Jamming Resistant Encoding For Non-Uniformly Distributed Information Batya Karp Yerucham Berkowitz Advisor: Dr. Osnat Keren

Motivation & Goal Improve detection of jamming attacks in systems with non-uniformly distributed information Solutions implemented in encoding layer for efficiency: Faster Less hardware overhead (fewer redundancy bits)

Platform - Keyboard Perfect example of a system with non-uniformly distributed information Important note: The proposed solutions are applicable to any similar system

Basic Concepts Error Masking Probability: Robust Codes 𝑸 𝒆 = 𝒄 | 𝒄, 𝒄+𝒆 ∈𝑪 𝑪 𝑈𝑛𝑑𝑒𝑟 𝑈𝑛𝑖𝑓𝑜𝑟𝑚 𝐷𝑖𝑠𝑡𝑟𝑖𝑏𝑢𝑡𝑖𝑜𝑛 𝑸 𝒆 = 𝒄∈𝑪 𝒑 𝒄 𝑷𝒓 𝒄+𝒆∈𝑪 𝑈𝑛𝑑𝑒𝑟 𝑁𝑜𝑛−𝑈𝑛𝑖𝑓𝑜𝑟𝑚 𝐷𝑖𝑠𝑡𝑟𝑖𝑏𝑢𝑡𝑖𝑜𝑛 Robust Codes A code C is robust if and only if 𝑄 𝑤𝑐 = max 𝑒≠0 𝑄 𝑒 <1 Linear codes are not sufficient! Punctured Cubic Code (Neumeier and Keren) : 𝑃 is a binary 𝑟×𝑘 matrix of rank 1<𝑟≤𝑘. 𝑪= 𝒙,𝒘 :𝒙 ∈𝑮𝑭 𝟐 𝒌 , 𝒘= 𝑷 𝒙 𝟑 ∈𝑮𝑭 𝟐 𝒓 , 𝑄 𝑒 ≤ 2 −𝑟+1

Attacker Profiles M – set of information words C – set of code words Method of attack: Add an error 𝑒 ∗ that maximizes the probability of the attack going undetected, i.e. Choose 𝑒 ∗ 𝑠𝑢𝑐ℎ 𝑡ℎ𝑎𝑡 𝑄 𝑒 ∗ = 𝑄 𝑤𝑐

Existing Solutions Algebraic Manipulation Detection Codes Systematic AMD Code (Cramer et. Al. 2008): 𝐶= 𝑠,𝑥,𝑓 𝑥,𝑠 : 𝑠∈ 𝐹 𝑞 𝑑 , 𝑥∈ 𝐹 𝑞 ,𝑓 𝑥,𝑠 = 𝑥 𝑑+2 + 𝑖=1 𝑑 𝑠 𝑖 𝑥 𝑖 ∈ 𝐹 𝑞 is a systematic AMD code with 𝑄 𝑤𝑐 = 𝑑+1 𝑞 Security Oriented State Assignment (Shumsky, Keren 2013) 𝑪 – robust code, 𝑯 – Set of most probable information symbols Assign each symbol a vector such that 𝐻𝑊 𝑥 𝑖 ≤𝐻𝑊 𝑥 𝑗 if 𝑝 𝑠 𝑖 ≥𝑝 𝑠 𝑗

Level Out Encoding Let 𝜃: 𝐹 2 𝑘 →{𝑆}⊆ 𝐹 2 𝑘+ 𝑟 𝑙𝑜 be a mapping such that: 𝜃 𝑚 𝑖 ∝𝑝 𝑚 𝑖 Encode the information word 𝜃 𝑚 𝑖 using a robust code

Simulation Results

Analysis & Conclusions SOSA: “Free” but not a viable solution as the EMP remains quite high. AMD: Best option for non-uniformly distributed information. Main drawbacks are the strict constraints and relatively complex computation involved. Level-Out: Not as effective as AMD codes, but much easier to design, and can require less time and hardware to implement.