Vectorial Resilient $PC(l)$ of Order $k$ Boolean Functions from AG-Codes

Propagation criteria and resiliency of vectorial Boolean functions are important for cryptographic purpose (see [1], [2], [3], [4], [7], [8], [10], [11] and [16]). Kurosawa , Stoh [8] and Carlet [1] gave a construction of Boolean functions satisfying PC(l) of order k from binary linear or nonlinear codes. In this paper algebraic-geometric codes over GF (2m) are used to modify the Carlet and Kurosawa-Satoh’s construction for giving vectorial resilient Boolean functions satisfying PC(l) of order k criterion. This new construction is compared with