Abstract: Systems and methods to produce cloaked keys and shared secret data are described. A first device may select a private key, for the first device, based on a first set of rewritten conjugates. The first device may receive a public key from a second device. The public key may be based on a private key of the second device. The private key of the second device may be based on a second set of rewritten conjugates. The first device may determine first and second cloaking elements based on the public key and the private key of the first device. The first device may produce a cloaked key based on the first and second cloaking elements, and the private key of the first device. The first device may produce shared secret data based on the private key of the first device and a second cloaked key from the second device.

Abstract: A system effective to communicate a message between two devices. A first device may include a plaintext to monoid element module effective to receive a plaintext message and apply a first function to the plaintext message to produce a first monoid element. A monoid element evaluator module may be effective to receive and insert submonoid generators into a monoid expression to produce a second monoid element in response. An encryption device module may be effective to apply a second function to the first monoid element, the second monoid element, the monoid expression, and a third monoid element to produce an encrypted plaintext message. Decryption may be performed on the encrypted plaintext message knowing the private key which includes the first function, the second function, the third monoid element and the submonoid generators list.

Abstract: Systems and methods for producing shared secret data are generally described. A first device may receive a public key from a second device. The public key may be based on a first secret element. The first device may generate a first ephemeral private key based on a second secret element, and may generate a second ephemeral private key based on a third secret element. The first device may generate a first element based on the public key and the first ephemeral private key, and may generate a second element based on the public key and the second ephemeral private key. The second element may relate to the shared secret data. The first device may generate a session public key based on the first element, the second secret element, and the third secret element. The shared secret data may be derivable, by the second device, from the session public key.

Abstract: A first module divides a string into a number of blocks. A second module associates the blocks with monoid elements in a list of first monoid elements to produce second monoid elements. A third module applies a first function to an initial monoid element and a first of the second monoid elements producing a first calculated monoid element and evaluates an action of the initial monoid element on the first function producing a second function. A fourth module applies the second function to the first calculated monoid element and to a second of the second monoid elements producing a second calculated monoid element and evaluates the action of the first calculated monoid element on the first function producing a third function.

Abstract: A system and method for generating a secret key to facilitate secure communications between users. A first and second and a function between the two monoids are selected, the function being a monoid homomorphism. A group and a group action of the group on the first monoid is selected. Each user is assigned a submonoid of the first monoid so that these submonoids satisfy a special symmetry property determined by the function, a structure of the first and second monoids, and the action of the group. A multiplication of an element in the second monoid and an element in the first monoid is obtained by combining the group action and the monoid homomorphism. First and second users choose private keys which are sequences of elements in their respective submonoids. A first result is obtained by multiplying an identity element by the first element of the sequence in a respective submonoid.

Abstract: Technologies are generally described for methods and devices for generating a final signature. The methods may comprise receiving a message by a processor. The methods may comprise generating a random number by a random number generator. The methods may comprise forwarding, by the processor, the random number to a cloaking element generator. The methods may comprise forwarding, by the processor, a private key to the cloaking element generator. The methods may comprise forwarding, by the processor, a group to the cloaking element generator. The methods may comprise forwarding, by the processor, a homomorphism to the cloaking element generator. The methods may comprise processing, by the cloaking element generator, the random number, the group, the private key, and the homomorphism to produce a cloaking element. The methods may comprise applying the cloaking element to transform the message into the final signature.

Abstract: A first module divides a string into a number of blocks. A second module associates the blocks with monoid elements in a list of first monoid elements to produce second monoid elements. A third module applies a first function to an initial monoid element and a first of the second monoid elements producing a first calculated monoid element and evaluates an action of the initial monoid element on the first function producing a second function. A fourth module applies the second function to the first calculated monoid element and to a second of the second monoid elements producing a second calculated monoid element and evaluates the action of the first calculated monoid element on the first function producing a third function.

Abstract: A first module divides a string into a number of blocks. A second module associates the blocks with monoid elements in a list of first monoid elements to produce second monoid elements. A third module applies a first function to an initial monoid element and a first of the second monoid elements producing a first calculated monoid element and evaluates an action of the initial monoid element on the first function producing a second function. A fourth module applies the second function to the first calculated monoid element and to a second of the second monoid elements producing a second calculated monoid element and evaluates the action of the first calculated monoid element on the first function producing a third function.

Abstract: A system effective to communicate a message between two devices. A first device may include a plaintext to monoid element module effective to receive a plaintext message and apply a first function to the plaintext message to produce a first monoid element. A monoid element evaluator module may be effective to receive and insert submonoid generators into a monoid expression to produce a second monoid element in response. An encryption device module may be effective to apply a second function to the first monoid element, the second monoid element, the monoid expression, and a third monoid element to produce an encrypted plaintext message. Decryption may be performed on the encrypted plaintext message knowing the private key which includes the first function, the second function, the third monoid element and the submonoid generators list.

Abstract: A system and method for generating a secret key to facilitate secure communications between users. A first and second and a function between the two monoids are selected, the function being a monoid homomorphism. A group and a group action of the group on the first monoid is selected. Each user is assigned a submonoid of the first monoid so that these submonoids satisfy a special symmetry property determined by the function, a structure of the first and second monoids, and the action of the group. A multiplication of an element in the second monoid and an element in the first monoid is obtained by combining the group action and the monoid homomorphism. First and second users choose private keys which are sequences of elements in their respective submonoids. A first result is obtained by multiplying an identity element by the first element of the sequence in a respective submonoid.

Abstract: A first module divides a string into a number of blocks. A second module associates the blocks with monoid elements in a list of first monoid elements to produce second monoid elements. A third module applies a first function to an initial monoid element and a first of the second monoid elements producing a first calculated monoid element and evaluates an action of the initial monoid element on the first function producing a second function. A fourth module applies the second function to the first calculated monoid element and to a second of the second monoid elements producing a second calculated monoid element and evaluates the action of the first calculated monoid element on the first function producing a third function.

Abstract: A system and method for generating a secret key to facilitate secure communications between users. A first and second and a function between the two monoids are selected, the function being a monoid homomorphism. A group and a group action of the group on the first monoid is selected. Each user is assigned a submonoid of the first monoid so that these submonoids satisfy a special symmetry property determined by the function, a structure of the first and second monoids, and the action of the group. A multiplication of an element in the second monoid and an element in the first monoid is obtained by combining the group action and the monoid homomorphism. First and second users choose private keys which are sequences of elements in their respective submonoids. A first result is obtained by multiplying an identity element by the first element of the sequence in a respective submonoid.

Abstract: A system effective to communicate a message between two devices. A first device may include a plaintext to monoid element module effective to receive a plaintext message and apply a first function to the plaintext message to produce a first monoid element. A monoid element evaluator module may be effective to receive and insert submonoid generators into a monoid expression to produce a second monoid element in response. An encryption device module may be effective to apply a second function to the first monoid element, the second monoid element, the monoid expression, and a third monoid element to produce an encrypted plaintext message. Decryption may be performed on the encrypted plaintext message knowing the private key which includes the first function, the second function, the third monoid element and the submonoid generators list.

Abstract: A system effective to communicate a message between two devices. A first device may include a plaintext to monoid element module effective to receive a plaintext message and apply a first function to the plaintext message to produce a first monoid element. A monoid element evaluator module may be effective to receive and insert submonoid generators into a monoid expression to produce a second monoid element in response. An encryption device module may be effective to apply a second function to the first monoid element, the second monoid element, the monoid expression, and a third monoid element to produce an encrypted plaintext message. Decryption may be performed on the encrypted plaintext message knowing the private key which includes the first function, the second function, the third monoid element and the submonoid generators list.

Abstract: A system and method for generating a secret key to facilitate secure communications between users. A first and second and a function between the two monoids are selected, the function being a monoid homomorphism. A group and a group action of the group on the first monoid is selected. Each user is assigned a submonoid of the first monoid so that these submonoids satisfy a special symmetry property determined by the function, a structure of the first and second monoids, and the action of the group. A multiplication of an element in the second monoid and an element in the first monoid is obtained by combining the group action and the monoid homomorphism. First and second users choose private keys which are sequences of elements in their respective submonoids. A first result is obtained by multiplying an identity element by the first element of the sequence in a respective submonoid.

Abstract: A first module divides a string into a number of blocks. A second module associates the blocks with monoid elements in a list of first monoid elements to produce second monoid elements. A third module applies a first function to an initial monoid element and a first of the second monoid elements producing a first calculated monoid element and evaluates an action of the initial monoid element on the first function producing a second function. A fourth module applies the second function to the first calculated monoid element and to a second of the second monoid elements producing a second calculated monoid element and evaluates the action of the first calculated monoid element on the first function producing a third function.

Abstract: A first module divides a string into blocks. A second module associates the blocks with monoid elements in a list of first monoid elements to produce second monoid elements. A third module applies a first function to an initial monoid element and a first of the second monoid elements producing a first calculated monoid element and evaluates an action of the initial monoid element on the first function producing a second function. A fourth module applies the second function to the first calculated monoid element and to a second of the second monoid elements producing a second calculated monoid element and evaluates the action of the first calculated monoid element on the first function producing a third function.

Abstract: A system and method for generating a secret key to facilitate secure communications between users. A first and second and a function between the two monoids are selected, the function being a monoid homomorphism. A group and a group action of the group on the first monoid is selected. Each user is assigned a submonoid of the first monoid so that these submonoids satisfy a special symmetry property determined by the function, a structure of the first and second monoids, and the action of the group. A multiplication of an element in the second monoid and an element in the first monoid is obtained by combining the group action and the monoid homomorphism. First and second users choose private keys which are sequences of elements in their respective submonoids. A first result is obtained by multiplying an identity element by the first element of the sequence in a respective submonoid.

Abstract: A first module divides a string into a number of blocks. A second module associates the blocks with monoid elements in a list of first monoid elements to produce second monoid elements. A third module applies a first function to an initial monoid element and a first of the second monoid elements producing a first calculated monoid element and evaluates an action of the initial monoid element on the first function producing a second function. A fourth module applies the second function to the first calculated monoid element and to a second of the second monoid elements producing a second calculated monoid element and evaluates the action of the first calculated monoid element on the first function producing a third function.

Abstract: A system effective to communicate a message between two devices. A first device may include a plaintext to monoid element module effective to receive a plaintext message and apply a first function to the plaintext message to produce a first monoid element. A monoid element evaluator module may be effective to receive and insert submonoid generators into a monoid expression to produce a second monoid element in response. An encryption device module may be effective to apply a second function to the first monoid element, the second monoid element, the monoid expression, and a third monoid element to produce an encrypted plaintext message. Decryption may be performed on the encrypted plaintext message knowing the private key which includes the first function, the second function, the third monoid element and the submonoid generators list.