3 research outputs found
Recommended from our members
Constructing Variable-Length PRPs and SPRPs from Fixed-Length PRPs
We create variable-length pseudorandom permutations (PRPs) and strong PRPs (SPRPs) accepting any input length chosen from the range of b to 2b bits from fixed-length, b-bit PRPs. We utilize the elastic network that underlies the recently introduced concrete design of elastic block ciphers, exploiting it as a network of PRPs. We prove that three and four-round elastic networks are variable-length PRPs and five-round elastic networks are variable-length SPRPs, accepting any input length that is fixed in the range of b to 2b bits, when the round functions are independently chosen fixed-length PRPs on b bits. We also prove that these are the minimum number of rounds required
Overloading the Nonce: Rugged PRPs, Nonce-Set AEAD, and Order-Resilient Channels
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 (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 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
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