I have been playing with an embedded system designed in 2008 that can communicate with a PC via a serial bus. The commands that the PC sends the embedded system are not very complex. However before the embedded system will accept any commands, the PC must get past a security problem. The embedded system generates a pseudo-random 32-bit seed and based on that seed the PC calculates a 64-bit key presumably based on a private key or algorithm known by both the PC and the embedded system. I assume that the serial line in encrypted so that you need to buy the PC software. I have bought the PC software (expensive) and this can get past the security by generating the correct key based on the seed given by the embedded system. I have attached 10 examples but I can supply more if required. My problem is that the PC software has some bugs/limitations that I would like to overcome and getting the manufacturer to make changes for me is a dead end. My goal is to be able to generate the correct key given any seed. Based on my research so far this seems well beyond my current abilities, but if anyone can solve this puzzle or at least point me off in the right direction to make some progress myself then it would be most appreciated.I have included 10 examples of seed/key pairs below.Seed1 0x0A,0x1D,0x15,0xC4  Key1  0x96,0x32,0x58,0x72,0xF2,0x66,0x90,0x3DSeed2 0x15,0x76,0xD6,0xEC  Key2  0x86,0xC5,0x62,0x58,0xFD,0x7D,0x06,0x28Seed3 0x1A,0xDA,0xB6,0x49  Key3  0x5D,0x72,0xF4,0x6E,0x9F,0x57,0xEC,0x3ESeed4 0x1F,0x66,0x3F,0x32  Key4  0x0D,0x8F,0x58,0x14,0x12,0x6D,0x01,0x6CSeed5 0x21,0xAA,0xC4,0xA9  Key5  0x06,0x45,0x26,0x16,0x9B,0xC6,0x05,0xC6Seed6 0x37,0xB1,0x4E,0x9E  Key6  0x72,0x66,0x98,0x03,0xFD,0x56,0x64,0xDESeed7 0x2C,0xC7,0xA7,0x8D  Key7  0x86,0xAD,0x8C,0xC4,0xAB,0x1E,0x5C,0xD9Seed8 0x7F,0x80,0x64,0x2D  Key8  0x7D,0xF2,0x22,0x26,0xCD,0x86,0x61,0xB6Seed9 0x35,0xEE,0x6C,0x22  Key9  0x06,0x7B,0x40,0xDE,0x2E,0x57,0x79,0x8ESeed10 0x38,0xDB,0xF2,0x47   Key10  0x46,0xED,0xAC,0x91,0x17,0x1E,0x39,0x2A
Can this cryptography problem be solved given just correct seed/key pairs?
cryptography;binary diagnosis