Abstract: A method of generating prevention and control data to verify validity of data to be transmitted, and an apparatus to perform the method, the method including generating the prevention and control data according to composing information of the data to be transmitted, and transmitting the prevention and control data along with the data to be transmitted to verify the validity of the data to be transmitted.

Abstract: A user key management method for a broadcast encryption includes assigning node path identifiers (IDs) to nodes arranged in sequence; assigning random seed value keys to the nodes according to the node path IDs; generating key values by repeatedly applying a hash function to the assigned random seed value keys; and assigning the generated key values to the nodes in sequence. Accordingly, it is possible to reduce the transmission overhead that is most important matter in the broadcast encryption to less than the number of the revoked users. Further, there is an advantage that the transmission overhead of the exemplary embodiments of the present invention is remarkably reduced compared with the Subset Difference method.

Abstract: A method of managing a user key for a broadcast encryption. The method includes assigning numbers to respective users and arranging the users on a ring-shaped structure in order to map hash chains onto the respective nodes of a ring-shaped structure. The method further includes making random node keys correspond to the respective nodes, one by one, constructing the hash chains from the corresponding node keys using a hash function, and successively mapping the constructed hash chains onto the nodes of the ring-shaped structure.

Abstract: An apparatus and method for generating a key for a broadcast encryption. The apparatus includes a node secret generator for managing a user that receives broadcast data in a tree structure and for generating a unique node secret for each node in the tree structure. The apparatus also includes an instant key generator for temporarily generating an instant key used at all nodes in common in the tree structure, and a node key generator for generating a node key for each node by operating the node secret generated at the node secret generator and the instant key generated at the instant key generator. Thus, key update can be efficiently achieved.

Abstract: A method of obtaining C=(c0, . . . , cn-1) of a product of two elements A and B of a finite field GF(2n). The method includes permuting the last d coefficients (an-1, . . . , an-d) of a multiplier A with predetermined variables (sn-1, . . . , sn-d); operating C:C=?(bi+j?A) for (I+j)th coefficient of a multiplicand B to update coefficients of C, where i and j are integers, and A:=(sn-1-j,?0, . . . ,?n-2)?(0,sn-1-j?f1, . . . ,sn-1-j?fn-d,0, . . . ,0) repeatedly for j=0 to (d?1) to update coefficients of A, where ? represents an XOR operation and ? represents an AND operation; and repeatedly performing the permuting and operating by increasing i from 0 to (n-1) by d.

Abstract: A security system using an RSA algorithm that includes a key input section for receiving a secret key and a public key used in one of encryption and decryption of a message, a random coefficient generating section for generating a random coefficient r having a bit of a predetermined size, a first calculation section for dividing the secret key into a first secret key and a second secret key by using the value of r, and performing an exponentiation of RSA algorithm by using the respective secret keys and the public key, and a second calculation section for performing one of the encryption and the decryption by combining results of exponentiation calculated respectively by using the first and the second secret keys.

Abstract: A method and apparatus to square an element A when a defining polynomial of a finite field GF(2n) is expressed as f ? ( x ) = x n + ? i = 1 i ? ? ? x k 1 + 1 , and the element A contained in the finite field is expressed as A?(a0,a1,a2 . . . ,an?1)?GF(2n).

Abstract: There are provided efficient basis conversion matrices Dsd and Dds and a basis conversion method in a finite field GF(2n) using the basis conversion matrices for a case where a defining polynomial is a pentanomial, xn+xk(3)+xk(2)+xk(1)+1, and the exponents n, k(3), k(2), and (k1) satisfy the condition, n−k(3)>k(3)−k(1). In addition, an apparatus for the basis conversion in the finite field GF(2n) is provided. Since a pentanomial having a general form in an arbitrary degree is used as the defining polynomial, basis conversion between a standard representation and a dual representation is efficiently performed. Consequently, a dual basis multiplier can be efficiently implemented.