-split-state tampering. Here, a codeword is split into two parts and the adversary can then independently tamper with each part using arbitrary functions. This model can be naturally extended to the secret sharing setting with several parties by having the adversary independently tamper with each share. Previous works on non-malleable coding and secret sharing in the split-state tampering model only considered the encoding of \emph{classical} messages. Furthermore, until recent work by Aggarwal, Boddu, and Jain (IEEE Trans.\ Inf.\ Theory 2024), adversaries with quantum capabilities and \emph{shared entanglement} had not been considered, and it is a priori not clear whether previous schemes remain secure in this model. In this work, we introduce the notions of split-state non-malleable codes and secret sharing schemes for quantum messages secure against quantum adversaries with shared entanglement. Then, we present explicit constructions of such schemes that achieve low-error non-malleability. More precisely, we construct efficiently encodable and decodable split-state non-malleable codes and secret sharing schemes for quantum messages preserving entanglement with external systems and achieving security against quantum adversaries having shared entanglement with codeword length

n

, any message length at most

n^{Ω(1)}

, and error

ε=2^{-{n^{Ω(1)}}}

. In the easier setting of \emph{average-case} non-malleability, we achieve efficient non-malleable coding with rate close to

1/11

DOI: 10.48550/arxiv.2308.06466

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Split-State Non-Malleable Codes and Secret Sharing Schemes for Quantum Messages

Naresh Goud Boddu, Vipul Goyal, Rahul Jain +1 more

Non-malleable codes are fundamental objects at the intersection of cryptography and coding theory. These codes provide security guarantees even in settings where error correction and detection are impossible, and have found applications to several other cryptographic tasks. One of the strongest and most well-studied adversarial tampering models is 2-split-state tampering. Here, a codeword is split into two parts which are stored in physically distant servers, and the adversary can then independently tamper with each part using arbitrary functions. This model can be naturally extended to the secret sharing setting with several parties by having the adversary independently tamper with each share. Previous works on non-malleable coding and secret sharing in the split-state tampering model only considered the encoding of classical messages. Furthermore, until recent work by Aggarwal, Boddu, and Jain (IEEE Trans. Inf. Theory 2024 & arXiv 2022), adversaries with quantum capabilities and shared entanglement had not been considered, and it is a priori not clear whether previous schemes remain secure in this model. In this work, we introduce the notions of split-state non-malleable codes and secret sharing schemes for quantum messages secure against quantum adversaries with shared entanglement. Then, we present explicit constructions of such schemes that achieve low-error non-malleability. More precisely, for some constant $c\gt 0$ , we construct efficiently encodable and decodable split-state non-malleable codes and secret sharing schemes for quantum messages preserving entanglement with external systems and achieving security against quantum adversaries having shared entanglement with codeword length n, any message length at most $n^{c}$ , and error $\varepsilon =2^{-{n^{c}}}$ . In the easier setting of average-case non-malleability, we achieve efficient non-malleable coding with rate close to $1/11$ .Non-malleable codes are fundamental objects at the intersection of cryptography and coding theory. These codes provide security guarantees even in settings where error correction and detection are impossible, and have found applications to several other cryptographic tasks. One of the strongest and most well-studied adversarial tampering models is 2-split-state tampering. Here, a codeword is split into two parts which are stored in physically distant servers, and the adversary can then independently tamper with each part using arbitrary functions. This model can be naturally extended to the secret sharing setting with several parties by having the adversary independently tamper with each share. Previous works on non-malleable coding and secret sharing in the split-state tampering model only considered the encoding of classical messages. Furthermore, until recent work by Aggarwal, Boddu, and Jain (IEEE Trans. Inf. Theory 2024 & arXiv 2022), adversaries with quantum capabilities and shared entanglement had not been considered, and it is a priori not clear whether previous schemes remain secure in this model. In this work, we introduce the notions of split-state non-malleable codes and secret sharing schemes for quantum messages secure against quantum adversaries with shared entanglement. Then, we present explicit constructions of such schemes that achieve low-error non-malleability. More precisely, for some constant$c\gt 0$, we construct efficiently encodable and decodable split-state non-malleable codes and secret sharing schemes for quantum messages preserving entanglement with external systems and achieving security against quantum adversaries having shared entanglement with codeword length n, any message length at most$n^{c}$, and error$\varepsilon =2^{-{n^{c}}}$. In the easier setting of average-case non-malleability, we achieve efficient non-malleable coding with rate close to$1/11$.

IEEE Transactions on Information TheoryJan 15, 20252 citations

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Naresh Goud Boddu

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quant-pharXiv:2609.39589Oct 1, 20260 citations

Quantum Secure Non-Malleable Codes in the Split-State Model

Divesh Aggarwal, Naresh Goud Boddu, Rahul Jain

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On Split-State Quantum Tamper Detection and Non-Malleability

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arXiv:2311.16009Nov 27, 20232 citations

Keyless secrecy against bounded adversaries

Anne Broadbent, Upendra Kapshikar, Denis Rochette

We introduce a keyless coding/cryptographic primitive that asks for two guarantees at once: the receiver is never fooled into accepting a message other than the one sent, and the adversary learns nothing about the message unless the receiver aborts. Neither the sender nor the receiver holds a secret key, and no computational hardness is assumed. The only restriction is on the adversary's online computation: the receiver aborts if nothing arrives by a fixed deadline, so the adversary must forward something before it, and her map in that window is computed by a circuit of size (or depth) at most $p$ ; before and after, she is unbounded. For every polynomial $p$ we construct such an efficient quantum scheme, encoding $k$ -bit messages into $n = O(k)$ qubits with circuits of size $\mathrm{poly}(n,p)$ . No classical scheme achieves this type of everlasting security, at any choice of parameters. Our techniques also resolve open questions about universal tamper detection against families restricted in cardinality rather than in circuit size. We settle a question of Broadbent, Kapshikar and Rochette on relaxed tamper detection. As a corollary, we obtain the first efficient non-malleable code secure against global quantum tampering, with no split-state restriction, whereas the current constructions in the literature require the codeword to be split into non-communicating shares.We introduce a keyless coding/cryptographic primitive that asks for two guarantees at once: the receiver is never fooled into accepting a message other than the one sent, and the adversary learns nothing about the message unless the receiver aborts. Neither the sender nor the receiver holds a secret key, and no computational hardness is assumed. The only restriction is on the adversary's online computation: the receiver aborts if nothing arrives by a fixed deadline, so the adversary must forward something before it, and her map in that window is computed by a circuit of size (or depth) at most $p$; before and after, she is unbounded. For every polynomial $p$ we construct such an efficient quantum scheme, encoding $k$-bit messages into $n = O(k)$ qubits with circuits of size $\mathrm{poly}(n,p)$. No classical scheme achieves this type of everlasting security, at any choice of parameters. Our techniques also resolve open questions about universal tamper detection against families restricted in cardinality rather than in circuit size. We settle a question of Broadbent, Kapshikar and Rochette on relaxed tamper detection. As a corollary, we obtain the first efficient non-malleable code secure against global quantum tampering, with no split-state restriction, whereas the current constructions in the literature require the codeword to be split into non-communicating shares.

quant-pharXiv:2609.12251Sep 14, 20260 citations

Explicit Non-Malleable Codes Resistant to Permutations.

Shashank Agrawal, Divya Gupta, Hemanta K. Maji +2 more

The notion of non-malleable codes was introduced as a relaxation of standard error-correction and error-detection. Informally, a code is non-malleable if the message contained in a modified codeword is either the original message, or a completely unrelated value. In the information theoretic setting, although existence of such codes for various rich classes of tampering functions is known, explicit constructions exist only for highly structured family of tampering functions. Prior explicit constructions of non-malleable codes rely on the “compartmentalized” structure of the tampering function, i.e. the codeword is partitioned into a priori fixed blocks and each block can only be tampered independently. The prominent examples of this model are the family of bit-wise independent tampering functions and the split-state model. We consider an infinitely large natural class of non-compartmentalized tampering functions. In our model, the tampering function can permute the bits of the encoding and (optionally) perturb them. In the information theoretic setting, we provide an explicit and efficient, rate-1 non-malleable code for multi-bit messages. Lack of explicit constructions of non-malleable codes for non-compartmentalized tampering functions severely inhibits their utility in cryptographic protocols. As a motivation for our construction, we show an application of non-malleable codes to cryptographic protocols. In an idealized setting, we show how string commitments can be based on one-bit commitments, if non-malleable codes exist. Further, as an example of a non-trivial use of non-malleable codes in standard cryptographic protocols (not in an idealized model), we show that if explicit nonmalleable codes are obtained for a slightly larger class of tampering functions than we currently handle, one can obtain a very simple non-malleable commitment scheme, under somewhat strong assumptions.The notion of non-malleable codes was introduced as a relaxation of standard error-correction and error-detection. Informally, a code is non-malleable if the message contained in a modified codeword is either the original message, or a completely unrelated value. In the information theoretic setting, although existence of such codes for various rich classes of tampering functions is known, explicit constructions exist only for highly structured family of tampering functions. Prior explicit constructions of non-malleable codes rely on the “compartmentalized” structure of the tampering function, i.e. the codeword is partitioned into a priori fixed blocks and each block can only be tampered independently. The prominent examples of this model are the family of bit-wise independent tampering functions and the split-state model. We consider an infinitely large natural class of non-compartmentalized tampering functions. In our model, the tampering function can permute the bits of the encoding and (optionally) perturb them. In the information theoretic setting, we provide an explicit and efficient, rate-1 non-malleable code for multi-bit messages. Lack of explicit constructions of non-malleable codes for non-compartmentalized tampering functions severely inhibits their utility in cryptographic protocols. As a motivation for our construction, we show an application of non-malleable codes to cryptographic protocols. In an idealized setting, we show how string commitments can be based on one-bit commitments, if non-malleable codes exist. Further, as an example of a non-trivial use of non-malleable codes in standard cryptographic protocols (not in an idealized model), we show that if explicit nonmalleable codes are obtained for a slightly larger class of tampering functions than we currently handle, one can obtain a very simple non-malleable commitment scheme, under somewhat strong assumptions.

Electronic colloquium on computational complexityJan 1, 201415 citations

2

n

, any message length at most

n^{Ω(1)}

, and error

ε=2^{-{n^{Ω(1)}}}

. In the easier setting of \emph{average-case} non-malleability, we achieve efficient non-malleable coding with rate close to

1/11

c\gt 0

, we construct efficiently encodable and decodable split-state non-malleable codes and secret sharing schemes for quantum messages preserving entanglement with external systems and achieving security against quantum adversaries having shared entanglement with codeword length n, any message length at most

n^{c}

, and error

\varepsilon =2^{-{n^{c}}}

. In the easier setting of average-case non-malleability, we achieve efficient non-malleable coding with rate close to

1/11

ξ>0

and all sufficiently large first-share lengths

n

, the codes have rate at least

1/5-ξ

, perfect correctness, and error

2^{-n^{Ω(1)}}

. Security holds for every message, with a single message-independent simulator for each attack. This resolves the constant-rate question for worst-case classical messages in the entangled two-split-state model. Our construction builds on the permutation-based two-split construction of Batra, Boddu, and Jain, which achieves rate approaching

1/5

for uniformly random messages. We retain their architecture but replace the uniform message input to the permutation with a prescribed message concatenated with fresh uniform padding. Our main contribution is a worst-case security reduction for this modification.

t

-split-state tampering model, where the codeword is divided into

t

shares, and each share is tampered with "locally". It is impossible to achieve tamper detection in the split-state model using classical codewords. Nevertheless, we demonstrate that the situation changes significantly if the message can be encoded into a multipartite quantum state, entangled across the

t

shares. Concretely, we define a family of quantum TDCs defined on any

t\geq 3

shares, which can detect arbitrary split-state tampering so long as the adversaries are unentangled, or even limited to a finite amount of pre-shared entanglement. Previously, this was only known in the limit of asymptotically large

t

. As our flagship application, we show how to augment threshold secret sharing schemes with similar tamper-detecting guarantees. We complement our results by establishing connections between quantum TDCs and quantum encryption schemes.

p

; before and after, she is unbounded. For every polynomial

p

we construct such an efficient quantum scheme, encoding

k

-bit messages into

n = O(k)

qubits with circuits of size

\mathrm{poly}(n,p)

. No classical scheme achieves this type of everlasting security, at any choice of parameters. Our techniques also resolve open questions about universal tamper detection against families restricted in cardinality rather than in circuit size. We settle a question of Broadbent, Kapshikar and Rochette on relaxed tamper detection. As a corollary, we obtain the first efficient non-malleable code secure against global quantum tampering, with no split-state restriction, whereas the current constructions in the literature require the codeword to be split into non-communicating shares.