Abstract: Method of identifying invalid digital signatures involving batch verification by receiving digital messages, digital signatures, and signer identifiers, computing Z0 as a function of the received information, and determining if the digital signatures are valid. If so, stopping. If not, assigning a signature identifier to each digital signature, setting w equal to 1, computing Zw as a function of the received information and signature identifiers, and searching for a multiplicative relationship amongst Z0, Z1, . . . , Zw. If one is found then determining the invalid digital signatures from the multiplicative relationship and stopping. Otherwise, incrementing w and returning to the step of computing for additional processing if desired.

Abstract: One embodiment of the present invention provides a system for establishing a shared cryptographic key between participating nodes in a network. The system operates by sending a first message from the first node to the second node requesting establishment of a shared key. The second node sends a second message containing identifiers and a message authentication code to a key distribution center (KDC). The authentication code is generated using a second node key belonging to the second node. The KDC recreates the previously created second node key using the second node identifier and a secret key known only to the key distribution center. The KDC then verifies the message authentication code using the second node key. If the message authentication code is verified, the KDC creates a shared key for the nodes to use while communicating with each other.

Abstract: The disposable safety eyewear has a lens portion having a bridge portion and a nose support thereon. Left and right temple bars are connected to the lens portion by living hinges. The living hinges are operable between an open position and a folded position. Mating formations secure the living hinges in its respective folded position.

Abstract: An apparatus is provided for installing a faucet on a top side of a deck. The apparatus includes a threaded member engaged with the faucet and extending through the mounting hole to be rotated from above the deck. A nut is threadedly connected to the threaded member to pass through the mounting hole to the underside of the deck. A second member associated with and parallel to the threaded member engages the nut to prevent rotation thereof during rotation of the threaded member whereby the nut will be shifted up or down along the length of the threaded member. A pair of retaining arms are provided whereby, upon rotation of the threaded member to raise the nut in the direction of the deck, the retaining arms will bend outwardly and engage the underside of the deck to clamp the faucet to the deck.

Abstract: One embodiment of the present invention provides a system for establishing a shared cryptographic key between participating nodes in a network. The system operates by sending a first message from the first node to the second node requesting establishment of a shared key. The second node sends a second message containing identifiers and a message authentication code to a key distribution center (KDC). The authentication code is generated using a second node key belonging to the second node. The KDC recreates the previously created second node key using the second node identifier and a secret key known only to the key distribution center. The KDC then verifies the message authentication code using the second node key. If the message authentication code is verified, the KDC creates a shared key for the nodes to use while communicating with each other.

Abstract: One embodiment of the present invention provides a system for establishing a cryptographic key between energy-limited nodes using a super node that has abundant energy. The node also sends a message to a super node including the partial key value encrypted using the super node's a public key. Note that the energy-limited node only encrypts with the public key, which requires less energy than decrypting with the corresponding private key. The super node then decrypts to recover the partial key value. Next, the super node securely communicates the partial key value to the second node. The second node then establishes the cryptographic key using the first and second node's partial key values.

Abstract: An apparatus is provided for installing a faucet or end body valve assembly on a top side of a deck. The apparatus includes a threaded member engaged with the faucet or end body and extending through the mounting hole to be rotated from above the deck. A wedge nut is threadedly connected to the threaded member to pass through the mounting hole to the underside of the deck. A second member associated with and parallel to the threaded member engages the nut to prevent rotation thereof during rotation of the threaded member whereby the nut will be shifted up or down along the length of the threaded member responsive to the direction of rotation of the threaded member. A retainer member is disposed around the threaded member and includes a plurality of legs which each include a foot portion at an end thereof.

Abstract: A retractable leash includes an integral light. The apparatus has a first housing section and a retractable leash section. The first housing section has a handle, a light connected to top front portion of the first housing section and a receiving area. A rechargeable battery is removably connected to the first housing in the handle. The retractable leash section has a second housing section pivotably mounted to the first housing section, in the receiving area, and a reel rotatably mounted to the second housing section. A leash is connected to the reel for extension and retraction relative to the first housing section. In an alternate embodiment, a light is located on the leash and electrically connected to a conductor extending along the leash.

Abstract: A retractable leash includes an integral light. The apparatus has a first housing section and a retractable leash section. The first housing section has a handle, a light connected to top front portion of the first housing section and a receiving area. A rechargeable battery is removably connected to the first housing in the handle. The retractable leash section has a second housing section pivotably mounted to the first housing section, in the receiving area, and a reel rotatably mounted to the second housing section. A leash is connected to the reel for extension and retraction relative to the first housing section. In an alternate embodiment, a light is located on the leash and electrically connected to a conductor extending along the leash.