Tham khảo tài liệu 'current trends and challenges in rfid part 10', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 260 Current Trends and Challenges in RFID Definition 2. PRNG Goldreich 2001 . A PRNG is a function g 0 1 m 0 1 n that takes as input an m-bit hidden seed and returns an n-bit string where n m. The output of the PRNG is called a pseudo random number which appears to be random. A t 6g -secure PRNG represents that the output of this PRNG cannot be discriminated with a true random string in time t with advantage at most Eg. The PRNG can be implemented using stream ciphers such as those proposed in the STREAM project Cid Robshaw 2009 and a secure stream cipher is seen as a PRF Billet et al 2010 . Definition 3. Universal Hash Functions Wegman Carter 1981 . A family of functions hu 0 1 0 1 - uEU is called a strongly universal hash family if Vx E 0 1 Vy E 0 1 m Pr MO y 2 m 4 and Vx1 E 0 1 Vy1 y2 E 0 1 m Pr hu x2 y2 hjxj yx 2 2m 5 where any hash function is easily selected by UE u. An ỈX m -bit Toeplitz matrix is a matrix for which the entries on every upper-left to lower-left diagonal have the same value. Since the diagonal values of a Toeplitz matrix are fixed the entire matrix is specified by the top row and the first column. Thus a Toeplitz matrix can be stored in Í m 1 bits rather than the ÍX m bits required for a truly random matrix. For any l m 1 -bit vector u let Tu denote the Toeplitz matrix whose top row and first column are represented by u. Definition 4. Toeplitz based Universal Hash Function Krawczyk 1994 . Let Tu uEU be the family of Toeplitz matrices where the Ỉ m 1 -bit vector u is chosen at random and z is a random m-bit vector. Then the following is a strongly universal hash function family KƠ Tu -X z 0 1 0 1 - UEU. 6 Meanwhile according to the property in 5 the Toeplitz based universal hash function is also a pairwise independent hash function Naor Reingold 1997 . Definition 5. LPN based MAC Kiltz et al. 2011 . Let hu 0 1 0 1 be a pairwise independent hash function p be a pairwise independent permutation on 0 1 xn n w v Bernfl Sj ER 0 1 rER 0 1 w and Ter
