Secure Function Extensions to Additively Homomorphic Cryptosystems

The number-theoretic literature has long studied the question of distributions of sequences of quadratic residue symbols modulo a prime number. In this paper, we present an efficient algorithm for generating primes containing chosen sequences of quadratic residue symbols and use it as the basis of a method extending the functionality of additively homomorphic cryptosystems. We present an algorithm for encoding a chosen Boolean function into the public key and an efficient two-party protocol for evaluating this function on an encrypted sum. We demonstrate concrete parameters for secure function evaluation on encrypted sums up to eight bits at standard key sizes in the integer factorization setting. Although the approach is limited to applications involving small sums, it is a practical way to extend the functionality of existing secure protocols built on partially homomorphic encryption schemes

Threshold Properties of Prime Power Subgroups with Application to Secure Integer Comparisons

We present a semantically secure somewhat homomorphic public-key cryptosystem working in sub-groups of $\mathbb{Z}_{n}^{*}$ of prime power order. Our scheme introduces a novel threshold homomorphic property, which we use to build a two-party protocol for secure integer comparison. In contrast to related work which encrypts and acts on each bit of the input separately, our protocol compares multiple input bits simultaneously within a single ciphertext. Compared to the related protocol of Damgård et al.~we present results showing this approach to be both several times faster in computation and lower in communication complexity

Indiscreet Logs: Persistent Diffie-Hellman Backdoors in TLS

Software implementations of discrete logarithm based cryptosystems over finite fields typically make the assumption that any domain parameters they are presented with are trustworthy, i.e., the parameters implement cyclic groups where the discrete logarithm problem is assumed to be hard. An informal and widespread justification for this seemingly exists that says validating parameters at run time is too computationally expensive relative to the perceived risk of a server sabotaging the privacy of its own connection. In this paper we explore this trust assumption and examine situations where it may not always be justified. We conducted an investigation of discrete logarithm domain parameters in use across the Internet and discovered evidence of a multitude of potentially backdoored moduli of unknown order in TLS and STARTTLS spanning numerous countries, organizations, and protocols. Although our disclosures resulted in a number of organizations taking down suspicious parameters, we argue the potential for TLS backdoors is systematic and will persist until either until better parameter hygiene is taken up by the community, or finite field based cryptography is eliminated altogether

Eperio: Mitigating Technical Complexity in Cryptographic Election Verification

Cryptographic (or end-to-end) election verification is a promising approach to providing transparent elections in an age of electronic voting technology. In terms of execution time and software complexity however, the technical requirements for conducting a cryptographic election audit can be prohibitive. In an effort to reduce these requirements we present Eperio: a new, provably secure construction for providing a tally that can be efficiently verified using only a small set of primitives. We show how common-place utilities, like the use of file encryption, can further simplify the verification process for election auditors. Using Python, verification code can be expressed in 50 lines of code. Compared to other proposed proof-verification methods for end-to-end election audits, Eperio lowers the technical requirements in terms of execution time, data download times, and code size. As an interesting alternative, we explain how verification can be implemented using TrueCrypt and the built-in functions of a spreadsheet, making Eperio the first end-to-end system to not require special-purpose verification software

Scantegrity Responds to Rice Study on Usability of the Scantegrity II Voting System

This note is a response to, and critique of, recent work by Acemyan, Kortum, Bryne, and Wallach regarding the usability of end-to-end verifiable voting systems, and in particular, to their analysis of the usability of the Scantegrity II voting system. Their work is given in a JETS paper [Ace14] and was presented at EVT/WOTE 2014; it was also described in an associated press release [Rut14]. We find that their study lacked an appropriate control voting system with which to compare effectiveness, and thus their conclusions regarding Scantegrity II are unsupported by the evidence they present. Furthermore, their conclusions are contradicted by the successful deployment experiences of Scantegrity II at Takoma Park

Scantegrity II Municipal Election at Takoma Park: The First E2E Binding Governmental Election with Ballot Privacy

On November 3, 2009, voters in Takoma Park, Maryland, cast ballots for the mayor and city council members using the Scantegrity II voting system—the first time any end-to-end (E2E) voting system with ballot privacy has been used in a binding governmental election. This case study describes the various efforts that went into the election—including the improved design and implementation of the voting system, streamlined procedures, agreements with the city, and assessments of the experiences of voters and poll workers. The election, with 1728 voters from six wards, involved paper ballots with invisible-ink confirmation codes, instant-runoff voting with write-ins, early and absentee (mail-in) voting, dual-language ballots, provisional ballots, privacy sleeves, any-which-way scanning with parallel conventional desktop scanners, end-to-end verifiability based on optional web-based voter verification of votes cast, a full hand recount, thresholded authorities, three independent outside auditors, fully-disclosed software, and exit surveys for voters and pollworkers. Despite some glitches, the use of Scantegrity II was a success, demonstrating that E2E cryptographic voting systems can be effectively used and accepted by the general public.United States. Dept. of Defense (IASP grant H98230-08-1-0334)United States. Dept. of Defense (IASP grant H98230-09-1-0404)National Science Foundation (U.S.) (Grant no. CNS 0831149

A Protocol for the Secure Linking of Registries for HPV Surveillance

In order to monitor the effectiveness of HPV vaccination in Canada the linkage of multiple data registries may be required. These registries may not always be managed by the same organization and, furthermore, privacy legislation or practices may restrict any data linkages of records that can actually be done among registries. The objective of this study was to develop a secure protocol for linking data from different registries and to allow on-going monitoring of HPV vaccine effectiveness.A secure linking protocol, using commutative hash functions and secure multi-party computation techniques was developed. This protocol allows for the exact matching of records among registries and the computation of statistics on the linked data while meeting five practical requirements to ensure patient confidentiality and privacy. The statistics considered were: odds ratio and its confidence interval, chi-square test, and relative risk and its confidence interval. Additional statistics on contingency tables, such as other measures of association, can be added using the same principles presented. The computation time performance of this protocol was evaluated.The protocol has acceptable computation time and scales linearly with the size of the data set and the size of the contingency table. The worse case computation time for up to 100,000 patients returned by each query and a 16 cell contingency table is less than 4 hours for basic statistics, and the best case is under 3 hours.A computationally practical protocol for the secure linking of data from multiple registries has been demonstrated in the context of HPV vaccine initiative impact assessment. The basic protocol can be generalized to the surveillance of other conditions, diseases, or vaccination programs