Avalanche effect

<h2 id="strict-avalanche-criterion">Strict avalanche criterion</h2>
<p>The strict avalanche criterion (SAC) is a formalization of the avalanche effect. It is satisfied if, whenever a single input bit is <a href="/facts/Signed_number_representations/cE0sEMau">complemented</a>, each of the output bits changes with a 50% probability. The SAC builds on the concepts of <a href="/facts/Completeness_(cryptography)/EpDSBbxk">completeness</a> and avalanche and was introduced by Webster and Tavares in 1985.<a class="footnote-ref" id="fnref:5" href="#fn:5"><sup>5</sup></a>
</p><p>Higher-order generalizations of SAC involve multiple input bits.
Boolean functions which satisfy the highest order SAC are always <a href="/facts/Bent_function/dgR6uAhQ">bent functions</a>,
also called maximally nonlinear functions,
also called "perfect nonlinear" functions.<a class="footnote-ref" id="fnref:6" href="#fn:6"><sup>6</sup></a>
</p>
<h2 id="bit-independence-criterion">Bit independence criterion</h2>
<p>The bit independence criterion (BIC) states that output bits <i>j</i> and <i>k</i> should change independently when any single input bit <i>i</i> is inverted, for all <i>i</i>, <i>j</i> and <i>k</i>.<a class="footnote-ref" id="fnref:7" href="#fn:7"><sup>7</sup></a>
</p>
<h2 id="see-also">See also</h2>
<ul><li><a href="/facts/Butterfly_effect/Iex6LFKu">Butterfly effect</a></li>
<li><a href="/facts/Confusion_and_diffusion/PKqvzyKY">Confusion and diffusion</a></li></ul>

<h2 id="external-links">External links</h2>

<h2 id="references">References</h2>

<ol>
<li id="fn:1"><p>Feistel, Horst (1973). "Cryptography and Computer Privacy". Scientific American. 228 (5): 15–23. Bibcode:1973SciAm.228e..15F. doi:10.1038/scientificamerican0573-15. <a href="https://www.apprendre-en-ligne.net/crypto/bibliotheque/feistel/index.html" target="_blank">https://www.apprendre-en-ligne.net/crypto/bibliotheque/feistel/index.html</a> <a href="#fnref:1" class="footnote-back-ref">↩</a></p></li>
<li id="fn:2"><p>Feistel, Horst (1973). "Cryptography and Computer Privacy". Scientific American. 228 (5): 15–23. Bibcode:1973SciAm.228e..15F. doi:10.1038/scientificamerican0573-15. <a href="https://www.apprendre-en-ligne.net/crypto/bibliotheque/feistel/index.html" target="_blank">https://www.apprendre-en-ligne.net/crypto/bibliotheque/feistel/index.html</a> <a href="#fnref:2" class="footnote-back-ref">↩</a></p></li>
<li id="fn:3"><p>Upadhyay, D., Gaikwad, N., Zaman, M., & Sampalli, S. (2022). Investigating the Avalanche Effect of Various Cryptographically Secure Hash Functions and Hash-Based Applications. IEEE Access, 10, 112472–112486. https://doi.org/10.1109/ACCESS.2022.3215778 <a href="https://doi.org/10.1109/ACCESS.2022.3215778" target="_blank">https://doi.org/10.1109/ACCESS.2022.3215778</a> <a href="#fnref:3" class="footnote-back-ref">↩</a></p></li>
<li id="fn:4"><p>Al-Kuwari, Saif; Davenport, James H.; Bradford, Russell J. (2011). Cryptographic Hash Functions: Recent Design Trends and Security Notions. Inscrypt '10. <a href="https://eprint.iacr.org/2011/565" target="_blank">https://eprint.iacr.org/2011/565</a> <a href="#fnref:4" class="footnote-back-ref">↩</a></p></li>
<li id="fn:5"><p>Webster, A. F.; Tavares, Stafford E. (1985). "On the design of S-boxes". Advances in Cryptology – Crypto '85. Lecture Notes in Computer Science. Vol. 218. New York, NY: Springer-Verlag New York, Inc. pp. 523–534. ISBN 0-387-16463-4. <a href="0-387-16463-4" target="_blank">0-387-16463-4</a> <a href="#fnref:5" class="footnote-back-ref">↩</a></p></li>
<li id="fn:6"><p>Adams, C. M.; Tavares, S. E. (January 1990). The Use of Bent Sequences to Achieve Higher-Order Strict Avalanche Criterion in S-box Design (Report). Technical Report TR 90-013. Queen's University. CiteSeerX 10.1.1.41.8374. <a href="/wiki/Carlisle_Adams" target="_blank">/wiki/Carlisle_Adams</a> <a href="#fnref:6" class="footnote-back-ref">↩</a></p></li>
<li id="fn:7"><p>William, Stallings (2016). Cryptography and network security : principles and practice (Seventh ed.). Boston. p. 136. ISBN 9780134444284. OCLC 933863805.{{cite book}}:  CS1 maint: location missing publisher (link) <a href="9780134444284" target="_blank">9780134444284</a> <a href="#fnref:7" class="footnote-back-ref">↩</a></p></li>
</ol>

Avalanche effect open-in-new

Avalanche effect