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We formally study iterated block ciphers that alternate between two sequencesof independent and identically distributed (i.i.d.) rounds. It is demonstratedthat, in some cases the effect of alternating increases security, while inother cases the effect may strictly decrease security relative to thecorresponding product of one of its component sequences. As this would appearto contradict conventional wisdom based on the ideal cipher approximation, weintroduce new machinery for provable security comparisons. The comparisons madehere simultaneously establish a coherent ordering of security metrics rangingfrom key-recovery cost to computational indistinguishability.

Alternating Product Ciphers: A Case for Provable Security Comparisons (extended abstract)