Background and definitions
The Boomerang attack, introduced in 1999 by Wagner , is a cryptanalysis technique against block ciphers based on differential cryptanalysis.
To study the resistance to this attack, Cid et al. introduced the Boomerang Connectivity Table (BCT).
Next, Boura and Canteaut , introduced the notion of boomerang uniformity.
For a permutation , the Boomerang Connectivity Table (BCT) is given by a table ,
The boomerang uniformity of is the maximal value, i.e.
For a permutation, the following properties on the boomerang uniformity were proven.
↑ Wagner D. The boomerang attack.In Lars R. Knudsen, editor, FSE'99, vol. 1636 of LNCS, pp. 156-170. Springer, Heidelberg, March 1999
↑ Cid C., Huang T., Peyrin T., Sasaki Y., Song L. Boomerang connectivity table: A new cryptanalysis tool. EUROCRYPT 2018, Part II, vol. 10821 of LNCS, pp. 683-714. Springer, Heidelberg, 2018
↑ Boura C., Canteaut A. On the boomerang uniformity of cryptographic Sboxes. IACR Transaction on Symmetric Cryptology, pp. 290-310, Sep 2018
- The boomerang uniformity is invariant for inverse and affine equivalence but not for EA- and CCZ-equivalence.
- For an affine equivalent permutation, , we have , with the linear part of .
- For the inverse we have .
- Relation with the differential uniformity: and if and only if .
- If is a power permutation, then .
- If is a quadratic permutation, then .