Date of Submission

2-1-2009

Date of Award

2-1-2009

Institute Name (Publisher)

Indian Statistical Institute

Document Type

Doctoral Thesis

Degree Name

Doctor of Philosophy

Subject Name

Statistics

Department

Applied Statistics Unit (ASU-Kolkata)

Supervisor

Sarkar, Palash

Abstract (Summary of the Work)

This thesis presents a comprehensive study of collision attacks on the SHA-2 cryptographic hash family, focusing on both linearized and nonlinear differential techniques. We systematically analyze 9-round local collisions for the SHA-2 round function, identifying 16 new linearized local collisions with no conflicting conditions, improving upon the Gilbert-Handschuh local collision. Utilizing one of these, we develop an efficient algorithm to generate colliding message pairs for 18-round SHA-256, along with novel differential paths for 19–23 rounds using coding-theoretic methods.

Extending to nonlinear attacks, we provide a unified combinatorial framework for 9-round nonlinear local collisions, generalizing the Nikolić-Biryukov construction and introducing a new local collision (SS) with superior properties. This enables deterministic collisions up to 22 rounds and improved attacks up to 24 rounds for both SHA-256 and SHA-512, yielding the first explicit 24-round SHA-512 colliding pair. These results outperform prior work in complexity and simplicity.

Finally, we propose enhancements to the SHA-2 design, including affine transformations, mixed modular/XOR operations, multiple feed-forward within rounds, and cross-block feed-forward. The resulting SShash family maintains near-identical efficiency while resisting all known reduced-round attacks and generic multi-collision techniques. Our work advances the understanding of SHA-2 security and offers practical directions for strengthening hash function designs.

Comments

System generated Abstract

Control Number

TH679

DOI

https://dspace.isical.ac.in/jspui/handle/10263/7654

DSpace Identifier

http://hdl.handle.net/10263/7655

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