Abstract: The public-key encryption method uses the sender-side apparatus by the creator of a ciphertest and creates the ciphertext of a plaintext x (?{0, 1}n), in y1=f(x0k1G(r)), y2=H(x0k1G(r))r with respect to the published trapdoor-equipped unidirectional function f and the random functions G, H. Meanwhile, the receiver of the ciphertext, who has received the ciphertext by the receiver-side apparatus via the communications line, performs the decryption processing with the use of f?1, i.e., the secret key, in accordance with the steps inverse to those of the encryption processing.

Abstract: A public key encryption system and an ID-based encryption system are provided, each exhibiting high security and having a tight security reduction, in which a BDH problem is a cryptographic assumption. A recipient-side device (110) serving as a recipient of a cryptogram selects random numbers s1 and s2, generates P, Q?G1 and a bilinear mapping e: G1×G1?G2 as part of public key information, and further generates P1=s1P and P2=s2P as part of the public key information. A sender-side device (120) serving as a sender of the cryptogram calculates e(Q, P1) and e(Q, P2) by use of the public key information Q of the recipient-side device (110) and the bilinear mapping e, and further generates a cryptogram to be transmitted to the recipient-side device (110) by use of those pieces of information e(Q, P1) and e(Q, P2).

Abstract: The public-key encryption method uses the sender-side apparatus by the creator of a ciphertest and creates the ciphertext of a plaintext x (? {0, 1}n), in y1=f (x0k1G(r)), y2=H (x0k1G(r))r with respect to the published trapdoor-equipped unidirectional function f and the random functions G, H. Meanwhile, the receiver of the ciphertext, who has received the ciphertext by the receiver-side apparatus via the communications line, performs the decryption processing with the use of f?1, i.e., the secret key, in accordance with the steps inverse to those of the encryption processing.

Abstract: The public-key encryption method uses the sender-side apparatus by the creator of a ciphertest and creates the ciphertext of a plaintext x (?{0, 1}n) in y1=f (x0k1G(r)), y2=H (x0k1G(r))r with respect to the published trapdoor-equipped unidirectional function f and the random functions G, H. Meanwhile, the receiver of the ciphertext, who has received the ciphertext by the receiver-side apparatus via the communications line, performs the decryption processing with the use of f?1, i.e., the secret key, in accordance with the steps inverse to those of the encryption processing.

Abstract: A public key cryptograph communication technology which can be verified to be secure even when an attacker to the public key cryptograph selects a random function giving random oracle is provided.

Abstract: A key distribution method and system are disclosed in which a sender and receivers share a common key information for performing a secure broadcast communication. By use of a center side apparatus, a center generates key information of a receiver in association with a subset inclusive of two or more elements of a proper finite set S1 on the basis of a space determined by a subset inclusive of two or more elements of another finite set S2. A sender side apparatus, a sender makes the multi-address transmission of key distribution data W inclusive of data generated corresponding to each element of the finite set S1 and data generated corresponding to a set of plural receivers through a communication network. By use of a receiver side apparatus, a receiver generates common key information between the sender and the receiver from the key distribution data W and the key information of the receiver.

Abstract: The public-key encryption method uses the sender-side apparatus by the creator of a ciphertest and creates the ciphertext of a plaintext x (∈{0, 1}n) in y1=f(x0klG(r)), Y2=H(x0klG(r))r with respect to the published trapdoor-equipped unidirectional function f and the random functions G, H. Meanwhile, the receiver of the ciphertext, who has received the ciphertext by the receiver-side apparatus via the communications line, performs the decryption processing with the use of f−1, i.e., the secret key, in accordance with the steps inverse to those of the encryption processing.

Abstract: A public-key cryptographic scheme of high efficiency capable of verifying security in a standard model. In order to retain security against adaptive chosen ciphertext attacks, a ciphertext is generated by a combination of a plaintext and random numbers so that an illegal ciphertext input to a (simulated) deciphering oracle is rejected.

Abstract: A method for cryptographic communications by public-key encryption is disclosed in which a sender generates a ciphertext, using a public key of a receiver, by the internal operation of the sender-end device 100, and transmits the ciphertext to the receiver-end device 200 over a network 300 and the receiver decrypts the ciphertext with the receiver's secret key. In accordance with this method, the procedures for encryption and decryption are set up, providing for both security features of the Rabin's Cryptosystem and the ElGamal's Cryptosystem. The feature of the former is one-way against chosen plaintext attacks, presupposing the difficulty of solving the problem of factorization into prime factors; the feature of the latter is indistinguishability, namely strong protection of secrecy against chosen plaintext attacks, presupposing the difficulty of solving the Diffie-Hallman decision problem.

Abstract: A cipher communication method by public key cryptosystem, being provably secure and highly efficient, wherein a sender generates ciphertext within a sender device using a receiver's public key and sends the ciphertext over a communication line, and a receiver decrypts the ciphertext using a secret key. For n=pdq (p and q are prime integers, and pq is k bits), a plaintext space is set to be a subset of an open set (0,2k−2) and small residue groups, and an algorithm is formed so that the relationship among solutions of plural second-order equations can be clarified. This has enabled security to be proved by equivalence with the difficulty of the problem of prime factorization, and has achieved faster decryption processing, compared with conventional methods.

Abstract: An electronic shopping method is provided by both an apparatus 10 and an apparatus 30 to hold a key K(A, C) in common, and both the apparatus 30 and an apparatus 40 to hold a key K(B, C) in common. The apparatus 10 transmits a cipher text C1 which is obtained by enciphering a written order P of the products to be purchased using a key K, a cipher text C2 which is obtained by enciphering the key K using the key K(A, C), and authentication information C3 relating to a part P2 of the written order P to the apparatus 30 and the like. The apparatus 40 deciphers the key K on the basis of the cipher text C2, transmits a cipher text C4 which is obtained by enciphering the key K using the key K(B, C) to the apparatus 30.

Abstract: A key distribution method and system are disclosed in which a sender and receivers share a common key information for performing a secure broadcast communication. By use of a center side apparatus, a center generates key information of a receiver in association with a subset inclusive of two or more elements of a proper finite set S1 on the basis of a space determined by a subset inclusive of two or more elements of another finite set S2. A sender side apparatus, a sender makes the multi-address transmission of key distribution data W inclusive of data generated corresponding to each element of the finite set S1 and data generated corresponding to a set of plural receivers through a communication network. By use of a receiver side apparatus, a receiver generates common key information between the sender and the receiver from the key distribution data W and the key information of the receiver.

Abstract: An electronic shopping method is provided by both an apparatus 10 and an apparatus 30 to hold a key K(A, C) in common, and both the apparatus 30 and an apparatus 40 to hold a key K(B, C) in common. The apparatus 10 transmits a cipher text C1 which is obtained by enciphering a written order P of the products to be purchased using a key K, a cipher text C2 which is obtained by enciphering the key K using the key K(A, C), and authentication information C3 relating to a part P2 of the written order P to the apparatus 30 and the like. The apparatus 40 deciphers the key K on the basis of the cipher text C2, transmits a cipher text C4 which is obtained by enciphering the key K using the key K(B, C) to the apparatus 30.

Abstract: An electronic shopping method is provided by both an apparatus 10 and an apparatus 30 to hold a key K(A, C) in common, and both the apparatus 30 and an apparatus 40 to hold a key K(B, C) in common. The apparatus 10 transmits a cipher text C1 which is obtained by enciphering a written order P of the products to be purchased using a key K, a cipher text C2 which is obtained by enciphering the key K using the key K(A, C), and authentication information C3 relating to a part P2 of the written order P to the apparatus 30 and the like. The apparatus 40 deciphers the key K on the basis of the cipher text C2, transmits a cipher text C4 which is obtained by enciphering the key K using the key K(B, C) to the apparatus 30.