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**2017/950**

**Title:**

Blockwise p-Tampering Attacks on Cryptographic Primitives, Extractors, and Learners

**Authors:**
Saeed Mahloujifar, Mohammad Mahmoody

**Abstract:**

Austrin, Chung, Mahmoody, Pass and Seth (Crypto’14) studied the notion of bitwise p-tampering attacks over randomized algorithms in which an efficient `virus' gets to control each bit of the randomness with independent probability $p$ in an online way. The work of Austrin et al. showed how to break certain `

privacy primitives’ (e.g., encryption, commitments, etc.) through bitwise p-tampering, by giving a bitwise p-tampering biasing attack for increasing the average E[f(U_n)] of any efficient function f \colon \{0,1\}^n \to [-1,+1] by \Omega(p \cdot Var[f(U_n)]) where Var[f(U_n)] is the variance of f(U_n). In this work, we revisit and extend the bitwise tampering model of Austrin et al. to blockwise setting, where blocks of randomness becomes tamperable with independent probability p. Our main result is an efficient blockwise p-tampering attack to bias the average E[f(X)] of any efficient function f mapping arbitrary X to [-1,+1] by \Omega(p \cdot Var[f(X)]) regardless of how X is partitioned into individually tamperable blocks X=(X_1,\dots,X_n). Relying on previous works, our main biasing attack immediately implies efficient attacks against the privacy primitives as well as seedless multi-source extractors, in a model where the attacker gets to tamper with each block (or source) of the randomness with independent probability p. Further, we show how to increase the classification error of deterministic learners in the so called `targeted poisoning' attack model under Valiant's adversarial noise. In this model, an attacker has a `

target’ test data d in mind and wishes to increase the error of classifying d while she gets to tamper with each training example with independent probability p an in an online way.

**ePrint:**
https://eprint.iacr.org/2017/950

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