A Zigzag-Decodable Ramp Secret Sharing Scheme

The classical threshold secret sharing scheme by Shamir requires high computation complexity. Many fast secret sharing schemes have been proposed to reduce the computation cost. Another problem of perfect secret sharing scheme is the large share size. Ramp sharing schemes were proposed as a solution to reduce the share size with sacrificing secrecy to some extent. This paper proposes a new ramp scheme, which is adapted from the zigzag-decodable erasure codes for data storage systems. The scheme is shown to approach a linear ramp scheme when the secret size grows to infinity. It is conceptually easy to understand, and has low computation cost, since both its encoding and decoding algorithms are based only on the XOR and bitwise-shift operations.