Generating k-Independent Variables in Constant Time

Christiani, Tobias; Pagh, Rasmus

doi:10.1109/focs.2014.29

Cited by 11 publications

(20 citation statements)

References 33 publications

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“…The construction combines results of Christiani and Pagh [CP14] and Siegel [Sie04]. Note that the parameter regime we are interested in here differs from that in [CP14].…”

Section: A2 Proofs For Sectionmentioning

confidence: 99%

“…In order to be able to use this lemma iteratively, as we will do shortly, an explicit finite family {Γ i } i is required such that n i = m i+1 and e i = de i+1 for all indices i. Christiani and Pagh [CP14] These results give immediate rise to the t-wise independence generator, which will be used in Lemma 5 to construct the secret-sharing scheme we require to implement our Construction 2. Note that the generator we construct here is F-linear.…”

Section: A2 Proofs For Sectionmentioning

confidence: 99%

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Linear-Time Non-Malleable Codes in the Bit-Wise Independent Tampering Model

Cramer

Damgård

Döttling

et al. 2017

Lecture Notes in Computer Science

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Abstract. Non-malleable codes were introduced by Dziembowski et al. (ICS 2010) as coding schemes that protect a message against tampering attacks. Roughly speaking, a code is non-malleable if decoding an adversarially tampered encoding of a message m produces the original message m or a value m (eventually ⊥) completely unrelated with m. It is known that non-malleability is possible only for restricted classes of tampering functions. Since their introduction, a long line of works has established feasibility results of non-malleable codes against different families of tampering functions. However, for many interesting families the challenge of finding "good" non-malleable codes remains open. In particular, we would like to have explicit constructions of non-malleable codes with high-rate and efficient encoding/decoding algorithms (i.e. low computational complexity). In this work we present two explicit constructions: the first one is a natural generalization of the work of Dziembowski et al. and gives rise to the first constant-rate non-malleable code with linear-time complexity (in a model including bit-wise independent tampering). The second construction is inspired by the recent works about non-malleable codes of Agrawal et al. (TCC 2015) and of Cheraghchi and Guruswami (TCC 2014) and improves the previous result in the bit-wise tampering model: it builds the first non-malleable codes with linear-time complexity and optimal-rate (i.e. rate 1 − o(1)).

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“…The construction combines results of Christiani and Pagh [CP14] and Siegel [Sie04]. Note that the parameter regime we are interested in here differs from that in [CP14].…”

Section: A2 Proofs For Sectionmentioning

confidence: 99%

Section: A2 Proofs For Sectionmentioning

confidence: 99%

Linear-Time Non-Malleable Codes in the Bit-Wise Independent Tampering Model

Cramer

Damgård

Döttling

et al. 2017

Lecture Notes in Computer Science

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“…i.e., the random selection of a memory segment 12 . If the random sequential evaluation protocol terminates incorrectly or the termination is untimely, or both, the verifier rejects.…”

Section: Handling Clock Jitter and Inter-processor Interferencementioning

confidence: 99%

Establishing Software Root of Trust Unconditionally

Gligor

Woo

2019

Proceedings 2019 Network and Distributed System Security Symposium

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Root-of-Trust (RoT) establishment ensures either that the state of an untrusted system contains all and only content chosen by a trusted local verifier and the system code begins execution in that state, or that the verifier discovers the existence of unaccounted for content. This ensures program booting into system states that are free of persistent malware. An adversary can no longer retain undetected control of one's local system. We establish RoT unconditionally; i.e., without secrets, trusted hardware modules and instructions, or bounds on the adversary's computational power. The specification of a system's chipset and device controllers, and an external source of true random numbers, such as a commercially available quantum RNG, is all that is needed. Our system specifications are those of a concrete Word Random Access Machine (cWRAM) model-the closest computation model to a real system with a large instruction set. We define the requirements for RoT establishment and explain their differences from past attestation protocols. Then we introduce a RoT establishment protocol based on a new computation primitive with concrete (non-asymptotic) optimal space-time bounds in adversarial evaluation on the cWRAM. The new primitive is a randomized polynomial, which has kindependent uniform coefficients in a prime order field. Its collision properties are stronger than those of a k-independent (almost) universal hash function in cWRAM evaluations, and are sufficient to prove existence of malware-free states before RoT is established. Preliminary measurements show that randomizedpolynomial performance is practical on commodity hardware even for very large k. To prove the concrete optimality of randomized polynomials, we present a result of independent complexity interest: a Hornerrule program is uniquely optimal whenever the cWRAM execution space and time are simultaneously minimized.

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“…Theorem 1 studies the number of balls landing a bin b which may be a function of the bin h ′ (q) of a query ball q ∈ [u] \ S. Thanks to the last statement of Theorem 5, we can condition on any value a of h(q), which determines h ′ (q) and hence b. Now, for x ∈ S, define Theorem 1,and (5) and (6) follow from (10) and (11), but with the improved error u −γ . This is important when m is small, e.g., if m = 2 corresponding to unbiased coin tosses.…”

Section: Theorem 5 ([42]) Choose a Random C-character Twisted Tabulatmentioning

confidence: 99%