Abstract: The invention is aimed to work on XOR operation safely in cryptographic communications with third party identification, wherein a sender in FIG. 1B encrypts an 1D plaintext with a 2D authorized image to get two ciphertexts, such that, one is sent directly to a receiver and the other is forwarded via a third party to the receiver, wherein the receiver recovers the plaintext just by XORing two ciphertexts. For transmission security, according to FIG. 2, the third party sends privately two different authorized images for building each separate secure channel linked to a sender and to a receiver; furthermore, at one channel from the sender to the third party, the forwarded ciphertext is re-encrypted with a random code and then sent to the third party; at the other channel from the third party to the receiver, the forwarded ciphertext is re-encrypted with another random code and then sent to the receiver.

Abstract: The invention is related to working with variable diffusion functions on a multidimensional diffusion-area (plaintext/ciphertext); every diffusion function run in a cycle times, wherein repeating one certain times on the plaintext to get a ciphertext, and afterward, repeating the other times on the ciphertext to recover the plaintext, is performed in sequence to complete the encryption and the decryption. According to FIG. 1, the system comprises of: inputting a plaintext in encryption or a ciphertext in decryption 100; reading every password segment in order, forward in encryption or backward in decryption 200; and further, converting the plaintext dimensions by the password segment 300; implementing the diffusion function of Point 410, Block 420 or Frame 430, repeated TE times in encryption, TD times in decryption 400; going back to 200 until completing all password segments 500, and outputting the ciphertext in encryption or the plaintext in decryption 600.

Abstract: The present invention applies with a diffused mechanism, as such, a variable series of diffusion functions embedded within a diffusion-medium, to generate a maximum diffusion-cycle and nonlinear complexity; additionally, it performs in a serial process for simple design, further, in a parallel process for saving time, or even in a hardware architecture, to gain greater acceleration. FIG. 1 shows an embodiment of the present invention in flow chart diagram form, comprising steps of: selecting a diffusion-area A, a diffusion-medium S, and a diffusion mechanism Ft1 100; initializing A by an input password 200; performing Ft1 to obtain a new value of A 300; inputting a plaintext in encryption or a ciphertext for decryption, bit by bit 400; XORing a plaintext bit in encryption or a ciphertext bit in decryption with a certain bit of A for stream output 500; continuing until completing the plaintext in encryption, or the ciphertext in decryption 600.

Abstract: The invention provides a diffusion function working on a multidimensional diffusion-area (plaintext/ciphertext), in which a multidimensional medium is meanwhile overlapped to the diffusion-area; accordingly, repeating the diffusion function for at least one time thus brings about the multilayer effect. FIG. 1 shows an embodiment of the present invention in flow chart diagram form, comprising of: inputting a plaintext in encryption or a ciphertext in decryption 100; inputting a series of password data forward in encryption or backward in decryption 200; further, by the password data, converting the dimensions of the plaintext 300, and implementing with a diffusion function, repeated TE times in encryption, TD times in decryption 400; outputting the ciphertext in encryption or the plaintext in decryption 600 if completing all password data 500.

Abstract: The present invention discloses a diffused data encryption/decryption processing method, which comprises a plaintext, being at least a 2D matrix; and a password, being at least a 2D matrix; such that the password determines the starting point of the diffusion, the length of the diffusion, the cycle of diffusion, the number of encrypted diffusions and the number of decrypted diffusions to perform the diffusion computation of the plaintext as to achieve the purpose of processing the encryption and decryption.

Abstract: The present invention applies with a diffused mechanism, as such, a variable series of diffusion functions embedded within a diffusion-medium, to generate a maximum diffusion-cycle and nonlinear complexity; additionally, it performs in a serial process for simple design, further, in a parallel process for saving time, or even in a hardware architecture, to gain greater acceleration. FIG. 1 shows an embodiment of the present invention in flow chart diagram form, comprising steps of: selecting a diffusion-area A, a diffusion-medium S, and a diffusion mechanism Ft1 100; initializing A by an input password 200; performing Ft1 to obtain a new value of A 300; inputting a plaintext in encryption or a ciphertext for decryption, bit by bit 400; XORing a plaintext bit in encryption or a ciphertext bit in decryption with a certain bit of A for stream output 500; continuing until completing the plaintext in encryption, or the ciphertext in decryption 600.

Abstract: The invention provides a diffusion function working on a multidimensional diffusion-area (plaintext/ciphertext), in which a multidimensional medium is meanwhile overlapped to the diffusion-area; accordingly, repeating the diffusion function for at least one time thus brings about the multilayer effect. FIG. 1 shows an embodiment of the present invention in flow chart diagram form, comprising of: inputting a plaintext in encryption or a ciphertext in decryption 100; inputting a series of password data forward in encryption or backward in decryption 200; further, by the password data, converting the dimensions of the plaintext 300, and implementing with a diffusion function, repeated TE times in encryption, TD times in decryption 400; outputting the ciphertext in encryption or the plaintext in decryption 600 if completing all password data 500.

Abstract: This invention discloses a symmetric encryption/decryption method with asymmetric keys processed by diffusion algebra, and more particularly to a multiplication method using one-dimensional matrix displacement and addition to generate a ciphertext by multiplying a public (or private) key with a plaintext or obtain the plaintext by multiplying the private (or public) key with the ciphertext.

Abstract: A symmetric encryption/decryption method includes the steps of selecting a diffused mechanism, and the diffused mechanism includes at least one selected from a shift point, a block and a frame; obtaining a plurality of bits required for a cipher by the diffused mechanism and the element number of each dimension of a plaintext; carrying out at least one diffused operation for the plaintext; repeating the foregoing steps to achieve the effect of encrypting the plaintext. Since the sum of the encryption diffused times and the decryption diffused times equals to the diffused cycle, the cipher can be read and at least one dimensional diffused operation of the ciphertext can be carried out, and thus achieving the effect of decrypting the ciphertext.

Abstract: An asymmetric encryption/decryption method comprises the steps of: selecting a plaintext (M) and a modulus (n); selecting a public key (e) and a private key (d) from the modulus (n); and generating a ciphertext (C) by M×e mod n=C, or recovering the plaintext (M) by C×d mod n=M.

Abstract: A symmetric encryption/decryption method of variable length and an application of using the method are disclosed. The method is established in a computational structure of diffusion algebra and includes a plaintext (M) and a private key (P). The length of a private key represents a cycle (T), and the cycle is a product of an encryption cycle (Te) and a decryption cycle (Td). The plaintext is encrypted by MTe mod P=C to produce a ciphertext (C), and the ciphertext is decrypted by CTd mod P=M back to the plaintext. In an application, the plaintext represents a check code, and the ciphertext represents a public key, and the private key set composed of at least one private key, several decryption operations of the private key can give a correct check to achieve the effect of one public key and many private keys.

Abstract: A block-based stream encryption/decryption processing method for applying a matrix architecture of diffusion algebra includes the steps of (a) selecting a private key and a pairing private key; (b) selecting a plaintext and multiplying the plaintext with the private key to produce a ciphertext; (c) multiplying the ciphertext with the pairing private key to obtain the plaintext; and (d) repeating the steps (b) and (c) to produce encrypted or decrypted block streams.

Abstract: The present invention discloses a diffused data encryption/decryption processing method, which comprises a plaintext, being at least a 2D matrix; and a password, being at least a 2D matrix; such that the password determines the starting point of the diffusion, the length of the diffusion, the cycle of diffusion, the number of encrypted diffusions and the number of decrypted diffusions to perform the diffusion computation of the plaintext as to achieve the purpose of processing the encryption and decryption.

Abstract: A diffusive game, comprising: a diffusive space having a plurality of regions; a plurality of variables for being put into the regions and producing actions in the regions. Each variable has an internal value, so that it has its own mode according to the internal value. A diffusive data processing unit performs a relational operation on the internal value of the variable in the diffusive space and the regions, and also produces diffusive operations. The method sets a region in the diffusive space as the triggering region and a specific action on a variable as the triggering action. When a player drives the variable to produce a triggering action, a diffusive data processing unit bases on the triggering region as the starting point to diffuse and transmit to each adjacent region according to the diffusive direction, and complete the diffusive and relational operation of the variable.

Abstract: This invention discloses a method and an apparatus for processing stream encryption/decryption and more particularly to a diffusion operation of a matrix of at least one dimension including a displacement and an exclusion or (XOR), so that a plurality of diffused starting positions is converted into a diffused function operation for quickly and continuously performing an XOR operation with a plaintext (or ciphertext) stream to generate a ciphertext (or plaintext) stream.

Abstract: This invention discloses an asymmetric encryption/decryption method processed by diffusion algebra, and more particularly to a multiplication method using one-dimensional matrix displacement and addition to generate a ciphertext by multiplying a public (or private) key with a plaintext or obtain the plaintext by multiplying the private (or public) key with the ciphertext.

Abstract: A data diffusion processing technique includes the steps of a) dividing a zone into a number of positions and giving a respective default value to each of the positions; and b) assigning one of the positions to be the triggering position and then using the assigned triggering position as the initial position to diffusely transfer data from the triggering position to at least one target position in a diffusion direction, for enabling each of the at least one target position to receive the diffusion data from the triggering position and then to diffusely transfer the diffusion data to at least one next target position after a relation operation of the default value the respective target position with the triggering value of the triggering position to convert the default value of the respective target position into a finished value.

Abstract: A brief numerical keypad is constructed to include four number keys aligned in X-axis and Y-axis directions and abutted against one another, each expressing one of the numbers from 1˜9, a plurality of double-bridging operation portions respectively bridging the abutted area of each two adjacent number keys, each double-bridging operation portion expressing a number equal to the sum of the numerals of the respective two abutted number keys, and a plurality of triple-bridging operation portions respectively bridging the abutted area of each three adjacent number keys, each triple-bridging operation portion expressing a number equal to the sum of the numerals of the respective three abutted number keys.

Abstract: A symmetric encryption/decryption method includes the steps of selecting a diffused mechanism, and the diffused mechanism includes at least one selected from a shift point, a block and a frame; obtaining a plurality of bits required for a cipher by the diffused mechanism and the element number of each dimension of a plaintext; carrying out at least one diffused operation for the plaintext; repeating the foregoing steps to achieve the effect of encrypting the plaintext. Since the sum of the encryption diffused times and the decryption diffused times equals to the diffused cycle, the cipher can be read and at least one dimensional diffused operation of the ciphertext can be carried out, and thus achieving the effect of decrypting the ciphertext.

Abstract: The present invention discloses a diffused data encryption/decryption processing method, which comprises a plaintext, being at least a 2D matrix; and a password, being at least a 2D matrix; such that the password determines the starting point of the diffusion, the length of the diffusion, the cycle of diffusion, the number of encrypted diffusions and the number of decrypted diffusions to perform the diffusion computation of the plaintext as to achieve the purpose of processing the encryption and decryption.