3 research outputs found

    Overloading the Nonce: Rugged PRPs, Nonce-Set AEAD, and Order-Resilient Channels

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    We introduce a new security notion that lies right in between pseudorandom permutations (PRPs) and strong pseudorandom permutations (SPRPs). We call this new security notion and any (tweakable) cipher that satisfies it a rugged pseudorandom permutation\textit{rugged pseudorandom permutation} (RPRP). Rugged pseudorandom permutations lend themselves to some interesting applications, have practical benefits, and lead to novel cryptographic constructions. Our focus is on variable-length tweakable RPRPs, and analogous to the encode-then-encipher paradigm of Bellare and Rogaway, we can generically transform any such cipher into different AEAD schemes with varying security properties. However, the benefit of RPRPs is that they can be constructed more efficiently as they are weaker primitives than SPRPs (the notion traditionally required by the encode-then-encipher paradigm). We can construct RPRPs using only two layers of processing, whereas SPRPs typically require three layers of processing over the input data. We also identify a new transformation that yields RUP-secure AEAD schemes with more compact ciphertexts than previously known. Further extending this approach, we arrive at a new generalized notion of authenticated encryption and a matching construction, which we refer to as nonce-set AEAD\textit{nonce-set AEAD}. Nonce-set AEAD is particularly well-suited in the context of secure channels, like QUIC and DTLS, that operate over unreliable transports and employ a window mechanism at the receiver\u27s end of the channel. We conclude by presenting a generic construction for transforming a nonce-set AEAD scheme into an order-resilient secure channel. Our channel construction sheds new light on order-resilient channels and additionally leads to more compact ciphertexts when instantiated from RPRPs

    Moving constraints as stabilizing controls in classical mechanics

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    The paper analyzes a Lagrangian system which is controlled by directly assigning some of the coordinates as functions of time, by means of frictionless constraints. In a natural system of coordinates, the equations of motions contain terms which are linear or quadratic w.r.t.time derivatives of the control functions. After reviewing the basic equations, we explain the significance of the quadratic terms, related to geodesics orthogonal to a given foliation. We then study the problem of stabilization of the system to a given point, by means of oscillating controls. This problem is first reduced to the weak stability for a related convex-valued differential inclusion, then studied by Lyapunov functions methods. In the last sections, we illustrate the results by means of various mechanical examples.Comment: 52 pages, 4 figure
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