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2019-11-22 19:59:09 +0200 | asked a question | Error: Tried to use Sage's Python which was not yet installed. I get the following error when I try to run Sage. I am using MAC. I did install both Python2 and Python3. I also upgraded my python to latest versions using I do not understand the problem. Please help me. |

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2019-05-30 15:36:51 +0200 | commented answer | Why is exponentiation of points on elliptic curve so fast? It took around 5 seconds for executing G = E.abelian_group(). But after that is done, for the exponentiation is taking very less time. I don't see any reason how exponentiation could be done so fast. Here is my output for your code. Time per operation = 2.93278694153e-06 seconds Time per operation = 2.42040157318e-06 seconds |

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2019-05-30 05:50:46 +0200 | asked a question | Why is exponentiation of points on elliptic curve so fast? I am working on elliptic curves in sagemath. I was trying to collect benchmarks for group operation and exponentiation of points on NIST P-256 elliptic curve. When I tried to perform a group operation on 2 points on the curve, it takes roughly 2 micro seconds. When I tried to perform exponentiation on a point in elliptic curve with a random exponent, it takes only 3 micro seconds. How is this even possible? Since I am exponentiating with a 256 bit value, this should at least take time required for 256 group operations, which is more than 1ms. I am worried if my code is wrong! |

2019-05-12 03:26:27 +0200 | asked a question | How to implement pairings on MNT curves? I have used elliptic curves in sagemath. But I do not how to use pairings in sagemath. I found a list of MNT curves at https://www.esat.kuleuven.be/cosic/pu... I also found some documentation on elliptic curves at https://doc.sagemath.org/html/en/refe... It provides ate_pairing, tate_pairing, weil_pairing functions. I don't know which one to use. I couldn't understand it. I do not know math behind pairings well enough. Please provide a simple code for performing pairing operations on these curves. |

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2018-12-24 00:32:36 +0200 | asked a question | Randomly generate a safe prime of given length A prime p is said to be safe prime if (p-1)/2 is also a prime. Safe primes are heavily used in cryptography. In order to generate a random prime of 512 bits, I use How to randomly generate a safe prime of given length? |

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2018-12-03 11:38:55 +0200 | asked a question | Get bit representation of an elliptic curve group element I can define an elliptic curve using
I can then compute a group on E using
I can then sample a random element in the group using
Is there a way I can get a bit string representation of this group element R? Actually, I am implementing a pseudo-random generator scheme, which finally outputs a group element on elliptic curve. I need to convert it to a bit string. |

2018-11-29 18:08:40 +0200 | asked a question | log base 2 in sagemath How to compute log base 2 in sagemath? I tried log(1000,2). It answers log(1000)/log(2). I want an exact numerical answer. |

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2018-11-28 07:34:28 +0200 | asked a question | generate random elliptic curve of prime order As required in many cryptographic algorithms, I would like to sample a group (in this case, an abelian group defined on elliptic curve) of a random prime order. I know how to define an elliptic curve with given parameters, and then calculate its order. But how to sample an elliptic curve of random prime order? |

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