Editing Avalanche effect (section)

== Strict avalanche criterion ==
The '''strict avalanche criterion''' ('''SAC''') is a formalization of the avalanche effect. It is satisfied if, whenever a single input bit is [[Signed number representations#Ones' complement|complemented]], each of the output bits changes with a 50% probability. The SAC builds on the concepts of [[completeness (cryptography)|completeness]] and avalanche and was introduced by Webster and Tavares in 1985.<ref name="webster_tavares_1985">{{cite book|first1=A. F.|last1= Webster |first2=Stafford E. |last2=Tavares|chapter=On the design of S-boxes|title=Advances in Cryptology – Crypto '85 |series=Lecture Notes in Computer Science|volume=218|pages= 523–534|year=1985|isbn=0-387-16463-4|publisher=Springer-Verlag New York, Inc. |location= New York, NY}}</ref>

Higher-order generalizations of SAC involve multiple input bits.
Boolean functions which satisfy the highest order SAC are always [[bent function]]s,
also called maximally nonlinear functions,
also called "perfect nonlinear" functions.<ref>{{cite report |last1=Adams |first1=C. M. |author-link1=Carlisle Adams |last2=Tavares |first2=S. E. |author-link2=Stafford Tavares |date=January 1990 |title=The Use of Bent Sequences to Achieve Higher-Order Strict Avalanche Criterion in S-box Design |version=Technical Report TR 90-013 |publisher=[[Queen's University at Kingston|Queen's University]] |citeseerx=10.1.1.41.8374}}</ref>