Improving the Security of United States Elections with Robust Optimization

For more than a century, election officials across the United States have inspected voting machines before elections using a procedure called Logic and Accuracy Testing (LAT). This procedure consists of election officials casting a test deck of ballots into each voting machine and confirming the machine produces the expected vote total for each candidate. We bring a scientific perspective to LAT by introducing the first formal approach to designing test decks with rigorous security guarantees. Specifically, our approach employs robust optimization to find test decks that are guaranteed to detect any voting machine misconfiguration that would cause votes to be swapped across candidates. Out of all the test decks with this security guarantee, our robust optimization problem yields the test deck with the minimum number of ballots, thereby minimizing implementation costs for election officials. To facilitate deployment at scale, we develop a practically efficient exact algorithm for solving our robust optimization problems based on the cutting plane method. In partnership with the Michigan Bureau of Elections, we retrospectively applied our approach to all 6928 ballot styles from Michigan's November 2022 general election; this retrospective study reveals that the test decks with rigorous security guarantees obtained by our approach require, on average, only 1.2% more ballots than current practice. Our approach has since been piloted in real-world elections by the Michigan Bureau of Elections as a low-cost way to improve election security and increase public trust in democratic institutions

Elliptic Curve Cryptography in Practice

In this paper, we perform a review of elliptic curve cryptography (ECC), as it is used in practice today, in order to reveal unique mistakes and vulnerabilities that arise in implementations of ECC. We study four popular protocols that make use of this type of public-key cryptography: Bitcoin, secure shell (SSH), transport layer security (TLS), and the Austrian e-ID card. We are pleased to observe that about 1 in 10 systems support ECC across the TLS and SSH protocols. However, we find that despite the high stakes of money, access and resources protected by ECC, implementations suffer from vulnerabilities similar to those that plague previous cryptographic systems

Measuring small subgroup attacks against Diffie-Hellman

Several recent standards, including NIST SP 800- 56A and RFC 5114, advocate the use of “DSA” parameters for Diffie-Hellman key exchange. While it is possible to use such parameters securely, additional validation checks are necessary to prevent well-known and potentially devastating attacks. In this paper, we observe that many Diffie-Hellman implementations do not properly validate key exchange inputs. Combined with other protocol properties and implementation choices, this can radically decrease security. We measure the prevalence of these parameter choices in the wild for HTTPS, POP3S, SMTP with STARTTLS, SSH, IKEv1, and IKEv2, finding millions of hosts using DSA and other non-“safe” primes for Diffie-Hellman key exchange, many of them in combination with potentially vulnerable behaviors. We examine over 20 open-source cryptographic libraries and applications and observe that until January 2016, not a single one validated subgroup orders by default. We found feasible full or partial key recovery vulnerabilities in OpenSSL, the Exim mail server, the Unbound DNS client, and Amazon’s load balancer, as well as susceptibility to weaker attacks in many other applications

Imperfect Forward Secrecy: How Diffie-Hellman Fails in Practice

International audienceWe investigate the security of Diffie-Hellman key exchange as used in popular Internet protocols and find it to be less secure than widely believed. First, we present Logjam, a novel flaw in TLS that lets a man-in-the-middle downgrade connections to " export-grade " Diffie-Hellman. To carry out this attack, we implement the number field sieve discrete log algorithm. After a week-long precomputation for a specified 512-bit group, we can compute arbitrary discrete logs in that group in about a minute. We find that 82% of vulnerable servers use a single 512-bit group, allowing us to compromise connections to 7% of Alexa Top Million HTTPS sites. In response, major browsers are being changed to reject short groups. We go on to consider Diffie-Hellman with 768-and 1024-bit groups. A small number of fixed or standardized groups are in use by millions of servers. Performing precomputations for just ten of these groups would allow a passive eavesdropper to decrypt traffic to up to 66% of IPsec VPN servers, 26% of SSH servers, 24% of popular HTTPS sites, or 16% of SMTP servers. In the 1024-bit case, we estimate that such computations are plausible given nation-state resources, and a close reading of published NSA leaks shows that the agency's attacks on VPNs are consistent with having achieved such a break. We conclude that moving to stronger key exchange methods should be a priority for the Internet community

Imperfect forward secrecy: How Diffie-Hellman fails in practice

International audienceWe investigate the security of Diffie-Hellman key exchange as used in popular Internet protocols and find it to be less secure than widely believed. First, we present Logjam, a novel flaw in TLS that lets a man-in-the-middle downgrade connections to "export-grade" Diffie-Hellman. To carry out this attack, we implement the number field sieve discrete logarithm algorithm. After a week-long precomputation for a specified 512-bit group, we can compute arbitrary discrete logarithms in that group in about a minute. We find that 82% of vulnerable servers use a single 512-bit group, and that 8.4% of Alexa Top Million HTTPS sites are vulnerable to the attack. a In response, major browsers have changed to reject short groups. We go on to consider Diffie-Hellman with 768-and 1024-bit groups. We estimate that even in the 1024-bit case, the computations are plausible given nation-state resources. A small number of fixed or standardized groups are used by millions of servers; performing precomputation for a single 1024-bit group would allow passive eavesdropping on 18% of popular HTTPS sites, and a second group would allow decryption of traffic to 66% of IPsec VPNs and 26% of SSH servers. A close reading of published NSA leaks shows that the agency's attacks on VPNs are consistent with having achieved such a break. We conclude that moving to stronger key exchange methods should be a priority for the Internet community

Harvesting verifiable challenges from oblivious online sources

Several important security protocols require parties to perform computations based on random challenges. Traditionally, proving that the challenges were randomly chosen has required interactive communication among the parties or the existence of a trusted server. We offer an alternative solution where challenges are harvested from oblivious servers on the Internet. This paper describes a framework for deriving “harvested challenges ” by mixing data from various pre-existing online sources. While individual sources may become predictable or fall under adversarial control, we provide a policy language that allows application developers to specify combinations of sources that meet their security needs. Participants can then convince each other that their challenges were formed freshly and in accordance with the policy. We present Combine, an open source implementation of our framework, and show how it can be applied to a variety of applications, including remote storage auditing and non-interactive client puzzles

A convenient method for securely managing passwords

Computer users are asked to generate, keep secret, and recall an increasing number of passwords for uses including host accounts, email servers, e-commerce sites, and online financial services. Unfortunately, the password entropy that users can comfortably memorize seems insufficient to store unique, secure passwords for all these accounts, and it is likely to remain constant as the number of passwords (and the adversary’s computational power) increases into the future. In this paper, we propose a technique that uses a strengthened cryptographic hash function to compute secure passwords for arbitrarily many accounts while requiring the user to memorize only a single short password. This mechanism functions entirely on the client; no server-side changes are needed. Unlike previous approaches, our design is both highly resistant to brute force attacks and nearly stateless, allowing users to retrieve their passwords from any location so long as they can execute our program and remember a short secret. This combination of security and convenience will, we believe, entice users to adopt our scheme. We discuss the construction of our algorithm in detail, compare its strengths and weaknesses to those of related approaches, and present Password Multiplier, an implementation in the form of an extension to the Mozilla Firefox web browser