Scrambling or information randomization has been effectively used in various applications to prevent the information falling into the hands of rogue attackers. In this paper, we use the idea of spectrum scrambling to proactively randomize the spectrum across multiple fiber cores to improve connections' security, while at the same time effectively defragmenting the spectrum to improve connections' blocking performance. To this end, we propose a scheme called random spectrum defragmentation (RSD), and model the occupancy pattern of a multi-core fiber link using a multi-class continuous-time Markov chain (CTMC) under the two different spectrum allocation methods, first-fit and random-fit. As the efforts have been on preventing unauthorized access to optical channels, we show that scrambling can be effectively used to help dealing with the physical layer attacks. At the same time, numerical results show that also the blocking can be improved for a particular so-called randomization process (RP) arrival rate, and lower connection reconfiguration time.