Description
Pseudorandom functions (PRFs) are one of the most fundamental primitives in cryptography. In this work, we provide a new algebraic framework which encompasses many of the existing algebraic PRFs, including the ones by Naor and Reingold (FOCS'97), by Lewko and Waters (CCS'09), and by Boneh, Montgomery, and Raghunathan (CCS'10), as well as the related-key-secure PRFs by Bellare and Cash (Crypto'10) and by Abdalla \etal (Crypto'14). To achieve this goal, we introduce two versions of our framework. The first, termed linearly independent polynomial security, states that the values $(g^{P_1(\vec{a})}, \ldots, g^{P_q(\vec{a})})$ are indistinguishable from a random tuple of the same size, when $P_1, \ldots, P_q$ are linearly independent multivariate polynomials of the secret key vector $\vec{a}$. The second, which is a natural generalization of the first framework, additionally deals with constructions based on the decision linear and matrix Diffie-Hellman assumptions. In addition to unifying and simplifying proofs for existing schemes, our new framework also yields several new results, such as related-key security with respect to arbitrary permutations of polynomials. All our constructions are in the standard model and do not require the existence of multilinear maps.
Next sessions
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Polytopes in the Fiat-Shamir with Aborts Paradigm
Speaker : Hugo Beguinet - ENS Paris / Thales
The Fiat-Shamir with Aborts paradigm (FSwA) uses rejection sampling to remove a secret’s dependency on a given source distribution. Recent results revealed that unlike the uniform distribution in the hypercube, both the continuous Gaussian and the uniform distribution within the hypersphere minimise the rejection rate and the size of the proof of knowledge. However, in practice both these[…]-
Cryptography
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Asymmetric primitive
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Mode and protocol
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Post-quantum Group-based Cryptography
Speaker : Delaram Kahrobaei - The City University of New York