Hassan Mostafa's profile - activity

if i defined the following finite field

F=GF(2^15,'x')

then i've generated it's irreducible polynomial

sage: IP=F.polynomial()
sage: IP
x^15 + x^5 + x^4 + x^2 + 1

how can i get the binary representation of this polynomial ?

how can i generate and use elliptic curve over 16-bit binary field.

when i generate an elliptic curve and work with it's points. it is always displaying with Z-coordinate =1 as following:

sage: EC=EllipticCurve(GF(101),[2,3])
sage: EC
Elliptic Curve defined by y^2 = x^3 + 2*x + 3 over Finite Field of size 101
sage: EC.random_point()
(60 : 65 : 1)
sage: point1=EC.random_point()
sage: point1
(3 : 6 : 1)
sage: point2=2*point1
sage: point2
(30 : 55 : 1)

as shown Z-coordinate always = 1. can i work with points with it's normal (original) Z- component ??

the points over elliptic curve defined over finite field always displayed in projective coordinates (X:Y:Z) with normalised Z component ( always Z = 1). i need points to be in normal projective coordinates ( Z component not always 1 )

it is worked fine. can i generate points directly with integer representation >> make E.random_point() generate random points in integer representation

i've created an Elliptic curve over finite field GF(2^101). when i generate a random point on this curve is appear as the following representation. p1=(z101^99 + z101^98 + z101^97 + z101^96 + z101^95 + z101^94 + z101^92 + z101^91 + z101^90 + z101^89 + z101^87 + z101^86 + z101^84 + z101^80 + z101^79 + z101^77 + z101^74 + z101^73 + z101^72 + z101^70 + z101^66 + z101^65 + z101^63 + z101^61 + z101^59 + z101^57 + z101^56 + z101^55 + z101^52 + z101^51 + z101^49 + z101^47 + z101^41 + z101^40 + z101^38 + z101^36 + z101^30 + z101^29 + z101^28 + z101^27 + z101^25 + z101^23 + z101^20 + z101^18 + z101^15 + z101^14 + z101^10 + z101^3 + z101^2 + z101 + 1 : z101^100 + z101^99 + z101^96 + z101^90 + z101^88 + z101^87 + z101^85 + z101^82 + z101^81 + z101^72 + z101^70 + z101^69 + z101^68 + z101^67 + z101^66 + z101^62 + z101^60 + z101^59 + z101^58 + z101^53 + z101^52 + z101^50 + z101^49 + z101^48 + z101^46 + z101^45 + z101^44 + z101^43 + z101^42 + z101^40 + z101^39 + z101^37 + z101^36 + z101^34 + z101^32 + z101^27 + z101^26 + z101^25 + z101^23 + z101^15 + z101^13 + z101^12 + z101^9 + z101^7 + z101^3 : 1).

i need this point coordinates to be numbers not polynomials. any recommendations?

when i did so it has been crashed and generated a report that i have sent to sage-support@googlegroups.com

it is working fine when i use

sudo ./sage

any recommendations ?

i am trying to install Sagemath 8.9 on ubuntu 18.04.3 LTS. i am doing the following :

1. downloaded the sage-8.9-Ubuntu_18.04-x86_64.tar.bz2 .

2. extracted it (with no sudo permission) using

tar xvf sage-8.9-Ubuntu_18.04-x86_64.tar.bz2

1. cd into the extracted directory named Sagemath and run

make

as mentioned in the readme file .. it takes long time then gve me the following error:

[dochtml] OSError: [Errno 13] Permission denied: '/home/hassan/.sage/cache/tmpwpNzXa' Makefile:2038: recipe for target 'doc-html' failed make[3]: * [doc-html] Error 1 make[3]: Leaving directory '/home/hassan/SageMath/build/make' Makefile:1849: recipe for target 'all-start' failed make[2]: * [all-start] Error 2 make[2]: Leaving directory '/home/hassan/SageMath/build/make'

real 1m8.422s user 0m40.632s sys 0m3.585s

Error building Sage.

The following package(s) may have failed to build (not necessarily during this run of 'make all-start'):

The build directory may contain configuration files and other potentially helpful information. WARNING: if you now run 'make' again, the build directory will, by default, be deleted. Set the environment variable SAGE_KEEP_BUILT_SPKGS to 'yes' to prevent this.

Makefile:31: recipe for target 'all-start' failed make[1]: * [all-start] Error 1 make[1]: Leaving directory '/home/hassan/SageMath' Makefile:13: recipe for target 'all' failed make: * [all] Error 2

no it is not a homework. it is related to sage as for example i am working with cryptography >> Rijndael-GF block cipher which sometimes i need to use binary key, message and ciphers. anyway i've found a function that do this role as following; # toggleBit() returns an integer with the bit at 'offset' inverted, 0 -> 1 and 1 -> 0.

def toggleBit(int_type, offset): mask = 1 << offset return(int_type ^ mask)

if i have a binary string for example x='0110101' and i need to inverse it's bits bit by bit. for example : inverse 1st bit >> x='1110101' inverse 2nd bit >> x='0010101' 3rd bit >> x='0100101'

and so on. how can i do that.

i've just installed sagemath 8.8 on windows 10 with trendmicro office scan installed. after installation and when double click on SageMath icon it is launched and then crash and closed without any error messages. i've tried to add SageMath paths to be excluded from antivirus and doesn't work also ..

for Rijndael-GF class which is implementation of AES cipher we define block size and key size but can't control number of round. is there any way to modify number of rounds. for example AES with 4 rounds or 6 rounds ?

sorry if the question is not clear. i will explain based on your example. given the point P. if i perform scalar multiplication 3*P that will give a new point say P2. my request is to how to calculate P from P2 .. can i make inverse scalar multiplication of P2 by 3 to get the original point P .

is that possible to calculate the multiplicative inverse for an elliptic curve point . for example X is a point i need to calculate inverse of X such that X*X^-1 give me unity.

i am working with elliptic cure NIST p-521. i am trying to do loop with the syntax " for i in range (n): ". but n is too large for ex: n= 6864797660130609714981900799081393217269435300143305409394463459185543183397653210140554620662074004704518954203785444253993810126864972419532086575239231303.

which give the error

overflowerror: range() result has too many items .

i've followed these steps but there is an issue. as i work on NIST-P521 curve so it's order is very large number so i am receiving the following error

OverflowError:range() result too many items

is there a way to solve this

i need to export an elliptic curve over finite field after it's generated as a lookup table.. like two columns ( finite field element, it's output point after multiplied by the generator point of the curve). how can i do this?