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...

Because the t-out-of-n oblivious transfer (OT) protocol can guarantee the privacy of both participants, i.e., the sender and the receiver, it has been used extensively in the study of cryptography. Recently, Chang and Lee presented a robust t-out-of-n OT protocol based on the Chinese remainder theorem (CRT). In this paper, we use the Aryabhata remainder theorem (ART) to achieve the functionalit...

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 . . . ....

9 Introduction to Number Theory and Cryptography 1 9.1 Subgroups of the Integers . . . . . . . . . . . . . . . . . . . . 1 9.2 Greatest Common Divisors . . . . . . . . . . . . . . . . . . . . 2 9.3 The Euclidean Algorithm . . . . . . . . . . . . . . . . . . . . . 3 9.4 Prime Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . 4 9.5 The Fundamental Theorem of Arithmetic . . . . . . . . ....