Abstract: High throughput in data computations and processing is maintained while minimizing latency. A binary tree architecture is provided in which two trees are used simultaneously, and initiation of the trees is staggered to allow for optimal use of bandwidth. These techniques are desirable for erasure codes and other computations where the addition operator is commutative. Additionally, a ternary tree architecture may be used, in which three trees co-exist on the same set of nodes to maintain high throughput while further improving latency.

Abstract: A signature {Sig, {Qi}} is generated on a message M by a signer Et in a hierarchical system including the entities E0, E1, . . . , Et, each entity Ei (i>0) being a child of Ei?1. Here Sig = S t + s t ? P M = ? i = 1 t ? s i - 1 ? P i , where: each Si is a secret key of Ei; each si is a secret of Si; PM is a public function of M; each Pi is a public function of the ID's of all entities Ej such that 1?j?i; each Qi=siP0 where P0 is public. The verifier confirms that e ^ ? ( P 0 , Sig ) e ^ ? ( Q t , P M ) ? ? i ? ? e ^ ? ( Q i - 1 , P i ) = V , where: the product ?iê(Qi?1,Pi) is taken over all integers i in a proper subset of the integers from 1 to t inclusive; ê is a bilinear non-degenerate mapping; V can be ê(Q0,Pi0) where i0 is predefined (e.g. 1), or V can be another expression is a verifier is part of the hierarchical system.

Abstract: Nodal pattern configuration is described, including generating successive values at a source node, processing the successive values using a plurality of intermediate nodes, sending the processed values from a node in the plurality of intermediate nodes to a destination node, and configuring the plurality of intermediate nodes such that each node of the plurality of intermediate nodes, concurrently performs at least two actions. Also, nodal pattern configuration includes generating a series of data blocks at a source node, processing data blocks from the series of data blocks using a plurality of intermediate nodes in data communication with the source node, each node of the plurality of intermediate nodes being configured to concurrently perform at least two operations, and sending processed data blocks from the plurality of intermediate nodes to a destination node, the destination node being in data communication with the plurality of intermediate nodes.

Abstract: Methods are provided for encoding and decoding a digital message between a sender and a recipient in a system including a plurality of private key generators (“PKGs”). The PKGs include at least a root PKG and n lower-level PKG in the hierarchy between the root PKG and the recipient. A root key generation secret is selected and is known only to the root PKG. A root key generation parameter is generated based on the root key generation secret. A lower-level key generation secret is selected for each of the n lower-level PKGs, wherein each lower-level key generation secret is known only to its associated lower-level PKG. A lower-level key generation parameter also is generated for each of the n lower-level PKGs using at least the lower-level key generation secret for its associated lower-level private key generator. The message is encoded to form a ciphertext using at least the root key generation parameter and recipient identity information associated with the recipient.

Abstract: A method and system are provided for determining a shared secret between two entities in a cryptosystem. A first random secret is selected that is known to the first entity and unknown to the second entity. A first intermediate shared secret component is determined using the first random secret and a system parameter. The first intermediate shared secret component is communicated to the second entity. A second random secret is selected that is known to the second entity, but unknown to the first entity. A second intermediate shared secret component is determined using the second random secret and the system parameter. The second intermediate shared secret component is communicated to the first entity. It is confirmed that both the first entity and the second entity know a non-interactive shared secret. An interactive shared secret is determined using the first random secret, the second random secret, and the system parameter.

Abstract: A method and system are provided for determining a shared secret between two entities in a cryptosystem. A first random secret is selected that is known to the first entity and unknown to the second entity. A first intermediate shared secret component is determined using the first random secret and a system parameter. The first intermediate shared secret component is communicated to the second entity. A second random secret is selected that is known to the second entity, but unknown to the first entity. A second intermediate shared secret component is determined using the second random secret and the system parameter. The second intermediate shared secret component is communicated to the first entity. It is confirmed that both the first entity and the second entity know a non-interactive shared secret. An interactive shared secret is determined using the first random secret, the second random secret, and the system parameter.

Abstract: Methods are provided for encoding and decoding a digital message between a sender and a recipient in a system including a plurality of private key generators (“PKGs”). The PKGs include at least a root PKG and n lower-level PKG in the hierarchy between the root PKG and the recipient. A root key generation secret is selected and is known only to the root PKG. A root key generation parameter is generated based on the root key generation secret. A lower-level key generation secret is selected for each of the n lower-level PKGs, wherein each lower-level key generation secret is known only to its associated lower-level PKG. A lower-level key generation parameter also is generated for each of the n lower-level PKGs using at least the lower-level key generation secret for its associated lower-level private key generator. The message is encoded to form a ciphertext using at least the root key generation parameter and recipient identity information associated with the recipient.

Abstract: A signature {Sig, {Qi}} is generated on a message M by a signer Et in a hierarchical system including the entities E0, E1, . . . , Et, each entity Ei (i>0) being a child of Ei?1. Here Sig = S t + s t ? P M = ? i = 1 t ? s i - 1 ? P i , where: each Si is a secret key of Ei; each si is a secret of Si; PM is a public function of M; each Pi is a public function of the ID's of all entities Ej such that 1?j?i; each Qi=siP0 where P0 is public. The verifier confirms that e ^ ? ( P 0 , Sig ) e ^ ? ( Q t , P M ) ? ? i ? ? ? e ^ ? ( Q i - 1 , P i ) = V , where: the product ?iê(Qi?1,Pi) is taken over all integers i in a proper subset of the integers from 1 to t inclusive; ê is a bilinear non-degenerate mapping; V can be ê(Q0,Pi0) where i0 is predefined (e.g. 1), or V can be another expression is a verifier is part of the hierarchical system.

Abstract: Methods are provided for encoding and decoding a digital message between a sender and a recipient in a system including a plurality of private key generators (“PKGs”). The PKGs include at least a root PKG and n lower-level PKG in the hierarchy between the root PKG and the recipient. A root key generation secret is selected and is known only to the root PKG. A root key generation parameter is generated based on the root key generation secret. A lower-level key generation secret is selected for each of the n lower-level PKGs, wherein each lower-level key generation secret is known only to its associated lower-level PKG. A lower-level key generation parameter also is generated for each of the n lower-level PKGs using at least the lower-level key generation secret for its associated lower-level private key generator. The message is encoded to form a ciphertext using at least the root key generation parameter and recipient identity information associated with the recipient.

Abstract: Methods are provided for encoding and decoding a digital message between a sender and a recipient in a system including a plurality of private key generators (“PKGs”). The PKGs include at least a root PKG and n lower-level PKG in the hierarchy between the root PKG and the recipient. A root key generation secret is selected and is known only to the root PKG. A root key generation parameter is generated based on the root key generation secret. A lower-level key generation secret is selected for each of the n lower-level PKGs, wherein each lower-level key generation secret is known only to its associated lower-level PKG. A lower-level key generation parameter also is generated for each of the n lower-level PKGs using at least the lower-level key generation secret for its associated lower-level private key generator. The message is encoded to form a ciphertext using at least the root key generation parameter and recipient identity information associated with the recipient.

Abstract: A method and system are provided for determining a shared secret between two entities in a cryptosystem. A first random secret is selected that is known to the first entity and unknown to the second entity. A first intermediate shared secret component is determined using the first random secret and a system parameter. The first intermediate shared secret component is communicated to the second entity. A second random secret is selected that is known to the second entity, but unknown to the first entity. A second intermediate shared secret component is determined using the second random secret and the system parameter. The second intermediate shared secret component is communicated to the first entity. It is confirmed that both the first entity and the second entity know a non-interactive shared secret. An interactive shared secret is determined using the first random secret, the second random secret, and the system parameter.

Abstract: Methods are provided for encoding and decoding a digital message between a sender and a recipient in a system including a plurality of private key generators (“PKGs”). The PKGs include at least a root PKG and n lower-level PKG in the hierarchy between the root PKG and the recipient. A root key generation secret is selected and is known only to the root PKG. A root key generation parameter is generated based on the root key generation secret. A lower-level key generation secret is selected for each of the n lower-level PKGs, wherein each lower-level key generation secret is known only to its associated lower-level PKG. A lower-level key generation parameter also is generated for each of the n lower-level PKGs using at least the lower-level key generation secret for its associated lower-level private key generator. The message is encoded to form a ciphertext using at least the root key generation parameter and recipient identity information associated with the recipient.

Abstract: Nodal pattern configuration is described, including generating successive values at a source node, processing the successive values using a plurality of intermediate nodes, sending the processed values from a node in the plurality of intermediate nodes to a destination node, and configuring the plurality of intermediate nodes such that each node of the plurality of intermediate nodes, concurrently performs at least two actions. Also, nodal pattern configuration includes generating a series of data blocks at a source node, processing data blocks from the series of data blocks using a plurality of intermediate nodes in data communication with the source node, each node of the plurality of intermediate nodes being configured to concurrently perform at least two operations, and sending processed data blocks from the plurality of intermediate nodes to a destination node, the destination node being in data communication with the plurality of intermediate nodes.

Abstract: A method and system are provided for determining a shared secret between two entities in a cryptosystem. A first random secret is selected that is known to the first entity and unknown to the second entity. A first intermediate shared secret component is determined using the first random secret and a system parameter. The first intermediate shared secret component is communicated to the second entity. A second random secret is selected that is known to the second entity, but unknown to the first entity. A second intermediate shared secret component is determined using the second random secret and the system parameter. The second intermediate shared secret component is communicated to the first entity. It is confirmed that both the first entity and the second entity know a non-interactive shared secret. An interactive shared secret is determined using the first random secret, the second random secret, and the system parameter.

Abstract: A method and system are provided for determining a shared secret between two entities in a cryptosystem. A first random secret is selected that is known to the first entity and unknown to the second entity. A first intermediate shared secret component is determined using the first random secret and a system parameter. The first intermediate shared secret component is communicated to the second entity. A second random secret is selected that is known to the second entity, but unknown to the first entity. A second intermediate shared secret component is determined using the second random secret and the system parameter. The second intermediate shared secret component is communicated to the first entity. It is confirmed that both the first entity and the second entity know a non-interactive shared secret. An interactive shared secret is determined using the first random secret, the second random secret, and the system parameter.

Abstract: A system and method are disclosed for securing neighbor discovery in IP networking system. A public key is generated using an IP address value of the host and routed prefix for the router. Thereafter, an Identity based Private Key Generator (IPKG) generates a private key using public cryptographic parameters, that corresponds to the host's or router's public key. Thereafter, neighbor discovery is authenticated with the public/private pair key and the public parameters.

Abstract: A system and method are disclosed for securing binding updates in a wireless telecommunications system. A public key is generating using a home address value of the mobile host. Thereafter, a home agent, such as a router, generates a private key using public cryptographic parameters, that corresponds to the mobile host and the public key. The correspondent node uses the public key to encrypt a shared key and sends the shared key to the mobile host. The mobile host decrypts the shared key using the private key and uses the shared key to sign the binding update. Thereafter, the correspondent node utilizes the shared key to verify the authenticity of the binding update.

Abstract: A method and system are provided for determining a shared secret between two entities in a cryptosystem. A first random secret is selected that is known to the first entity and unknown to the second entity. A first intermediate shared secret component is determined using the first random secret and a system parameter. The first intermediate shared secret component is communicated to the second entity. A second random secret is selected that is known to the second entity, but unknown to the first entity. A second intermediate shared secret component is determined using the second random secret and the system parameter. The second intermediate shared secret component is communicated to the first entity. It is confirmed that both the first entity and the second entity know a non-interactive shared secret. An interactive shared secret is determined using the first random secret, the second random secret, and the system parameter.

Abstract: Methods are provided for encoding and decoding a digital message between a sender and a recipient in a system including a plurality of private key generators (“PKGs”). The PKGs include at least a root PKG and n lower-level PKG in the hierarchy between the root PKG and the recipient. A root key generation secret is selected and is known only to the root PKG. A root key generation parameter is generated based on the root key generation secret. A lower-level key generation secret is selected for each of the n lower-level PKGs, wherein each lower-level key generation secret is known only to its associated lower-level PKG. A lower-level key generation parameter also is generated for each of the n lower-level PKGs using at least the lower-level key generation secret for its associated lower-level private key generator. The message is encoded to form a ciphertext using at least the root key generation parameter and recipient identity information associated with the recipient.