Moderately Hard Functions: From Complexity to Spam Fighting

Naor, Moni

doi:10.1007/978-3-540-24597-1_37

Cited by 6 publications

(4 citation statements)

References 41 publications

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“…Similar to time-lock puzzles, VDFs are about ensuring a given bound on the computation delay is satisfied (and that parallelism is not effective in attacking the scheme) rather than the amount of computation. On the other hand, the notion of pricing functions [24,41], where the proof-of-work mining is an example of such functions, are similar in spirit to our work. The goal is to utilize moderately hard functions to put a price on some actions (e.g., sending spam emails) in terms of amount of computation.…”

Section: Related Workmentioning

confidence: 80%

Gage MPC: Bypassing Residual Function Leakage for Non-Interactive MPC

Almashaqbeh¹,

Benhamouda²,

Han

et al. 2021

Proceedings on Privacy Enhancing Technologies

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Existing models for non-interactive MPC cannot provide full privacy for inputs, because they inherently leak the residual function (i.e., the output of the function on the honest parties’ input together with all possible values of the adversarial inputs). For example, in any non-interactive sealed-bid auction, the last bidder can figure out what was the highest previous bid. We present a new MPC model which avoids this privacy leak. To achieve this, we utilize a blockchain in a novel way, incorporating smart contracts and arbitrary parties that can be incentivized to perform computation (“bounty hunters,” akin to miners). Security is maintained under a monetary assumption about the parties: an honest party can temporarily supply a recoverable collateral of value higher than the computational cost an adversary can expend. We thus construct non-interactive MPC protocols with strong security guarantees (full security, no residual leakage) in the short term. Over time, as the adversary can invest more and more computational resources, the security guarantee decays. Thus, our model, which we call Gage MPC, is suitable for secure computation with limited-time secrecy, such as auctions. A key ingredient in our protocols is a primitive we call “Gage Time Capsules” (GaTC): a time capsule that allows a party to commit to a value that others are able to reveal but only at a designated computational cost. A GaTC allows a party to commit to a value together with a monetary collateral. If the original party properly opens the GaTC, it can recover the collateral. Otherwise, the collateral is used to incentivize bounty hunters to open the GaTC. This primitive is used to ensure completion of Gage MPC protocols on the desired inputs. As a requisite tool (of independent interest), we present a generalization of garbled circuit that are more robust: they can tolerate exposure of extra input labels. This is in contrast to Yao’s garbled circuits, whose secrecy breaks down if even a single extra label is exposed. Finally, we present a proof-of-concept implementation of a special case of our construction, yielding an auction functionality over an Ethereum-like blockchain.

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Section: Related Workmentioning

confidence: 80%

Gage MPC: Bypassing Residual Function Leakage for Non-Interactive MPC

Almashaqbeh¹,

Benhamouda²,

Han

et al. 2021

Proceedings on Privacy Enhancing Technologies

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“…As pointed out by Naor [8], there is no rigorous treatment of moderately hard functions and only a small number of candidates have been proposed. In this paper, we try to address these issues.…”

Section: Our Contributionmentioning

confidence: 99%

“…This phenomenon is dubbed as "memory wall" [13]. It motivates cryptographers to design memory-bounded functions, which have found applications in complexity theory and computer security [8].…”

Section: Introductionmentioning

confidence: 99%

A Number Theoretic Memory Bounded Function and Its Applications

Cheng

2008

2008 the 9th International Conference for Young Computer Scientists

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Memory bounded functions have been designed to combat email spams in a sequence of papers [1,2,4]. The cost of computing the functions is usually dominated by random walks over large tables that cannot be put in CPU cache. In this paper, we propose a simple number theoretic way of generating such tables based on exponentiations of sparse polynomials modulo sparse irreducible polynomials over finite fields. We also present a formal definition of memory bounded functions that can be used to construct such tables.

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“…Timed commitments are one example of moderately hard functions [Nao03], which have recently been used for other kinds of secure multiparty computation. Pinkas [Pin03] uses timed commitments for twoparty computation, and Garay, MacKenzie and Yang [GMY04] use a different moderately hard function for general multiparty computation.…”

Section: Introductionmentioning

confidence: 99%

Secure random number agreement for peer-to-peer applications

Corman

Schachte

Teague

2007

2007 International Conference on Parallel and Distributed Systems

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We propose a protocol for a group of peers in a peerto-peer network to securely generate an agreed random value without the use of a central authority. We can vary the security parameters to maintain security (to a desired probability) in the presence of a high percentage of corrupt and colluding peers. We envision using this protocol to generate random content in a peer-to-peer game. It could also be used for generating input into peer-to-peer protocols that require random values, such as group selection.

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Moderately Hard Functions: From Complexity to Spam Fighting

Cited by 6 publications

References 41 publications

Gage MPC: Bypassing Residual Function Leakage for Non-Interactive MPC

Gage MPC: Bypassing Residual Function Leakage for Non-Interactive MPC

A Number Theoretic Memory Bounded Function and Its Applications

Secure random number agreement for peer-to-peer applications

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