(Suggestion for the first time through: use P=257 and N=3)

Fix a modulus P = _________ and a base N = _________, which are known to everybody (typically, P is prime for this system and N is a "primitive root" meaning the powers of N are all different modulo P, until the (P-1) power of N is 1, by Fermat's little theorem).

Pick your secret exponent E = ________ (E and (P-1) should have no common factors, besides 1.).

Find all of the powers of N modulo P listed below, reducing modulo P after every step:

N (mod P) | = | ________ | N^{2} (mod P) | = | ________ | N^{4} (mod P) | = | ________ |

N^{8} (mod P) | = | ________ | N^{16} (mod P) | = | ________ | N^{32} (mod P) | = | ________ |

N^{64} (mod P) | = | ________ | N^{128} (mod P) | = | ________ |

Now, find the powers above that sum to E, and compute
J = N^{E} (mod P) by multiplying those powers of N together.
[For example, if E = 113, E = 64 + 32 + 16 + 1. Then,
J = N^{E} (mod P) = N^{64} * N^{32} * N^{16}
* N (mod P).]

J = _________

Trade your J with another group (call theirs K).

Now compute K^{E} (mod P) by the same repeated squaring method:

K (mod P) | = | ________ | K^{2} (mod P) | = | ________ | K^{4} (mod P) | = | ________ |

K^{8} (mod P) | = | ________ | K^{16} (mod P) | = | ________ | K^{32} (mod P) | = | ________ |

K^{64} (mod P) | = | ________ | K^{128} (mod P) | = | ________ |

K^{E} (mod P) is the secret number you have with the other group!