Learn More
The difficulty of integer factorization is fundamental to modern cryptographic security using RSA encryption and signatures. Although a 512-bit RSA modulus was first factored in 1999, 512-bit RSA remains surprisingly common in practice across many cryptographic protocols. Popular understanding of the difficulty of 512-bit factorization does not seem to have(More)
In December 2015, Juniper Networks announced multiple security vulnerabilities stemming from unauthorized code in ScreenOS, the operating system for their NetScreen VPN routers. The more sophisticated of these vulnerabilities was a passive VPN decryption capability, enabled by a change to one of the elliptic curve points used by the Dual EC pseudorandom(More)
1. Introduction Little more than twenty years ago, when the number three and six retailers in the Los Angeles grocery market attempted to merge into the region's number two ranked competitor, the response from the Department of Justice and the Supreme Court was swift. 1 In interpreting the Clayton Act, the high court struck down the proposed merger, noting(More)
— 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(More)
In 2012, two academic groups reported having computed the RSA private keys for 0.5% of HTTPS hosts on the internet, and traced the underlying issue to widespread random number generation failures on networked devices. The vulnerability was reported to dozens of vendors, several of whom responded with security advisories, and the Linux kernel was patched to(More)
We perform a special number field sieve discrete logarithm computation in a 1024-bit prime field. To our knowledge, this is the first kilobit-sized discrete logarithm computation ever reported for prime fields. This computation took a little over two months of calendar time on an academic cluster using the open-source CADO-NFS software. Our chosen prime $p$(More)
  • 1