Counting points on elliptic curves over Zp

The mathematics of elliptic curves has been studied since ancient times. These mathematical structures have found applications in varied fields. More recently, there has been a growing interest in applying these structures to cryptography. Various such applications have been proposed. Elliptic curve based cryptographic algorithms have been shown to provide greater security with shorter key sizes than the conventional RSA based cryptosystems, making them more memory e cient and less processor intensive. One of the fundamental requirements of all such elliptic curve cryptographic algorithms is that the order of the group of points satisfying the elliptic curve meet a certain set of requirements. However, finding the group order is not a trivial task. There are numerous special cases of elliptic curves where determining the group order is trivial. This thesis however, deals with the study of general point counting algorithms and their performances, which are applicable to all the curves. Possible improvements to the algorithms are provided where possible

A cross-sectional survey to assess knowledge, attitude, and practice of Yoga among cancer patients at a tertiary care hospital

Background: Cancer incidence and mortality are rapidly growing worldwide. Cancer affects the overall quality of life of cancer patients. Yoga has its origin in the ancient times. This ancient practice has been used for holistic well-being for ages. Yoga as an alternative therapy might be beneficial for cancer patients too. This study was conducted to assess knowledge, attitudes, and yoga practices among cancer patients. Materials and Methods: For this cross-sectional survey, a self-designed questionnaire was validated and distributed among 25 cancer patients for a pilot study. Then, a full-fledged study was conducted based on the interviews of 1000 cancer patients at a tertiary care oncology unit and the data were analyzed using R 3.6. Results: A total of 1000 participants were enrolled in this cross-sectional survey. Out of 1000 participants, 91 were excluded as they responded that they were not familiar with the term “Yoga” in the first question of the questionnaire. Of 919 participants, 238 strongly agreed and 395 agreed with the question that people who practice yoga are less prone to diseases, showing that 68.87% of cancer patients have a positive attitude toward yoga. However, only 145 (15.77%) of the participants practice yoga regularly. Lack of time was the most common reason for not practicing yoga, and the other reasons were the lack of interest and insufficient facilities. Conclusion: The present study on 1000 patients from the yoga capital of the world, Rishikesh, highlights the fact that the majority of cancer patients are aware of yoga practice's benefits and if given the opportunity to learn appropriate techniques, yoga can further improve the outcome in such patients. There is a need to design the effective yoga programs for cancer patients to promote suitable yoga practices in this population

Geo-archeology at Khajnawar in Western Uttar Pradesh plain

Khajnawar village in Saharanpur district of western Utter Pradesh is inhabited over the remains of an ancient archaeological settlement. Field observations and archaeological investigation reveal two periods of settlement: settlement I with grey ware and iron objects and settlement II with painted red ware. Radiocarbon and optical stimulated luminescence (OSL) dating indicate 2600a-1400a age for settlement I and 850a-350a for settlement II. A hiatus of ~550a between the two settlements may have been caused either by an earthquake or climate change. A southfacing and NW-SE trending scarp on the southern end of the Khajnawar has been interpreted as a tectonic scarp that is a continuation of the Piedmont Fault with right-step. The scarp should have formed due to an earlier earthquake that may have caused the hiatus. Climate change can be another possibility for the hiatus, because periods of settlement and occupation seem to coincide with drier and wetter conditions recorded in the subcontinent. Collapsed and tilted walls with brick rubble and infilling by sands in the settlement II layers was probably caused by a later earthquake post-dating 350a (OSL age), suggesting that this most likely corresponds to the large Mw > 7 1803 earthquake of Garhwal Himalaya