encryption unit 200 is configured by cascading these normal/inverse data transformation units 211, 221, and 231. And this encryption unit 200 can be also used as the decryption unit 500.
Besides, if a set of the 6-round non-linear data transformation unit 210, the 6-round non-linear data transformation unit 220, the normal data transformation unit (FL) 251, and the inverse data transformation unit (FL−1) 271 is assumed to be a non-linear data transformation unit 1210, the non-linear data transformation unit 1210 is a circuit that can be used for encryption and decryption. Here, a normal/inverse data transformation unit 1211 consists of the non-linear data transformation unit 1210, the normal data transformation unit (FL) 250, and the inverse data transformation unit (FL−1) 273.
Further, if a set of the 6-round non-linear data transformation unit 220, the 6-round non-linear data transformation unit 230, and the normal data transformation unit (FL) 253, and the inverse data transformation unit (FL−1) 273 is assumed to be a non-linear data transformation unit 1220, a normal/inverse data transformation unit 1221 consists of the non-linear data transformation unit 1220, the normal data transformation unit (FL) 251, and the inverse data transformation unit (FL−1) 275.
The normal/inverse data transformation units 1211 and 1221 can be used for the decryption unit.
Further, if a set of the 6-round non-linear data transformation units 210 through 230 is assumed to be a non-linear data transformation unit 2210, the non-linear data transformation unit 2210 is a circuit that can be used for both encryption and decryption.
Here, the non-linear data transformation unit 2210, the normal data transformation unit (FL) 250, and the inverse data transformation unit (FL−1) 275 form a normal/inverse data transformation unit 2211.
The normal/inverse data transformation unit 2211 can be used for the decryption unit.
As described above, the encryption unit 200 or the decryption unit 500 can be configured by cascading multiple normal/inverse data transformation units.
Further, in the encryption unit 200 or the decryption unit 500, the normal/inverse data transformation unit can be formed hierarchically by nesting the normal/inverse data transformation unit within the normal/inverse data transformation unit.
In
The data A1′ output from the first output port 263 of the encryption unit 200 is input to the second input port 262 of the decryption unit 500 as the data A1′. The data B1′ output from the second output inverse data transformation unit 279 is input to the first input normal data transformation unit 256 as the data B1′, and output as the data B1.
The non-linear data transformation unit 210 inputs the data B, and outputs the data B. Further, the non-linear transformation unit 210 inputs the data A1′ and outputs the data A′. The second output inverse data transformation unit 279 inputs the data A′ and outputs the data A.
In
The data B1 output from the first output port 262 of the encryption unit 200 is input to the second input port 262 of the decryption unit 500 as the data B1. The data A1″ output from the second output inverse data transformation unit 279 of the encryption unit 200 is input to the decryption unit 500 as the data A1″ and input to the first input normal data transformation unit 256.
In cases of
Another case can be implemented by combining
The non-linear function unit F inputs F function input data 10, performs non-linear transformation, and outputs F function output data 40. The F function input data 10 having 64 bits is divided into eight pieces of data, and processed in the unit of 8 bits. Each 8-bit data is input to each of eight XOR circuits 12 of a key function unit 25, XORed with an extension key 11, and performed non-linear transformation using substitution at an S function unit 20. Then, at a P function unit 30, two pieces of 8-bit data are XORed by sixteen XOR circuits 815, and the 64-bit F function output data 40 is output. In the S function unit 20, four S-box first transformation units 13 and four S-box second transformation units 14 are provided.
Inside the S-box first transformation unit 13, a transformation table T is provided. The transformation table T previously stores values of 0 through 255 arbitrarily (at random) corresponding to values of 0 through 255. The transformation table T inputs values of 0 through 255 and outputs the value (value of 0 through 255) corresponding to each value. For example, when 1 is input, the transformation table T outputs 7. The transformation table T performs non-linear transformation determined under consideration of security, e.g., checking if the function is bijective or not, the maximum differential probability is sufficiently small or not, and so on.
The S-box second transformation unit 14 includes the S-box first transformation unit 13 and a 1-bit left rotational shifting unit 22 (in the figure, “<<<” of “<<<1” shows the left rotational left shift and “1” shows 1 bit). The 1-bit left rotational shifting unit 22 performs left rotational shift by 1 bit to an output from the S-box first transformation unit 13. For example, when 1 is input, the S-box first transformation unit 13 outputs 7, and 1-bit left rotational shifting unit 22 outputs 14.
If the S-box first transformation unit 13 and the S-box second transformation unit 14 are configured as shown in
Further, as shown in
Another configuration of the P function unit 30 is shown in
From 8-bit input data y1, y2, y3, y4, 32-bit data Z1, Z2, Z3, Z4 are obtained by referring to S1, S2, S3, S4, respectively, and they are XORed at a circuit 913. From 8-bit input data y5, y6, y7, y8, 32-bit data Z5, Z6, Z7, Z8 are obtained by referring to S2, S3, S4, S1, respectively, and they are XORed at a circuit 916. This XORed result U2 and the former XORed result U1 are XORed at a circuit 917 to output z1′, z2′, z3′, z4′. Then, the XORed result U1 from the circuit 913 is shifted to the left by 1 byte (in
As shown in (a) through (d) of
The 1-byte rotational shift of the circuit 918 is a cyclic shifting by a unit of bit length (8 bits=1 byte) which is processed by the S-box.
From 8-bit input data y1, y2, y3, y4, 32-bit data Z1, Z2, Z3, Z4 are obtained by referring to S5, S6, S7, S8, and they are XORed at a circuit 933 to output an operation result A. From 8-bit input data y5, y6, y7, y8, 32-bit data Z5, Z6, Z7, Z8 are obtained by referring to S9, SA, SB XORed at a circuit 936 to output an operation result B. The operation result B is shifted rotationally to the right by 1 byte (in
S5 and SC are configured using the S-box first transformation unit 13 and a logical shift, S6 and S9 are configured using the S-box second transformation unit 14 and a logical shift, S7 and SA are configured using the S-box third transformation unit 15 and a logical shift, S8 and SB are configured using the S-box fourth transformation unit 16 and a logical shift. The logical shift is used for outputting 8-bit output data from each transformation unit to a predetermined location within the 32-bit output data. The logical shift is set to shift to the left by 0 byte in S5 and SA, 1 byte in S6 and SB, 2 bytes in S7 and SC, 3 bytes in S8 and S9. Namely, assuming 8-bit output from the transformation unit as z, 32-bit output can be represented as [0,0,0,z] (0 shows each of eight bits is 0) in S5 and SA, [0,0,z,0] in S6 and SB, [0,z,0,0] in S7 and SC, [z,0,0,0] in S8 and S9.
It is possible to implement using substitution tables whose input is 8-bit and output is 32-bit, which is calculated for directly producing predetermined output.
In cases of
In
Further, eight pieces of 8-bit data are input time-divisionally to the S-box first transformation unit 13 and the S-box second transformation unit 14 shown in
The concrete configuration is explained in detail in Matui, Sakurai, “Galois Field division circuit and shared circuit for multiplication and division” (Japanese Patent Registration No. 2641285 [May 2, 1997]).
8-bit data is input to the S-box transformation unit 21, and 8-bit data is output. The S-box transformation unit 21 is configured by an N-bit (here, N=8) linear transformation unit 17, a subfield transformation unit 18, and an N-bit linear transformation unit 19. The N-bit linear transformation unit 17 performs operations of 8-bit data. The subfield transformation unit 18 performs operations of only 4-bit data which are elements of Galois Field GF (24). The N-bit linear transformation unit 19 performs an operation of 8-bit data. A linear transformation unit 85 of the N-bit linear transformation unit 17 is a circuit which performs the linear transformation shown in
The linear transformation unit 85 can be replaced by a circuit which performs an affine transformation (a linear transformation can be considered as one style of affine transformations). Similarly, the linear transformation unit 87 can be replaced by a circuit which performs another affine transformation. The linear transformation unit 85 transforms 8-bit data (X) into 8-bit data (X′). The obtained 8-bit data (X′) is assumed to be an element of Galois Field (28). The upper 4-bit data and the lower 4-bit data (X1 and X0) of data X′ are respectively assumed as elements of the subfield Galois Field (24) and output to the subfield transformation unit 18. Here, for example, let an element β of GF (28) be an element which satisfies the irreducible polynomial X8+X6+X5+X3+1=0, and α=β238, a base of the subfield GF (24) can be represented as [1, α, α2, α3], If the elements of GF (24), X0, X1, are represented using this, the following relationship can be established as X′=X0+βX1. (For details, refer to Matui, Sakurai, “Galois Field division circuit and shared circuit for multiplication and division” (Japanese Patent Registration No. 2641285 [May 2, 1997])). The subfield transformation unit 18 is configured only by operation units each of which performs operations of 4-bit data.
Here, as an example of extracting “subfield”, the subfield GF (2m) where n=2m can be considered for given GF (2n). In this example, n=8, m=4.
The subfield transformation unit 18 is an inverse element circuit using the subfield constructed by the circuit shown in “Galois Field division circuit and shared circuit for multiplication and division” (Patent Registration No. 2641285 [May 2, 1997]). As an operation result of this inverse element circuit, upper 4-bit data and lower 4-bit data (Y1 and Y0), each of which can be assumed as an element of GF (24), are output to the linear transformation unit 87 as 8-bit data Y which can be assumed as an element of GF (28), where Y=Y0+βY1. As explained above, this inverse element circuit is a circuit for computing Y=Y0+βY1=1/(X0+βX1). Further, there are some ways of taking a “basis”, such as a “polynomial basis” and a “normal basis”, in representing the element of “finite field” (how to take a basis) in the inverse element circuit.
A first characteristic of the S-box transformation unit 21 shown in
Although the computation speed may be decreased by performing only 4-bit operations. This case has an advantage in that a scale of a whole circuit can be much smaller than a case of performing operations of 8-bit data.
Further, a second characteristic of the S-box transformation unit 21 is that the N-bit linear transformation unit 17 and the N-bit linear transformation unit 19, where N=8, are provided at both sides of the subfield transformation unit 18. When the S-box transformation unit 21 is implemented using the subfield transformation unit 18, there is an advantage that a scale of the whole circuit can be reduced and the configuration becomes simpler compared with a case employing a transformation table T storing random values, while on the contrary, the security may be decreased. Accordingly, the linear transformations or the affine transformations are performed at both sides of the subfield transformation unit 18, so that the reduction of the security level due to implementing using the subfield transformation unit 18 can be recovered.
In
By employing the configuration shown in
Left data is input to the non-linear transformation unit F as F function input data 10, and F function output data 40 is output. The F function output data 40 is XORed with right data, and the XORed result becomes left data of the next round. When the left data is input to the non-linear transformation unit F as the F function input data 10, at the same time, the left data is used as right data of the next round. In the configuration shown in
On the other hand, the key generating units 300, 600 perform an XOR operation of the extension keys k1 and k2 and output the modified extension key k1+k3. The output R1 of the XOR circuit 891 and the extension key k1+k3 are XORed at an XOR circuit 298 to output the right data. The key generating units 300, 600 modify the extension keys to generate and output k1+k3, k2+k4, k3+k5, . . . , k16+k18. The key generating units 300, 600 supply the modified extension keys to the processes other than the non-linear function process (F) to operate with the data. As a result, left data L18 and right data R18 become the same as the left data L18 and the right data R18 in case of
The modified extension keys are supplied to the processes other than the non-linear function process (F) and operated with the data, and consequently, the operations with the key data can be performed outside the non-linear function unit F′, namely, at the XOR circuits 297 and 298, while the operations of the S function unit 20 and the P function unit 30 are performed in the non-linear function unit F′. Therefore, the operations of the key function unit 25 are eliminated from the non-linear function unit F, and the load of the non-linear function unit F is distributed, which enables a high-speed implementation.
The figure also shows a case in which the key generating unit previously performs an XOR operation of a part of the whitening extension key kw1low and the second extension key k2 (namely, the key generating unit modifies the extension key) and supplies the operation result to the XOR circuit 297.
In this way, the operation at the XOR circuit 293 shown in
In this way, the operation of the XOR circuit 296 shown in
The key generating unit 300 includes a bit length transformation unit 310, a first G-bit key transformation unit 320, a second G-bit key transformation unit 330, and a key shifting unit 340. From the input key data having 128 bits, 192 bits, or 256 bits, the key generating unit 300 generates 128-bit key data K1 and 128-bit key data K2, and outputs plural 64-bit extension keys. The bit length transformation unit 310 converts the bit length of the key data to be output so that the bit length of the output key data becomes fixed even if the key data having different number of bits is input. In other words, the bit length transformation unit 310 generates key data SKhigh of upper 128 bits and key data SKlow of lower 128 bits and outputs the former to the first G-bit key transformation unit 320 and the key shifting unit 340. Further, the latter is output to the second G-bit key transformation unit 330 and the key shifting unit 340. Further, 128-bit key data which is an XORed result of the former and the latter is output to the first G-bit key transformation unit 320.
When the 128-bit key data is input to the bit length transformation unit 310, the input key data is output as key data SKhigh of the upper 128 bits without any change. Further, key data SKlow of the lower 128 bits is set to 0 and output.
When the 192-bit key data is input to the bit length transformation unit 310, the upper 128-bit data of the input key data is output as the upper 128-bit key data SKhigh without any change. Further, the lower 128-bit key data SKlow is generated by combining the lower 64 bits of the input 192-bit key data and the inverse 64-bit data, which is generated by inverting the lower 64-bit data of the input 192-bit key data, and output.
When 256-bit key data is input, the upper 128-bit data of the input key data is output as SKhigh, and the lower 128-bit data is output as SKlow.
An XOR data of the 128-bit key data SKhigh and SKlow is input to the first G-bit key transformation unit 320 from the bit length transformation unit 310, operated by two round non-linear transformations, XORed with the upper 128-bit key data SKhigh, further operated by two round non-linear transformations, and 128-bit key data K1 is output.
When the length of the key data input to the bit length transformation unit 310 is 128 bits, the key shifting unit 340 generates the extension key using the 128-bit key data output from the first G-bit key transformation unit 320 and the key data originally input. When the length of the key data input to the bit length transformation unit 310 is 192 bits or 256 bits, the 128-bit key data output from the first G-bit key transformation unit 320 is further input to the second G-bit key transformation unit 330, XORed with the lower 128-bit key data SKlow, operated by two round non-linear transformations, and 128-bit key data K2 is output. Two pieces of 128-bit key data, from the first G-bit key transformation unit 320 and the second G-bit key transformation unit 330, are output to the key shifting unit 340. The key shifting unit 340 generates the extension key using the two pieces of 128-bit key data and the key data originally input.
The key shifting unit 340 includes a shift register A 341, a shift register B 342, a shift register C 343, a shift register D 344, and a shift control unit 345. The shift control unit 345 outputs a select signal 346 to each of the shift registers to control the operations of the shift registers.
The shift register A 341 includes a selector A 347 having a group of switches for 128 bits and a register A 348 having 128 bits. A select signal 346 includes a switch signal to indicate to connect all the switches of the selector A 347 at the same time to either of A side and B side. The figure shows a case in which the group of switches of the selector A 347 has selected A based on the select signal 346, and in this case, the register A 348 performs a rotational shift to the left by 17 bits. Further, when the group of switches is connected to B, the register A performs the rotational shift to the left by 15 bits. The 15-bit shift or 17-bit shift is performed by one clock cycle.
The number of shifting bits (15, 17) is one of examples, and other number of shifting bits can be applied.
The control table is a table storing how many bits the register shifts at each clock. For example, in the register A control table, at the first clock, it is specified to shift by 15 bits. And, at the second clock, it is specified to shift by further 15 bits. Similarly, at each of the third clock and the fourth clock, it is specified to shift by 15 bits. At each of the fifth through the eighth clock, it is specified to shift by 17 bits.
The upper 128-bit key data SKhigh input from the bit length transformation unit 310 is set in the shift register A 341. The 128-bit key data K1 output from the first G-bit key transformation unit 320 is set in the shift register B 342. Under this condition, the shift register A 341 and the shift register B 342 operate based on the control table shown in
Namely, the upper 128-bit key data SKhigh input from the bit length transformation unit 310 is set in the shift register A 341, the lower 128-bit key data SKlow is set in the shift register B 342, the 128-bit key data K1 output from the first G-bit key transformation unit 320 is set in the shift register C 343, and the 128-bit key data K2 output from the second G-bit key transformation unit 330 is set in the shift register D 344.
Data in a column having a slant shows keys not used for the extension keys.
The keys not used for the extension keys and the correspondence between the value of the register and the extension key shown in
As shown in
The sum of the number of shifting bits becomes 15+15+15+15+17+17+17+17=128, so that the 128-bit register performs the 128-bit rotational shift and the register returns to the initial status.
The reason why the sum of the number of shifting bits is made 128 bits (the number of bits of the register) to return to the initial status is that the next processing can be started at once if the next processing is assigned to the register of the initial status. Further, in case of performing an inverse transformation (decryption), the process for generating the extension key is started from the initial status, and accordingly, both of the transformation (encryption) and the inverse transformation (decryption) can be performed by setting the initial status. Further, the reason why the sum of the number of shifting bits is not made greater than 128 bits (the number of bits of the register) is to prevent the generation of identical values as the status within the same shift register due to performing the shift more than one cycle (greater than 128 bits of shift). This is because, for example, performing the rotational shift by 2 bits, which is less than 128 bits (the number of bits of the register) and performing the rotational shift of 130 bits, which is greater than 128 bits (the number of bits of the register), produce the identical value. It is desirable to set such values in the register A control table that, on performing the shifts of the register by one cycle, the number of shifting bits varies irregularly through the one cycle. However, in order to facilitate the configuration of the shift register, it is desired to shift by the fixed number of bits. Therefore, one register is configured to perform two kinds of shifts by 15 bits and 17 bits (at one clock), and the shift operation by different number of bits can be implemented using the two kinds of shifts, according to the following procedure.
Set the relation so that Z1−Z0=15 (here, Z1−Z0=B1), Z2−Z1=30 (namely, Z2−Z1=2B1), therefore, Z2−Z1=2(Z1−Z0). Further, as shown in the shift register B control table, set the relation so that Z5−Z4=34 (here, Z5−Z4=2B2), Z6−Z5=17 (namely, Z6−Z5=B2), therefore, Z5−Z4=2(Z6−Z5). Namely, the differences between the numbers of shifting bits are made 15 bits and 30 bits, or 17 bits and 34 bits, and the number of shifting bits (30 bits or 34 bits) is set to an integral multiple (2 times=I times) of the number of bits (15 bits and 17 bits) for one time shifting.
In this way, as the differences of the number of shifting bits are set to either the number of shifting bits for one time or the multiple by the integer which is greater than two (I times, I is an integer greater than 2) and the number of shifting bits for one time, by operating the shift register A 341 one time or two times (I times), it is possible to easily implement shift operations of which the number of shifting bits stored in the control table. To operate two times (I times) means that the shift operation finishes with two clocks (I clocks) of the operation clock supplied for operating the shift register A 341.
Here, on shifting I times (two times), both the higher data and the lower data of the shifted data up to I−1 times (2−1=1 time) are ignored and are not used for the extension key. For example, in case of shifting from Z1=15 to Z2=45, I=(Z2−Z1)/(the number of shifting bits at one time)=(45−15)/15=2, and both the higher data and the lower data of the shifted data after shifting I−1 times (2−1=1 time) are ignored and are not used for the extension key. This can be seen in
The reasons why the shift operation based on multiple by the integer greater than two is employed as described above are to enable to perform the shifting of not only 15 bits or 17 bits, but also 30 (=15×2) bits, 34 (=17×2) bits (or 45 (=15×3) bits or 51 (=17×3) bits, etc.), which varies the number of shifts and further to improve the security. And, the reason why the cases are provided in which the shifted data is not used for the extension key is also to improve the security.
It is desired to generate the data which is not used for the extension key (in
The characteristics of the control table shown in
In the above description of the bit length transformation unit 310, three kinds of bit widths of key data are input. Even when the key data having Q bit length, in which Q is between 128 bits (G bits) and 256 bits (2G bits) (G<Q<2G), the bit length transformation unit 310 can extend the key data to the same size of the key data when the 256-bit key data is input, using some kind of algorithm. Namely, when the key data having length of Q, which is between G bits and 2G bits, is input, the bit length transformation unit 310 can convert the key data of Q bits into the key data of 2G bits.
Next, non-existence proof of an equivalent key will be explained referring to
In the following explanation of
Here, it is assumed to input two 128-bit key data SK1 and SK2 (SK1≠SK2), and that the bit length transformation unit 310 outputs SK1high=SK1=(SKH1|SKL1) from SK1 and SK2high=SK2=(SKH2|SKL2) from SK2. Here, SKHi (i=1,2) means the upper 64-bit data of SKi and SKLi (i=1,2) means the lower 64-bit data of SKi.
Assuming that XOR data of SKH1 and SKH2 is ΔA and XOR data of SKL1 and SKL2 is Δ B, it can be said “at least ΔA≠0 or ΔB≠0” since SK1≠SK2.
As shown in
On the other hand, as shown in
Not only the above-mentioned case of three-round non-linear transformation, a general non-linear transformation may output the equivalent K1 from different SK1 and SK2, that means an equivalent key may exist. However, it is possible to prove the non-existence of the equivalent key when the two-round non-linear transformation according to the present embodiment is employed.
Further, there may be another case in which the non-existence of the equivalent key is proved other than the two-round non-linear transformation according to the present embodiment, however, it is preferable to use the two-round non-linear transformation because of a simple configuration in addition to the proved non-existence of the equivalent key.
The data transformation unit for encryption 100 and/or the data transformation unit for decryption 400 is connected to the bus as a printed circuit board. This printed circuit board is provided with a CPU, a memory, and a logical circuit element, and encrypts plaintexts supplied from the CPU into ciphertexts using the above-mentioned operation and returns the data to the CPU. Or it decrypts ciphertexts supplied from the CPU and returns the plaintexts to the CPU.
In this way, the data transformation unit for encryption 100 or the data transformation unit for decryption 400 can be implemented by the hardware. Further, the data transformation unit for encryption 100 or the data transformation unit for decryption 400 can be also implemented by the software as the data transformation method. Namely, the above operation can be performed using the program stored in a magnetic disk drive or a flexible disk drive. In another way, the above operation can be implemented by combining the hardware and the software, though this is not shown in the figure. Further, it is not required to implement all the above operation using one computer, but it is possible to implement the above operation by a distributed system such as a server and a client, or a host computer and a terminal computer, though this is not shown in the figure.
In the foregoing
In the foregoing embodiments, a case in which 128-bit plaintexts and ciphertexts are used has been explained, but the data can be 256-bit plaintexts and ciphertexts, or plaintexts and ciphertexts having another number of bits.
Further, in the foregoing embodiments, a case in which 128-bit, 192-bit, 256-bit key data and 64-bit extension keys are used, but the key data can have another number of bits.
If the bit length of the plaintexts and the ciphertexts, the key data and the extension key are changed, of course, the bit length to be processed by each unit, each step, or each process is changed according to the bit length.
According to the embodiment of the present invention, the normal data transformation unit (FL) 251 and the inverse data transformation unit (FL−1) are provided for implementing the encryption and the decryption using the same algorithm, so that the encryption unit 200 and the decryption unit 500 can share the circuit.
Further, according to the embodiment of the present invention, the transformation table T is shared by the S-box first transformation unit 13 and the S-box second transformation unit 14, so that the configuration is simplified.
Further, according to the embodiment of the present invention, the subfield transformation unit 18 is used, which makes the configuration simpler, and the linear transformation unit 85 and the linear transformation unit 87 are provided, so that the security is improved even if the subfield transformation unit 18 is used.
Further, according to the embodiment of the present invention, the shift control unit 345 can make the shift register operate integer number of times to perform the shifting of the key data with the number of shifting bits (for example, 30 bits or 34 bits) which is not a fixed number of bits such as only 15 bits or 17 bits, and improves the security.
Further, according to the embodiment of the present invention, a case is provided in which the shifted data in the shift register is not used for the extension key, which further improves the security.
Further, according to the embodiment of the present invention, even if the key data having different number of bits is input, the bit length transformation unit 310 changes to the key data with a fixed length, which enables to operate a flexible key generation.
Further, according to the embodiment of the present invention, the two-round non-linear transformation is used in the first G-bit key transformation unit 320, so that non-existence of the key being equivalent to K1 can be proved, which improves the security.
Further, according to the embodiment of the present invention, the location of the key function 25 is altered, which enables a high-speed processing.
| Number | Date | Country | Kind |
|---|---|---|---|
| 2000-064614 | Mar 2000 | JP | national |
This application is a Divisional of co-pending application Ser. No. 09/959,853 filed on Jan. 8, 2002, and for which priority is claimed under 35 U.S.C. § 120. application Ser. No. 09/959,853 is the national phase of PCT International Application No. PCT/JP01/01796 filed on Mar. 8, 2001, under 35 U.S.C. § 371. The entire contents of each of the above-identified applications are hereby incorporated by reference.
| Number | Date | Country | |
|---|---|---|---|
| Parent | 09959853 | Jan 2002 | US |
| Child | 11260110 | Oct 2005 | US |
