Socat: “the hard coded 1024 bit DH p parameter was not prime”

Keep up the tests until you have ten or twenty nines of certainty. I'd call that proof.

Previously:

    915       static unsigned char dh1024_p[] = {                                                           
    916      0xCC,0x17,0xF2,0xDC,0x96,0xDF,0x59,0xA4,0x46,0xC5,0x3E,0x0E,
    917      0xB8,0x26,0x55,0x0C,0xE3,0x88,0xC1,0xCE,0xA7,0xBC,0xB3,0xBF,
    918      0x16,0x94,0xD8,0xA9,0x45,0xA2,0xCE,0xA9,0x5B,0x22,0x25,0x5F,
    919      0x92,0x59,0x94,0x1C,0x22,0xBF,0xCB,0xC8,0xC8,0x57,0xCB,0xBF,
    920      0xBC,0x0E,0xE8,0x40,0xF9,0x87,0x03,0xBF,0x60,0x9B,0x08,0xC6,
    921      0x8E,0x99,0xC6,0x05,0xFC,0x00,0xD6,0x6D,0x90,0xA8,0xF5,0xF8,
    922      0xD3,0x8D,0x43,0xC8,0x8F,0x7A,0xBD,0xBB,0x28,0xAC,0x04,0x69,
    923      0x4A,0x0B,0x86,0x73,0x37,0xF0,0x6D,0x4F,0x04,0xF6,0xF5,0xAF,
    924      0xBF,0xAB,0x8E,0xCE,0x75,0x53,0x4D,0x7F,0x7D,0x17,0x78,0x0E,
    925      0x12,0x46,0x4A,0xAF,0x95,0x99,0xEF,0xBC,0xA6,0xC5,0x41,0x77, 
    926      0x43,0x7A,0xB9,0xEC,0x8E,0x07,0x3C,0x6D,
    927       };

  $ echo 'isprime(143319364394905942617148968085785991039146683740268996579566827015580969124702493833109074343879894586653465192222251909074832038151585448034731101690454685781999248641772509287801359980318348021809541131200479989220793925941518568143721972993251823166164933334796625008174851430377966394594186901123322297453)' | gp -q
  0

With fix

    xio-openssl.c
    915       static unsigned char dh2048_p[] = {
    916      0x00,0xdc,0x21,0x64,0x56,0xbd,0x9c,0xb2,0xac,0xbe,0xc9,0x98,0xef,0x95,0x3e,
    917      0x26,0xfa,0xb5,0x57,0xbc,0xd9,0xe6,0x75,0xc0,0x43,0xa2,0x1c,0x7a,0x85,0xdf,
    918      0x34,0xab,0x57,0xa8,0xf6,0xbc,0xf6,0x84,0x7d,0x05,0x69,0x04,0x83,0x4c,0xd5,
    919      0x56,0xd3,0x85,0x09,0x0a,0x08,0xff,0xb5,0x37,0xa1,0xa3,0x8a,0x37,0x04,0x46,
    920      0xd2,0x93,0x31,0x96,0xf4,0xe4,0x0d,0x9f,0xbd,0x3e,0x7f,0x9e,0x4d,0xaf,0x08,
    921      0xe2,0xe8,0x03,0x94,0x73,0xc4,0xdc,0x06,0x87,0xbb,0x6d,0xae,0x66,0x2d,0x18,
    922      0x1f,0xd8,0x47,0x06,0x5c,0xcf,0x8a,0xb5,0x00,0x51,0x57,0x9b,0xea,0x1e,0xd8,
    923      0xdb,0x8e,0x3c,0x1f,0xd3,0x2f,0xba,0x1f,0x5f,0x3d,0x15,0xc1,0x3b,0x2c,0x82,
    924      0x42,0xc8,0x8c,0x87,0x79,0x5b,0x38,0x86,0x3a,0xeb,0xfd,0x81,0xa9,0xba,0xf7,
    925      0x26,0x5b,0x93,0xc5,0x3e,0x03,0x30,0x4b,0x00,0x5c,0xb6,0x23,0x3e,0xea,0x94,
    926      0xc3,0xb4,0x71,0xc7,0x6e,0x64,0x3b,0xf8,0x92,0x65,0xad,0x60,0x6c,0xd4,0x7b,
    927      0xa9,0x67,0x26,0x04,0xa8,0x0a,0xb2,0x06,0xeb,0xe0,0x7d,0x90,0xdd,0xdd,0xf5,
    928      0xcf,0xb4,0x11,0x7c,0xab,0xc1,0xa3,0x84,0xbe,0x27,0x77,0xc7,0xde,0x20,0x57,
    929      0x66,0x47,0xa7,0x35,0xfe,0x0d,0x6a,0x1c,0x52,0xb8,0x58,0xbf,0x26,0x33,0x81,
    930      0x5e,0xb7,0xa9,0xc0,0xee,0x58,0x11,0x74,0x86,0x19,0x08,0x89,0x1c,0x37,0x0d,
    931      0x52,0x47,0x70,0x75,0x8b,0xa8,0x8b,0x30,0x11,0x71,0x36,0x62,0xf0,0x73,0x41,
    932      0xee,0x34,0x9d,0x0a,0x2b,0x67,0x4e,0x6a,0xa3,0xe2,0x99,0x92,0x1b,0xf5,0x32,
    933      0x73,0x63
    934       };

  $ echo 'isprime(27788893276069724796504555675597658900595616769773727063231875314156885361379100133264804184710789407128574011804155595735704837674243828066040543912171576627544718762752948158991754559261759162739343094515270757451837630913502740443023902769553802723685440839891240497710460941757089246131322686180648463540974702859210630184042730717698427486397505787974799692901205514386555272667298045803284972074823213104807295638814082142694729938965663710648170010420323923305528998108799706139846097432481556448740855888110797022123731105964852194684036975049177742094726795060211226322344210328442014189175085444396370522979)' | gp -q
  1

The original error could have been checked with a quick code review verifying that the provided number was in fact prime. This should have been done when the original patch was submitted.

But once you have the factorization for p, since it's hardcoded, it's now much easier to break every DH key exchange used by this application. Getting that factorization would be very very difficult, but once you have it you can use it on everyone.

I always wonder if when things like this get found, there's someone in the NSA going "Wow they finally found it, only took them x years"

I hate to say that a polynomial-time test isn't efficient because many people use that as the very definition of efficient, but my understanding is that AKS is incredibly impractical because the polynomial is ginormous, even though its asymptotic behavior is nice. So if you actually wanted to know if, say, a 1024-bit number was definitely prime, you wouldn't be able to run AKS on it in a "reasonable time" on a real computer.