信息安全概论课件lecture.ppt

The Secure Hill Cipher The Scenario The Scenario The Scenario The Scenario The Scenario The Scenario Beforehand… Alice and Bob privately share matrix K, invertible over Zm To encrypt a matrix X over Zm… Compute Y = KX Send Y To decrypt Y… Compute X = K–1Y Why the Hill Cipher Isn’t Secure Why the Hill Cipher Isn’t Secure Why the Hill Cipher Isn’t Secure Why the Hill Cipher Isn’t Secure Why the Hill Cipher Isn’t Secure Why the Hill Cipher Isn’t Secure Why the Hill Cipher Isn’t Secure Why the Hill Cipher Isn’t Secure Why the Hill Cipher Isn’t Secure Beforehand… Alice and Bob privately share matrix K, invertible over Zm To encrypt a matrix X over Zm… Compute Y = KX Send Y To decrypt Y… Compute X = K–1Y Permutation Matrices Permutation Matrices Permutation Matrices Permutation Matrices Vector Representation Beforehand… Alice and Bob privately share matrix K, invertible over Zm To encrypt a matrix X over Zm… Compute Y = KX Send Y To decrypt Y… Compute X = K–1Y The Easy Way to Encrypt Require t to be the vector representation of a permutation matrix N.B.: This is for example only—it is not practical “in the field.” An Example An Example An Example An Example An Example An Example An Example The Scenario The Scenario The Scenario The Scenario An Example An Example An Example An Example An Example The Actual Really Secure Hill Cipher Jeff Overbey MA464-01 ? Dr. Jerzy Wojdy?o ? April 29, 2003 The Actual Really Secure Hill Cipher or How to Secure the Secure Hill Cipher Ensuring Security X should have two columns Why? Suppose K is n × n and X is n × s. If s ? n… If 2 s n… If s = 2… Pt should be different for each encryption Theoretically, this can be ensured by choosing a different t for each encryption We did this by requiring t to be a vector representation of a permutation matrix, but this is not the best solution. The ? Function Let ?n denote the set of n × n permutation matrices. ?: Zmn ? ?n The ? Function Let ?n denote the set of n × n permutation matrices. ?: Zmn