Key Pair Agreement?

[Anton Stiglic]

>I can see how Alice
> can easily generate two primes whose product will have
> that *high* order part, but it seems hard to
> generate an RSA modulus with a specific *low* order
> 64 bits.

It is easy in both cases, here are examples I easily came up
with:

(low order DEADBEEF))
p = A093CD75C6B7A577B99897B323BE30936448D25E6F0E3ED3FC6FEA2BD8229B62994A\
4ECB72A6C54BBC4A5A7D38192D857602A016E7821D113F47200754547826C27B6993\
D43B8977BC20199C9C0EE2DA2BA63A55A73EE108787295AAE717E30D9AE257741899\
9D0C4B447BA62B2D95A9CC90E3939206A03FD21D5503DEADBEEF
q = BDDA82F4039620F351EBAEA1EC4AC4D3595DFBE44CB9554669419182720AE6E6113F\
4EF79CAB365072E37B06CBF33237E639B500F31BEBBF12E262D4ECA1D3F0FE823BC2\
D2C77EF793A0991290203240C8EC5DA9354726038CD2EC2F42B189E68C53E09FF24C\
28871F753AE721FB0726A6536AC38EEB645161596D1700000001
p*q 
77162EB107765764D2BE25B4A88CEB6954B18DBBFC72D868FC4EEBF000F01F1A9E06\
D72BFA3D95F6A629BFCE1F2CDF4809D987BF68196836469DC5FFDA88DA0900B8527D\
869DCC9B4C7603CB7B50B60B0C1915A0E90C73F0ED72B5585C7BCC6DE5DA71841BBA\
DE3AA25110E0FA0E35BAC7D8BEB6DC58CDDE212631B6438E424739870E96026BB526\
DD027D6FE9EB392C09EA5AA9757DFFAB1C4EEE5B2852B160972E8BF77BB281CCFA56\
F7DE0903D4C43FDB7B339067DB6361A75E57B93B59E70D8FF7E6DA9A5FE0D31A4FB6\
8E89859C4C99C85FBF5B83B2569D32ACEDF9EB0B0D34537340C87129B29E23D9A717\
053D33A537D82087EEC7BE1C3F7CDEADBEEF

(high order DEADBEEF)
p = DEADBEEFB782E95FCB1B04C7A90F501FEC0F6FE8B5EDC31A0996DBF9CC088C7C07AE\
E9039616955FCEF1920730EE82B21E93B0E86A0160D2B3E0BDEF8B5E29BEC1D5A4CE\
F5E5F247B9765E05FE3BC285C485367CCE797FD244AC4B6AD3FCE4AFDFC93E3782F5\
AC11D9B541BD881BA35BF46F7E5DF5F996B681CF3D564B29F117
q = 10000000023A78BC3DE4851ED3909CB37A402021766289052B9F7C9F00826E49117D\
C342EDAF5E4C6F7F76B54401C5F7AF599AA33EBBD76B07B50A89F38F8553CCEEF849\
B4B06A26F18095E82765930F119BFF11368A8D317B441C496E3B930356159AFD996A\
86506614ECE175D8C28CF646BB4761F3F4340D64787118C1BF79
p*q 
DEADBEEFD6866764D5F0CE07C3303C39FF638B810AA7BFFF0C19F1F284056DB2A831\
D1BC4733564A17F19EEA00A332BCD7CA5A250206243A7FFF0DA0AE9E3407E3DD7AAE\
7498860439CF8F59D14DA9D1AF1B1AC185AE55105A9FAA2FE5648B02F465BAEE244A\
656D8AA4D5D5013C6AD3A8E91721387ED2AE77B53BA027560CF1A70937F3A3245C0F\
59D7FE11D1FAD66BBC3AD3DC15B7F79C549E59C736E967724D2AAEA789552D28737E\
CEA5729860928BBA669BF249A9C266057DBCBC48A66C1B985AED8DF48B79F24A4740\
62EECA3D844BBE7027BD80B9805CDD74CA760BDD16140277EDF792488CEB2F5FCBF9\
EF8D38E9769CD129AB97D542C3DBC0A1CDF

--Anton


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