[原创]RSA公钥密码的破解

ysr

风花飘飘 发表于 2021-11-14 17:07
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谢谢朋友，哈哈哈！改过来了！

ysr

今天花了很大精力，才把前面那个，关于F的一元四次方程化为标准形式：（有点复杂，算是个细化公式吧）

(2B+1)F^4+2N(2B+1)F^3+(4N+1)(2B+1)F^3-N^2(2B+1)F^2+2N(4N+1)(2B+1)F^2+N(2N+1)(2B+1)F^2
-N^2(4N+1)(2B+1)F+2N^2(2N+1)(2B+1)F+2DN^2-N^3(2N+1)(2B+1)=0.

其中D=M/4.

2023.1.31日 写

ysr

算是修正误差的细化公式，成败在此一举，如果不能得到接近实际的精确解，那此法就宣告失败。

有空了试试吧，解个一元四次方程对我不是强项，好在解四次方程的方法早已不是啥难题和高科技了。

弄个方法不容易，有机会了试试吧。欢迎爱好者沟通探讨！

ysr

(2B+1)F^4+【2N(2B+1)+(4N+1)(2B+1)】F^3-【N^2(2B+1)-2N(4N+1)(2B+1)-N(2N+1)(2B+1)】F^2
-【N^2(4N+1)(2B+1)-2N^2(2N+1)(2B+1)】F+【2DN^2-N^3(2N+1)(2B+1)】=0

注意符号，首先计算一下方程的系数a，b，c，d，e

ysr

Private Sub Command1_Click()
Dim M, P, B, c, d
M = DeleteSpace(Trim(Text1.Text))
P = DeleteSpace(Trim(Text2.Text))
jd = zhengchuqy(MCC1(Trim(M), 4))
sd = 22
a2 = zhengliys2(Trim(M), Val(sd))
b2 = zhengliys2(Trim(P), Val(sd))
q = mcc2(Trim(a2), Trim(b2), Val(sd))
q1 = zhengliys2(1, Val(sd))
q2 = MPC(Trim(q), Trim(q1))
p2 = MPC(Trim(b2), Trim(q1))
A = mcc2(Trim(q2), Trim(p2), Val(sd))
n = MCC1(MPC(Trim(P), 1), 2)
n1 = MPC1(MbC(Trim(n), 2), 1)
n2 = MPC1(MbC(Trim(n), 4), 1)
n = zhengliys2(Trim(n), Val(sd))
n1 = zhengliys2(Trim(n1), Val(sd))
n2 = zhengliys2(Trim(n2), Val(sd))
B = MPC1(mbc2(mbc2(Trim(n), Trim(A), Val(sd)), 2 & String(Val(sd), "0"), Val(sd)), mbc2(Trim(n2), Trim(A), Val(sd)))
c = MPC1(mbc2(mbc2(Trim(n), 2 & String(Val(sd), "0"), Val(sd)), mbc2(Trim(n2), Trim(A), Val(sd)), Val(sd)), mbc2(mbc2(Trim(n), Trim(n1), Val(sd)), Trim(A), Val(sd)))
c = mpc2(Trim(c), mbc2(mbc2(Trim(n), Trim(n), Val(sd)), Trim(A), Val(sd)))
n3 = mbc2(Trim(n), Trim(n), Val(sd))
n4 = mbc2(Trim(n3), Trim(n), Val(sd))
d = mpc2(mbc2(mbc2(Trim(n3), 2 & String(Val(sd), "0"), Val(sd)), mbc2(Trim(n1), Trim(A), Val(sd)), Val(sd)), mbc2(mbc2(Trim(n3), Trim(n2), Val(sd)), Trim(A), Val(sd)))
e = mpc2(mbc2(mbc2(Trim(jd), Trim(n3), Val(sd)), 2 & String(Val(sd), "0"), Val(sd)), mbc2(mbc2(Trim(n1), Trim(A), Val(sd)), Trim(n4), Val(sd)))
a1 = shuchujg(Trim(A), Val(sd))
B1 = shuchujg(Trim(B), Val(sd))
C1 = shuchujg(Trim(c), Val(sd))
D1 = shuchujg(Trim(d), Val(sd))
e1 = shuchujg(Trim(e), Val(sd))

Text3 = a1
Text4 = B1
Text5 = C1
Text6 = D1
Text7 = e1


End Sub

Private Sub Command2_Click()
Text1 = ""
Text2 = ""
Text3 = ""
Text4 = ""
Text5 = ""
Text6 = ""
Text7 = ""

End Sub