Resynchronization Interval of Self-synchronizing Modes of Block Ciphers

In some communication systems, some of the transmitted bits or bit groups are lost or, on the contrary, repeated. Lost or repeated bits or bit groups are called slips. In the case of cipher transmission, these slips produce a loss of the synchronization between transmitter and receiver, which is accompanied by the loss of the information being transmitted. Self-synchronizing modes of block ciphers are used for the elimination of this phenomenon. An important characteristic of these mode types is the average number of bits that were transmitted between the end of the slip and the moment of synchronization recovery - so-called resynchronization interval. In this paper, the probability distribution of the occurrence of a synchronization sequence in the cryptogram is derived first. On this basis, formulas for computing the resynchronization interval of OCFB and modified SCFB statistical self-synchronizing modes of block ciphers are then derived. The formulas obtained are compared with the formula for the resynchronization interval of the CFB mode. The results obtained may be used to choose a suitable self-synchronizing mode of a block cipher.