Question

There are four persons A, B, C, D in a room, and one of them is a foreign spy. Other three participants share a secret using the Shamir’s threshold scheme with secret in Zp, where p = 11. Any two of them can recover the secret. The foreign spy chooses his share randomly. As a result, these four participants have the following four shares:

A : (1, 7), B : (3, 0), C : (5, 10), D : (7, 9).

Find out who is the foreign spy and calculate the secret.

Answer 1

hiven: and D(,9) Sinte any o he two secvets s enough e hae by Sha miy's Hves hold we haue Secset cuvu s a straight livl Here thvu points ave inthe sety ft lin and o poin is out he lnu utas take A-C,-) and BF (3-0) to Jind he line mod l

Let chck does it sutiiJies poinf C and o Point n clso not satisfied. ae suey corvert because C ad ons one pint Ts EYO ine usina Now we con and n suhsti tute n and C einol }(1)-9 and (5): 10 2

. Point (3) satisties he line avn bu C andl and point A doesnt Satisty Me lne Phe h A is not din tre line A is he secret spy an seint lines/ ha)=(tsx) (rody) the (mod