Naresh Goud Boddu

Divesh Aggarwal, Naresh Goud Boddu, Rahul Jain

Non-malleable-codes introduced by Dziembowski, Pietrzak and Wichs [DPW18] encode a classical message $S$ in a manner such that tampering the codeword results in the decoder either outputting the original message $S$ or a message that is unrelated/independent of $S$. Providing such non-malleable security for various tampering function families has received significant attention in recent years. We consider the well-studied (2-part) split-state model, in which the message $S$ is encoded into two parts $X$ and $Y$, and the adversary is allowed to arbitrarily tamper with each $X$ and $Y$ individually. We consider the security of non-malleable-codes in the split-state model when the adversary is allowed to make use of arbitrary entanglement to tamper the parts $X$ and $Y$. We construct explicit quantum secure non-malleable-codes in the split-state model. Our construction of quantum secure non-malleable-codes is based on the recent construction of quantum secure $2$-source non-malleable-extractors by Boddu, Jain and Kapshikar [BJK21].

Naresh Goud Boddu, Rahul Jain, Upendra Kapshikar

We construct several explicit quantum secure non-malleable-extractors. All the quantum secure non-malleable-extractors we construct are based on the constructions by Chattopadhyay, Goyal and Li [2015] and Cohen [2015]. 1) We construct the first explicit quantum secure non-malleable-extractor for (source) min-entropy $k \geq \textsf{poly}\left(\log \left( \frac{n}ε \right)\right)$ ($n$ is the length of the source and $ε$ is the error parameter). Previously Aggarwal, Chung, Lin, and Vidick [2019] have shown that the inner-product based non-malleable-extractor proposed by Li [2012] is quantum secure, however it required linear (in $n$) min-entropy and seed length. Using the connection between non-malleable-extractors and privacy amplification (established first in the quantum setting by Cohen and Vidick [2017]), we get a $2$-round privacy amplification protocol that is secure against active quantum adversaries with communication $\textsf{poly}\left(\log \left( \frac{n}ε \right)\right)$, exponentially improving upon the linear communication required by the protocol due to [2019]. 2) We construct an explicit quantum secure $2$-source non-malleable-extractor for min-entropy $k \geq n- n^{Ω(1)}$, with an output of size $n^{Ω(1)}$ and error $2^{- n^{Ω(1)}}$. 3) We also study their natural extensions when the tampering of the inputs is performed $t$-times. We construct explicit quantum secure $t$-non-malleable-extractors for both seeded ($t=d^{Ω(1)}$) as well as $2$-source case ($t=n^{Ω(1)}$).

Divesh Aggarwal, Naresh Goud Boddu, Rahul Jain et al.

Multi-source-extractors are functions that extract uniform randomness from multiple (weak) sources of randomness. Quantum multi-source-extractors were considered by Kasher and Kempe (for the quantum-independent-adversary and the quantum-bounded-storage-adversary), Chung, Li and Wu (for the general-entangled-adversary) and Arnon-Friedman, Portmann and Scholz (for the quantum-Markov-adversary). One of the main objectives of this work is to unify all the existing quantum multi-source adversary models. We propose two new models of adversaries: 1) the quantum-measurement-adversary (qm-adv), which generates side-information using entanglement and on post-measurement and 2) the quantum-communication-adversary (qc-adv), which generates side-information using entanglement and communication between multiple sources. We show that, 1. qm-adv is the strongest adversary among all the known adversaries, in the sense that the side-information of all other adversaries can be generated by qm-adv. 2. The (generalized) inner-product function (in fact a general class of two-wise independent functions) continues to work as a good extractor against qm-adv with matching parameters as that of Chor and Goldreich. 3. A non-malleable-extractor proposed by Li (against classical-adversaries) continues to be secure against quantum side-information. This result implies a non-malleable-extractor result of Aggarwal, Chung, Lin and Vidick with uniform seed. We strengthen their result via a completely different proof to make the non-malleable-extractor of Li secure against quantum side-information even when the seed is not uniform. 4. A modification (working with weak sources instead of uniform sources) of the Dodis and Wichs protocol for privacy-amplification is secure against active quantum adversaries. This strengthens on a recent result due to Aggarwal, Chung, Lin and Vidick which uses uniform sources.

Naresh Goud Boddu, Upendra S. Kapshikar

Security of a storage device against a tampering adversary has been a well-studied topic in classical cryptography. Such models give black-box access to an adversary, and the aim is to protect the stored message or abort the protocol if there is any tampering. In this work, we extend the scope of the theory of tamper detection codes against an adversary with quantum capabilities. We consider encoding and decoding schemes that are used to encode a $k$-qubit quantum message $\vert m\rangle$ to obtain an $n$-qubit quantum codeword $\vert {ψ_m} \rangle$. A quantum codeword $\vert {ψ_m} \rangle$ can be adversarially tampered via a unitary $U$ from some known tampering unitary family $\mathcal{U}_{\mathsf{Adv}}$ (acting on $\mathbb{C}^{2^n}$). Firstly, we initiate the general study of \emph{quantum tamper detection codes}, which detect if there is any tampering caused by the action of a unitary operator. In case there was no tampering, we would like to output the original message. We show that quantum tamper detection codes exist for any family of unitary operators $\mathcal{U}_{\mathsf{Adv}}$, such that $\vert\mathcal{U}_{\mathsf{Adv}} \vert < 2^{2^{αn}}$ for some constant $α\in (0,1/6)$; provided that unitary operators are not too close to the identity operator. Quantum tamper detection codes that we construct can be considered to be quantum variants of \emph{classical tamper detection codes} studied by Jafargholi and Wichs~['15], which are also known to exist under similar restrictions. Additionally, we show that when the message set $\mathcal{M}$ is classical, such a construction can be realized as a \emph{non-malleable code} against any $\mathcal{U}_{\mathsf{Adv}}$ of size up to $2^{2^{αn}}$.