Abstract. We present PEP, which is a new construction of a tweak-able strong pseudo-random permutation. PEP uses a hash-encrypt-hash approach which has been recently used in the construction of HCTR. This approach is different from the encrypt-mask-encrypt approach of constructions such as CMC, EME and EME∗. The general hash-encrypt-hash approach was earlier used by Naor-Reingold to provide a generic construction technique for an SPRP (but not a tweakable SPRP). PEP can be seen as the development of the Naor-Reingold approach into a fully specified mode of operation with a concrete security reduction for a tweakable strong pseudo-random permutation. HCTR is also based on the Naor-Reingold approach but its security bound is weaker than PEP. Compared to previous known constructions, PEP is the only known con-struction of tweakable SPRP which uses a single key, is efficiently paral-lelizable and can handle an arbitrary number of blocks.

Abstract. This paper improves the Finiasz-Vaudenay construction of TCHo, a hardware-oriented public-key cryptosystem, whose security re-lies on the hardness of finding a low-weight multiple of a given polynomial, and on the decoding of certain noisy cyclic linear codes. Our improvement makes it possible to decrypt in polynomial time (instead of exponential time), to directly prove semantic security (instead of one-wayness), and to achieve pretty good asymptotic performances. We further build IND-CCA secure schemes using the KEM/DEM and Fujisaki-Okamoto hybrid encryption frameworks in the random oracle model. This can encrypt an arbitrary message with an overhead of about 5 Kb in less than 15 ms, on an ASIC of about 10 000 gates at 4 MHz.

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