Given n relatively prime integers p1 < · · · < pn and an integer k < n, the Chinese Remainder Code, CRTp1,...,pn;k, has as its message space M = {0, . . . , ∏k i=1 pi − 1}, and encodes a message m ∈ M as the vector 〈m1, . . . ,mn〉, where mi = m(mod pi). The soft-decision decoding problem for the Chinese remainder code is given as input a vector of residues ~r = 〈r1, . . . , rn〉, a vector of wei...

A group key distribution protocol can enable members of a group to share a secret group key and use it for secret communications. In 2010, Harn and Lin proposed an authenticated group key distribution protocol using polynomial-based secret sharing scheme. Recently, Guo and Chang proposed a similar protocol based on the generalized Chinese remainder theorem. In this paper, we point out that ther...

9 Introduction to Number Theory 63 9.1 Subgroups of the Integers . . . . . . . . . . . . . . . . . . . . 63 9.2 Greatest Common Divisors . . . . . . . . . . . . . . . . . . . . 63 9.3 The Euclidean Algorithm . . . . . . . . . . . . . . . . . . . . . 64 9.4 Prime Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . 67 9.5 The Fundamental Theorem of Arithmetic . . . . . . . . . . . . 68 9....

5 Introduction to Number Theory and Cryptography 72 5.1 Subgroups of the Integers . . . . . . . . . . . . . . . . . . . . 72 5.2 Greatest Common Divisors . . . . . . . . . . . . . . . . . . . . 72 5.3 The Euclidean Algorithm . . . . . . . . . . . . . . . . . . . . . 73 5.4 Prime Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . 76 5.5 The Fundamental Theorem of Arithmetic . . . . . . ...

9 Introduction to Number Theory 168 9.1 Subgroups of the Integers . . . . . . . . . . . . . . . . . . . . 168 9.2 Greatest Common Divisors . . . . . . . . . . . . . . . . . . . . 168 9.3 The Euclidean Algorithm . . . . . . . . . . . . . . . . . . . . . 169 9.4 Prime Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . 172 9.5 The Fundamental Theorem of Arithmetic . . . . . . . . . . . . ...

8 Introduction to Number Theory and Cryptography 125 8.1 Subgroups of the Integers . . . . . . . . . . . . . . . . . . . . 125 8.2 Greatest Common Divisors . . . . . . . . . . . . . . . . . . . . 125 8.3 The Euclidean Algorithm . . . . . . . . . . . . . . . . . . . . . 126 8.4 Prime Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . 129 8.5 The Fundamental Theorem of Arithmetic . . . ....