New LFSR-Based Cryptosystems and the Trace Discrete Log Problem (Trace-DLP)

In order to reduce key sizes and bandwidth, cryptographic systems have been proposed using minimal polynomials to represent finite field elements. These systems are essentially equivalent to systems based on characteristic sequences generated by a linear feedback shift register (LFSR). We propose a general class of LFSR-based key agreement and signature schemes based on n-th order characteristic sequences. These schemes have the advantage that they do not require as much bandwidth as their counterparts based on finite fields. In particular, we present a signature scheme based on a new computational problem, the Trace Discrete Logarithm Problem (Trace-DLP). The Trace-DLP and its variants are discussed and their relationship with well-known finite fieldbased computational problems is examined. In addition, we prove the equivalence between several LFSR-based computational problems and their finite field-based counterparts.