crytography & security 1

Brief

Data Confidentiality

prevent unauthorized reading of data(transimission and storage)

Approaches:

• encryption and decryption = CIPHER

Data Integrity

prevent being modified and replaced or check if data is modified or replaced.

Authentication of Sender and Receiver

make sure the send is the REAL sender

make sure the receiver is the REAL receiver

Nonrepudiation

类似于指纹和手写签名

双方签名后不能反悔

数字签名

Secret Sharing

Cryptographic Protocols

Some Math Foundations

Let x ∈ Zn = {0, 1, · · · , n − 1}. If there is an integer y ∈ Zn such that

$x ⊗n y =: (x × y ) mod n = 1.$

The integer y is called a multiplicative inverse of x, usually denoted x−1 (it is
unique if it exists).

== 模的倒数不一定存在 ==

当 a和n互质时，a有且唯一有一个multiplicative inverse

Apply the Extended Euclidean Algorithm to a
and n to compute the two integers u and v such that 1 = ua + vn. Then
u mod n is the inverse of a modulo n.