initial commit for ctnt talk

.gitignore

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+## Core latex/pdflatex auxiliary files:
+*.aux
+*.lof
+*.log
+*.lot
+*.fls
+*.out
+*.toc
+*.fmt
+*.fot
+*.cb
+*.cb2
+.*.lb
+
+## Intermediate documents:
+*.dvi
+*.xdv
+*-converted-to.*
+# these rules might exclude image files for figures etc.
+# *.ps
+# *.eps
+# *.pdf
+
+## Generated if empty string is given at "Please type another file name for output:"
+.pdf
+
+## Bibliography auxiliary files (bibtex/biblatex/biber):
+*.bbl
+*.bcf
+*.blg
+*-blx.aux
+*-blx.bib
+*.run.xml
+
+## Build tool auxiliary files:
+*.fdb_latexmk
+*.synctex
+*.synctex(busy)
+*.synctex.gz
+*.synctex.gz(busy)
+*.pdfsync
+
+## Build tool directories for auxiliary files
+# latexrun
+latex.out/
+
+## Auxiliary and intermediate files from other packages:
+# algorithms
+*.alg
+*.loa
+
+# achemso
+acs-*.bib
+
+# amsthm
+*.thm
+
+# beamer
+*.nav
+*.pre
+*.snm
+*.vrb
+
+# changes
+*.soc
+
+# cprotect
+*.cpt
+
+# elsarticle (documentclass of Elsevier journals)
+*.spl
+
+# endnotes
+*.ent
+
+# fixme
+*.lox
+
+# feynmf/feynmp
+*.mf
+*.mp
+*.t[1-9]
+*.t[1-9][0-9]
+*.tfm
+
+#(r)(e)ledmac/(r)(e)ledpar
+*.end
+*.?end
+*.[1-9]
+*.[1-9][0-9]
+*.[1-9][0-9][0-9]
+*.[1-9]R
+*.[1-9][0-9]R
+*.[1-9][0-9][0-9]R
+*.eledsec[1-9]
+*.eledsec[1-9]R
+*.eledsec[1-9][0-9]
+*.eledsec[1-9][0-9]R
+*.eledsec[1-9][0-9][0-9]
+*.eledsec[1-9][0-9][0-9]R
+
+# glossaries
+*.acn
+*.acr
+*.glg
+*.glo
+*.gls
+*.glsdefs
+
+# gnuplottex
+*-gnuplottex-*
+
+# gregoriotex
+*.gaux
+*.gtex
+
+# htlatex
+*.4ct
+*.4tc
+*.idv
+*.lg
+*.trc
+*.xref
+
+# hyperref
+*.brf
+
+# knitr
+*-concordance.tex
+# TODO Comment the next line if you want to keep your tikz graphics files
+*.tikz
+*-tikzDictionary
+
+# listings
+*.lol
+
+# makeidx
+*.idx
+*.ilg
+*.ind
+*.ist
+
+# minitoc
+*.maf
+*.mlf
+*.mlt
+*.mtc[0-9]*
+*.slf[0-9]*
+*.slt[0-9]*
+*.stc[0-9]*
+
+# minted
+_minted*
+*.pyg
+
+# morewrites
+*.mw
+
+# nomencl
+*.nlg
+*.nlo
+*.nls
+
+# pax
+*.pax
+
+# pdfpcnotes
+*.pdfpc
+
+# sagetex
+*.sagetex.sage
+*.sagetex.py
+*.sagetex.scmd
+
+# scrwfile
+*.wrt
+
+# sympy
+*.sout
+*.sympy
+sympy-plots-for-*.tex/
+
+# pdfcomment
+*.upa
+*.upb
+
+# pythontex
+*.pytxcode
+pythontex-files-*/
+
+# thmtools
+*.loe
+
+# TikZ & PGF
+*.dpth
+*.md5
+*.auxlock
+
+# todonotes
+*.tdo
+
+# easy-todo
+*.lod
+
+# xmpincl
+*.xmpi
+
+# xindy
+*.xdy
+
+# xypic precompiled matrices
+*.xyc
+
+# endfloat
+*.ttt
+*.fff
+
+# Latexian
+TSWLatexianTemp*
+
+## Editors:
+# WinEdt
+*.bak
+*.sav
+
+# Texpad
+.texpadtmp
+
+# Kile
+*.backup
+
+# KBibTeX
+*~[0-9]*
+
+# auto folder when using emacs and auctex
+./auto/*
+*.el
+
+# expex forward references with \gathertags
+*-tags.tex
+
+# standalone packages
+*.sta
+
+# generated if using elsarticle.cls
+*.spl

ECM.py

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+# %load ec3.py
+from math import factorial, gcd, log
+import numpy as np
+P=np.zeros(1000)
+P[0]=1
+P[1]=1
+for i in range(2,100):
+    if P[i]==0:
+        j=2
+        while i*j<100:
+            P[i*j]=1
+            j=j+1
+Primes1000=[i for i,x in enumerate(P) if x==0 ]  
+
+
+def mexp(a,x,N):
+    m,s=1,a
+    while x>0:
+        if x % 2 ==1:
+            m=((m*s) % N)
+        s=((s*s) % N)
+        x=x//2
+    return m
+
+def euclid(u,v):
+    if v==0:
+        raise ArithmeticError('Division by Zero')
+    x0,x1=u,v
+    a0,a1=1,0
+    b0,b1=0,1
+    while x1!=0:
+        q=x0//x1
+        x2=x0-q*x1
+        a2=a0-q*a1
+        b2=b0-q*b1
+        x0,a0,b0=x1,a1,b1
+        x1,a1,b1=x2,a2,b2
+    if x0<0:
+        return -x0,-a0,-b0
+    else:
+        return x0,a0,b0
+
+def mod_inv(u,N):
+    d,a,b=euclid(u,N)
+    if d==1:
+        return a
+    else:
+        raise ArithmeticError('Common factor is '+str(d))
+
+def two_p(x,y,a,b,N):
+    Lu=(3*x**2+a) % N
+   # print(Lu)
+    Lb=mod_inv(2*y,N)
+  #  print(Lb)
+    L=Lu*Lb % N
+    x_two=(L*L-2*x) % N
+    y_two=(L*(x-x_two)-y) %N
+    return x_two,y_two
+
+def sum_p(x1,y1,x2,y2,a,b,N):
+    Lu=(y2-y1) % N
+    Lb=mod_inv(x2-x1,N)
+    L=(Lu*Lb) % N
+    x_sum=(L*L-x1-x2) %N
+    y_sum=(L*(x1-x_sum)-y1) %N
+    return x_sum,y_sum
+
+def exp_p(x,y,a,b,m,N):
+    sx,sy=x,y
+    first=True
+    while m>0:
+        if m%2==1:
+            if first:
+                xm,ym=sx,sy
+                first=False
+            else:
+                xm,ym=sum_p(xm,ym,sx,sy,a,b,N)
+        sx,sy=two_p(sx,sy,a,b,N)
+        m=m//2
+    return xm,ym
+
+#def mexp(a,x,N):
+ #   m,s=1,a
+ #   while x>0:
+ #       if x % 2 ==1:
+ #           m=((m*s) % N)
+ #       s=((s*s) % N)
+ #       x=x//2
+ #   return m
+
+def ecm_trial(N,arange=50,krange=30):
+    for a in range(-arange,arange):
+        xm,ym=0,1
+        print(a) 
+        for k in range(2,krange):
+            try:
+                xm,ym=exp_p(xm,ym,a,1,k,N)
+            except ArithmeticError:
+                print('try the following: a=',a,' and k=',k)
+                break
+
+
+
+#N=149185656432189838133
+#ecm_trial(N,arange=20,krange=10000)
+N=2**128+1
+#ecm_trial(N,arange=100,krange=10000)
+xm,ym=exp_p(0,1,-91,1,factorial(7883),N)
+
+
+
+