A family of perpendicular arrays achieving perfect 4-fold secrecy

A family of perpendicular arrays achieving perfect 4-fold secrecy

A perpendicular array PA,(t, k, u) is a n(y) by k array A of u distinct symbols, which satisfies: (i) every row of A contains k distinct symbols, (ii) for any t columns, and for any t distinct symbols, there are precisely 2 rows with the given symbols in the given columns. Such a structure may also be described as a A-uniform, t-homogeneous set of injective mappings from a k-set into a u-set. A...

Constructing Optimal Authentication Codes with Perfect Multi-fold Secrecy

We establish a construction of optimal authentication codes achieving perfect multi-fold secrecy by means of combinatorial designs. This continues the author’s work (ISIT 2009, cf. [1]) and answers an open question posed therein. As an application, we present the first infinite class of optimal codes that provide two-fold security against spoofing attacks and at the same time perfect two-fold s...

Perfect Secrecy and Statistical

There are two key properties of the above. First, given only c, Eve should not be able to learn what m is. Second, Dec(Enc(m)) = m, so that Bob can accurately determine the message that Alice wanted to send. Creating functions Enc and Dec which satisfy this is a fundamental problem of cryptography. But given the above encryption scheme, knowing what these functions are is enough for anyone to d...

Theory of Perpendicular Arrays

A large-deviations notion of perfect secrecy

We consider the Shannon cipher system with a variable key rate, and study the necessary and sufficient conditions for perfect secrecy in the sense that the exponential rate of the probability of breaking into the system would not be improved by observing the cryptogram. For a memoryless plaintext source, we derive achievable lower bounds on the number of key bits needed for almost every plainte...