Abstract :
In this paper, we provide a new generalized construction method for (n, m, t) resilient functions with satisfying synthetical cryptographic criteria. These synthetical cryptographic criteria include high nonlinearity, good resiliency, high algebraic degree, and nonexistence of nonzero linear structure and so on. The construction is based on the use of linear error-correcting code. Given a linear [u, m, t + 1] code and its dual code [u, u - m, t* + 1], we show that it is possible to construct (n, m, d) resilient functions with satisfying synthetical cryptographic criteria, where d = min(t, t*) and n > u > 2m. The method provides a new idea in designing cryptographic functions.
Keywords :
cryptography; dual codes; error correction codes; linear codes; cryptographic function design; dual code; error-correcting codes; good resiliency; high algebraic degree; high nonlinearity; linear codes; nonzero linear structure nonexistence; resilient function construction; synthetical cryptographic criteria; Art; Boolean functions; Cryptography; Distributed computing; Educational technology; Error correction codes; Information security; Laboratories; Quantum computing; Random sequences;
