#凯撒密码：将每一个字母替换为字母表中下一位字母，比如a变成b。
english.letters <- c('a', 'b', 'c', 'd', 'e', 'f', 'g', 'h', 'i', 'j', 'k',
'l', 'm', 'n', 'o', 'p', 'q', 'r', 's', 't', 'u', 'v',
'w', 'x', 'y', 'z')
caesar.cipher <- list()
inverse.caesar.cipher <- list()
#加密LIST和解密LIST
for (index in 1:length(english.letters))
{
caesar.cipher[[english.letters[index]]] <- english.letters[index %% 26 + 1]
inverse.caesar.cipher[[english.letters[index %% 26 + 1]]] <- english.letters[index]
}
print(caesar.cipher)
# 单字符串加密
apply.cipher.to.string <- function(string, cipher)
{
output <- ''
for (i in 1:nchar(string))
{
output <- paste(output, cipher[[substr(string, i, i)]], sep = '')
}
return(output)
}
#向量字符串加密
apply.cipher.to.text <- function(text, cipher)
{
output <- c()
for (string in text)
{
output <- c(output, apply.cipher.to.string(string, cipher))
}
return(output)
}
apply.cipher.to.text(c('sample', 'text'), caesar.cipher)
#贪心优化：只有当新解密规则得到的解密串的概率变高时，才接受新的解密规则
#思路：
#1.如果解密规则B解密出的解密串的概率大于解密规则A对应的解密串，那么我们用B代替A
#2.如果解密规则B解密出的解密串的概率小于解密规则A对应的解密串，我们仍然有可能用B代替A，不过并不是每次都替换。
#如果解密规则B对应的解密串的概率是p1，解密规则A对应的解密串的概率是p2，以p1/p2的概率从解密规则A替换到解密规则B（表示有一定的概率接受B，这使得不会陷入贪心优化陷阱中）
#随便产生一个加密规则
generate.random.cipher <- function()
{
cipher <- list()
inputs <- english.letters
outputs <- english.letters[sample(1:length(english.letters), length(english.letters))]
for (index in 1:length(english.letters))
{
cipher[[inputs[index]]] <- outputs[index] }
return(cipher)
}
modify.cipher <- function(cipher, input, output)
{
new.cipher <- cipher
new.cipher[[input]] <- output
old.output <- cipher[[input]]
collateral.input <- names(which(sapply(names(cipher), function (key) {cipher[[key]]}) == output))
new.cipher[[collateral.input]] <- old.output
return(new.cipher)
}
#对加密算法作一些修改
propose.modified.cipher <- function(cipher)
{
input <- sample(names(cipher), 1)
output <- sample(english.letters, 1)
return(modify.cipher(cipher, input, output))
}
#加载词典
load(file.path('G:\dataguru\ML_for_Hackers\ML_for_Hackers-master\07-Optimization\data\lexical_database.Rdata'))
#看一下里面的数据
lexical.database[['a']]
lexical.database[['the']]
lexical.database[['he']]
lexical.database[['she']]
lexical.database[['data']]
#取概率的,词典里有就返回,词典里没有返回一个最小的浮点数
one.gram.probability <- function(one.gram, lexical.database = list())
{
lexical.probability <- lexical.database[[one.gram]]
if (is.null(lexical.probability) || is.na(lexical.probability))
{
return(.Machine$double.eps)
}
else
{
return(lexical.probability)
}
}
#给定一个字符串向量,计算概率,概率不用连乘,用求和
log.probability.of.text <- function(text, cipher, lexical.database = list())
{
log.probability <- 0.0
for (string in text)
{
decrypted.string <- apply.cipher.to.string(string, cipher)
log.probability <- log.probability +
log(one.gram.probability(decrypted.string, lexical.database))
}
return(log.probability)
}
#
metropolis.step <- function(text, cipher, lexical.database = list())
{
#对加密规则作一下修改
proposed.cipher <- propose.modified.cipher(cipher)
#计算原加密规则及修改过的加密规则的概率
lp1 <- log.probability.of.text(text, cipher, lexical.database)
lp2 <- log.probability.of.text(text, proposed.cipher, lexical.database)
#如果新的比较好,直接换掉
if (lp2 > lp1)
{
return(proposed.cipher)
}
else
{
#如果旧的比较好,
a <- exp(lp2 - lp1)
#x是均匀分布的0~1间随机数
x <- runif(1)
if (x < a)
{
return(proposed.cipher)
}
else
{
return(cipher)
}
}
}
# 5个字符串的向量
decrypted.text <- c('here', 'is', 'some', 'sample', 'text')
#用凯撒加密规则加一下密
encrypted.text <- apply.cipher.to.text(decrypted.text, caesar.cipher)
set.seed(1)
#生成随机加密规则
cipher <- generate.random.cipher()
results <- data.frame()
#50000次迭代
number.of.iterations <- 50000
for (iteration in 1:number.of.iterations)
{
#算一下加密结果的概率
log.probability <- log.probability.of.text(encrypted.text,cipher,lexical.database)
#得出解密结果
current.decrypted.text <- paste(apply.cipher.to.text(encrypted.text, cipher),collapse = ' ')
#得出判断结果,1为正确,0为不正确
correct.text <- as.numeric(current.decrypted.text == paste(decrypted.text,
collapse = ' '))
#形成数据框,包括迭代次数,概率及解密后的结果,以及正确率
results <- rbind(results,data.frame(Iteration = iteration, LogProbability = log.probability,CurrentDecryptedText = current.decrypted.text,CorrectText = correct.text))
cipher <- metropolis.step(encrypted.text, cipher, lexical.database)
}