Diffie-Helman key exchange example:

p=123456789011 (a prime) g= 2 (a primitive root modulo p) A sends to B 98669960721 (modulo p) B sends to A 66675120784 (modulo p) Find the key that A and B have exchanged.

El Gamal cipher example:

p=123456789011 (a prime) b=2 (a primitive root modulo p) c=32890691253 ( b raised to the power l) Suppose that A makes public the data above (but not l) and B encrypts a plaintext X by choosing a secret r and sending A the header b^r=60577479993 (modulo p) the ciphertext Xc^r=59778139972 (modulo p) Find the value of X.

RSA public key example:

A publishes the following information modulus m=15241578759079409808671 encryption key: e=3429235932423923 Using this data and the RSA public key cipher B sends to A ciphertext 11482879856055838066711 Find the message that B encrypted and sent to A.