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:
“Of course we will continue to work for cheaper electricity in the homes and on the farms of America; for better and cheaper transportation; for low interest rates; for sounder home financing; for better banking; for the regulation of security issues; for reciprocal trade among nations and for the wiping out of slums. And my friends, for all of these we have only begun to fight.”
—Franklin D. Roosevelt (1882–1945)
“Is a Bill of Rights a security for [religious liberty]? If there were but one sect in America, a Bill of Rights would be a small protection for liberty.... Freedom derives from a multiplicity of sects, which pervade America, and which is the best and only security for religious liberty in any society. For where there is such a variety of sects, there cannot be a majority of any one sect to oppress and persecute the rest.”
—James Madison (1751–1836)
“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 (1751–1836)