Security
A necessary condition for a three-pass algorithm to be secure is that an attacker cannot determine any information about the message m from the three transmitted messages E(s,m), E(r,E(s,m)) and E(r,m).
For the encryption functions used in the Shamir algorithm and the Massey-Omura algorithm described above, the security relies on the difficulty of computing discrete logarithms in a finite field. If an attacker could compute discrete logarithms in GF(p) for the Shamir method or GF(2n) for the Massey-Omura method then the protocol could be broken. The key s could be computed from the messages mr and mrs. When s is known, it is easy to compute the decryption exponent t. Then the attacker could compute m by raising the intercepted message ms to the t power. K. Sakurai and H. Shizuya show that under certain assumptions breaking Massey-Omura cryptosystem is equivalent to the Diffie-Hellman assumption.
Read more about this topic: Three-pass Protocol
Famous quotes containing the word security:
“Learned institutions ought to be favorite objects with every free people. They throw light over the public mind which is the best security against crafty and dangerous encroachments on the public liberty.”
—James Madison (17511836)
“The most disgusting cad in the world is the man who, on grounds of decorum and morality, avoids the game of love. He is one who puts his own ease and security above the most laudable of philanthropies.”
—H.L. (Henry Lewis)
“Those words freedom and opportunity do not mean a license to climb upwards by pushing other people down. Any paternalistic system that tries to provide for security for everyone from above only calls for an impossible task and a regimentation utterly uncongenial to the spirit of our people.”
—Franklin D. Roosevelt (18821945)