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20200118 08:11:20 0600  asked a question  how to check backend algorithm for particular function in sage math I want to check the computation of trace () function in sagemath. what the formula they have used for computation over a prime field. 
20191230 21:01:00 0600  asked a question  symbolic expression how to write symbolic expression over finite field 
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20190808 02:10:29 0600  commented question  the following codes for 2^3 field. for the same field how to check the curve parameter A,B are the element of the field what is the sage command to check A and B belongs to the field F. 
20190806 23:23:51 0600  asked a question  which function give accurate time result timeit or start time to end time timeit() or start time to end time 
20190805 02:28:17 0600  asked a question  the following codes for 2^3 field. for the same field how to check the curve parameter A,B are the element of the field . 
20190805 02:15:29 0600  commented question  how to check element A and B are field element? for following code 
20190804 09:22:00 0600  asked a question  how to check element A and B are field element? for following code `p=(2^131) p1=GF(p) F1.<x>=GF(2)[] F.=GF(2^3,'a',modulus=x^3+x+1);F.modulus();F for i,x in enumerate(F): print("{} {}".format(i, x)) A=a^2+a;A B=a+1 E = EllipticCurve(F, (1,A,0,0,B));` 
20190804 00:13:57 0600  asked a question  how to check the element is field element
how to check the element B is Field element, the command which i have written gave me attribute error. 
20190802 05:51:15 0600  asked a question  characteristics three field elliptic curve lliptic curve for characteristics three field How to generate elliptic curve from the following code as Elliptic Curve defined by $y^2 = x^3 + x^2 + 1$ over Finite Field in $a$ of size $3^{151}$ 
20190801 05:39:15 0600  commented question  point tripling over characteristics three field not getting proper result Paper: Efficient Arithmetic on Elliptic Curves over Fields of Characteristics three 
20190801 03:43:49 0600  asked a question  point tripling over characteristics three field not getting proper result import time p=(3^151) after executing the code the error is point are not on the curve. I have written the equation for x3 and y3 by different ways. 
20190702 01:21:02 0600  asked a question  computation time I using timtit command to compute time the result is 625 loops, best of 3: 38.1 ns per loop what is the meaning of 625 loops, best of 3. 
20190609 09:56:26 0600  asked a question  roots of third degree polynomial roots of polynomial x^3+7x+25 over field F(37) 
20190609 00:17:00 0600  asked a question  roots of polynomial f= z^3 + (3a + 4)z^2 + 3z + 3a + 2 # z is variable f1=f.roots() [(3a + 1, 1), (2a, 2)]# what is 1 and 2 represent in the bracket 
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20180906 10:16:19 0600  asked a question  Scalar Multiplication over extension field I want to perform scalar multiplication but when i will take some random point and order of that point as scalar it gives me error. 
20180813 01:16:29 0600  asked a question  Elliptic curve secp224r1 p=2^2242^96+1 A=3#(0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFFFFFFFFFFFFFFFFE) B=(0xB4050A850C04B3ABF541325650440B7D7BFD8BA270B39432355FFB4) F=GF(p) E = EllipticCurve( F, [A,B] );E G=E(0xb70e0cbd6bb4bf7f321390b94a03c1d356c21122343280d6115c1d21,0xbd376388b5f723fb4c22dfe6cd4375a05a07476444d5819985007e34);G the above domain parameter (p,A,B,G) taken from SEC2(standard for efficient cryptography) Recommended Elliptic curve. But when i run the code the error is the point G coordinate do not define point on elliptic curve. 
20180723 09:19:18 0600  asked a question  Elliptic curve arithmetic the below code is performed mod arithmetic of two polynomial fE and fL over prime field P= 5 and the extension is 5^2. the mod of two polynomial is always third degree polynomial. My fE polynomial is always 3p degree and fL polynomial is p degree. my question is whatever p(large p = 112 bit ,128 bit 160 bit) I will take my mod is always third degree. is it because of any polynomial property. p=5 A=4 B=4 print"\n p=",p print"\n A=",A print"\n B=",B F = GF(p) E = EllipticCurve( F, [A,B] );E S. = PolynomialRing( F ) K. = GF( p**2);#K.modulus#, modulus=W^2+W+1 ) print "\n Modulus of K is =", K.modulus() R.<z> = PolynomialRing( K, sparse=True ) fE=z^15 + (4a + 4)z^11 + 2z^10 + (a + 3)z^7 + z^6 + (2a + 2)z^5 + z^3 + 2z^2 + (3a + 4)z + 1 fL=(4az^5 + (a + 4)z + 3);fL f1= (fE%fL).monic;f1 z^3 + (3a + 4)z^2 + 3z + 3a + 2 
20180723 09:18:16 0600  asked a question  Elliptic curve arithmetic the below code is performed mod arithmetic of two polynomial fE and fL over prime field P= 5 and the extension is 5^2. the mod of two polynomial is always third degree polynomial. My fE polynomial is always 3p degree and fL polynomial is p degree. my question is whatever p(large p = 112 bit ,128 bit 160 bit) I will take my mod is always third degree. is it because of any polynomial property. 
20180711 23:17:29 0600  asked a question  computation time why the computation time required in the following way of execution is different. 1.to run the algorithm I am writing the code /algorithm directly on the sage terminal window and execute the code.

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20180704 02:23:26 0600  asked a question  how to use NTL library for huge polynomial gcd’s over finite fields very quickly). how to use NTL library for huge polynomial gcd’s over finite fields very quickly. 
20180701 06:53:42 0600  asked a question  gcd computation of two polynomial the following code for gcd computation for two polynomials . the code for 112bit elliptic curve but as the polynomials are two large it is difficult to compute gcd. the codes are given below. what is the solution for large polynomials. 
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