Symmetric cryptography considers algorithms and schemes that provide confidentiality and/or authenticity to data, protected by a single secret key. It includes block ciphers, stream ciphers, Message Authentication Code (MAC) algorithms, and Authenticated Encryption schemes. These are some of the most widely-used building blocks in cryptography, and as such must be rigorously studied to determine whether they provide the required level of security.

In general, the most efficient known class of attacks against symmetric ciphers are statistical attacks, such as linear or differential cryptanalysis against block ciphers. In this area, researchers in the ISG have pioneered some of the fundamental techniques and continue to clarify and refine the statistics underlying these attacks and their variants.

Another class of attacks against symmetric key constructions are algebraic attacks. These attacks model the algorithm as a system of equations which is then tackled using standard algebraic techniques, e.g. Gröbner basis algorithms. Here too, researchers in the ISG made fundamental and foundational contributions to applications of algebraic techniques to symmetric key cryptanalysis. 

Recent years have witnessed a spur of activity in the study of ciphers designed for algebraic platforms. That is, instead of designing block ciphers for CPUs or hardware, they are designed to be efficiently run as part of a secure computation protocol (e.g. MPC or FHE based) or in a zero-knowledge proof (ZKPoK). Used in this way these block ciphers enable many modern privacy-preserving protocols. The novel design strategies employed in these ciphers make them however interesting targets for algebraic attacks. This is an area of research pioneered by researchers in the ISG, with several contributions in new designs, and in the cryptanalysis of new proposals.

• Martin Albrecht
• Carlos Cid
• Chris Mitchell
• Sean Murphy

• Martin R. Albrecht, Carlos Cid, Lorenzo Grassi, Dmitry Khovratovich, Reinhard Lüftenegger, Christian Rechberger, Markus Schofnegger: Algebraic Cryptanalysis of STARK-Friendly Designs: Application to MARVELlous and MiMC. ASIACRYPT (3) 2019: 371-397 https://ia.cr/2019/419
• Carlos Cid, Tao Huang, Thomas Peyrin, Yu Sasaki, Ling Song: Boomerang Connectivity Table: A New Cryptanalysis Tool. EUROCRYPT (2) 2018: 683-714 https://ia.cr/2018/161
• Carlos Cid, Tao Huang, Thomas Peyrin, Yu Sasaki, Ling Song: A Security Analysis of Deoxys and its Internal Tweakable Block Ciphers. IACR Trans. Symmetric Cryptol. 2017(3): 73-107 (2017) https://ia.cr/2017/693
• Martin R. Albrecht, Lorenzo Grassi, Christian Rechberger, Arnab Roy, Tyge Tiessen: MiMC: Efficient Encryption and Cryptographic Hashing with Minimal Multiplicative Complexity. ASIACRYPT (1) 2016: 191-219 https://ia.cr/2016/492
• Chris J. Mitchell: On the Security of 2-Key Triple DES. IEEE Trans. Inf. Theory 62(11): 6260-6267 (2016) https://arxiv.org/abs/1602.06229
• Gordon Procter, Carlos Cid: On Weak Keys and Forgery Attacks Against Polynomial-Based MAC Schemes. Journal of Cryptology 28(4): 769-795 (2015) https://doi.org/10.1007/s00145-014-9178-9 
• Martin R. Albrecht, Christian Rechberger, Thomas Schneider, Tyge Tiessen, Michael Zohner: Ciphers for MPC and FHE. EUROCRYPT (1) 2015: 430-454 https://ia.cr/2016/687
• Martin R. Albrecht, Benedikt Driessen, Elif Bilge Kavun, Gregor Leander, Christof Paar, Tolga Yalçin: Block Ciphers - Focus on the Linear Layer (feat. PRIDE). CRYPTO (1) 2014: 57-76
• Sean Murphy: The Return of the Cryptographic Boomerang. IEEE Trans. Inf. Theory 57(4): 2517-2521 (2011) https://www.isg.rhul.ac.uk/~sean/CLN9-909_IEEE_Final0.pdf
• Carlos Cid, Sean Murphy, Matthew J. B. Robshaw: Algebraic aspects of the advanced encryption standard. Springer 2006, ISBN 978-0-387-24363-4, pp. I-VI, 1-145
• Xuejia Lai, James L. Massey, Sean Murphy: Markov Ciphers and Differential Cryptanalysis. EUROCRYPT 1991: 17-38 https://link.springer.com/chapter/10.1007/3-540-46416-6_2
• Sean Murphy: The Cryptanalysis of FEAL-4 with 20 Chosen Plaintexts. J. Cryptol. 2(3): 145-154 (1990) https://www.isg.rhul.ac.uk/~sean/feal.pdf