HTTPS aims at securing communication over the Web by providing a cryptographic protection layer that ensures the confidentiality and integrity of communication and enables client/server authentication. However, HTTPS is based on the SSL/TLS protocol suites that have been shown to be vulnerable to various attacks in the years. This has required fixes and mitigations both in the servers and in the browsers, producing a complicated mixture of protocol versions and implementations in the wild, which makes it unclear which attacks are still effective on the modern Web and what is their import on web application security. In this paper, we present the first systematic quantitative evaluation of web application insecurity due to cryptographic vulnerabilities. We specify attack conditions against TLS using attack trees and we crawl the Alexa Top 10k to assess the import of these issues on page integrity, authentication credentials and web tracking. Our results show that the security of a consistent number of websites is severely harmed by cryptographic weaknesses that, in many cases, are due to external or related-domain hosts. This empirically, yet systematically demonstrates how a relatively limited number of exploitable HTTPS vulnerabilities are amplified by the complexity of the web ecosystem.

We measure the popularity of cryptographic libraries in large datasets of RSA public keys. We do so by improving a recently proposed method based on biases introduced by alternative implementations of prime selection in different cryptographic libraries. We extend the previous work by applying statistical inference to approximate a share of libraries matching an observed distribution of RSA keys in an inspected dataset (e.g., Internet-wide scan of TLS handshakes). The sensitivity of our method is sufficient to detect transient events such as a periodic insertion of keys from a specific library into Certificate Transparency logs and inconsistencies in archived datasets.

We report on our discovery of an algorithmic flaw in the construction of primes for RSA key generation in a widely-used library of a major manufacturer of cryptographic hardware. The primes generated by the library suffer from a significant loss of entropy. We propose a practical factorization method for various key lengths including 1024 and 2048 bits. Our method requires no additional information except for the value of the public modulus and does not depend on a weak or a faulty random number generator. We devised an extension of Coppersmith's factorization attack utilizing an alternative form of the primes in question. The library in question is found in NIST FIPS 140-2 and CC~EAL~5+ certified devices used for a wide range of real-world applications, including identity cards, passports, Trusted Platform Modules, PGP and tokens for authentication or software signing. As the relevant library code was introduced in 2012 at the latest (and probably earlier), the impacted devices are now widespread. Tens of thousands of such keys were directly identified, many with significant impacts, especially for electronic identity documents, software signing, Trusted Computing and PGP. We estimate the number of affected devices to be in the order of at least tens of millions.