Iwasawa theory and p-adic L-functions over Zp2-extensions

We construct a two-variable analogue of Perrin-Riou’s p-adic regulator map for the Iwasawa cohomology of a crystalline representation of the absolute Galois group of Q p , over a Galois extension whose Galois group is an abelian p-adic Lie group of dimension 2. We use this regulator map to study p-adic representations of global Galois groups over certain abelian extensions of number fields whose localisation at the primes above p is an extension of the above type. In the example of the restriction to an imaginary quadratic field of the representation attached to a modular form, we formulate a conjecture on the existence of a “zeta element”, whose image under the regulator map is a p-adic L-function. We show that this conjecture implies the known properties of the 2-variable p-adic L-functions constructed by Perrin-Riou and Kim

Amicable pairs and aliquot cycles for elliptic curves

An amicable pair for an elliptic curve E/Q is a pair of primes (p,q) of good reduction for E satisfying #E(F_p) = q and #E(F_q) = p. In this paper we study elliptic amicable pairs and analogously defined longer elliptic aliquot cycles. We show that there exist elliptic curves with arbitrarily long aliqout cycles, but that CM elliptic curves (with j not 0) have no aliqout cycles of length greater than two. We give conjectural formulas for the frequency of amicable pairs. For CM curves, the derivation of precise conjectural formulas involves a detailed analysis of the values of the Grossencharacter evaluated at a prime ideal P in End(E) having the property that #E(F_P) is prime. This is especially intricate for the family of curves with j = 0.Comment: 53 page

Polymorphism C677T MTHFR gene and metabolic syndrome in young residents of the northern region

The aim of the work was to study the association of polymorphism C677T (rs1801133) of the MTHFR gene with components of the metabolic syndrome in young indigenous and non-indigenous people of the northern region. 834 young people aged 18-44 years were examined, of them 695 parents with manifestations of metabolic syndrome and 139 healthy young people. It was revealed that 28.7% of all surveyed were carriers of the T is1801133 (C677T) allele of the MTHFR gene as-sodated with the risk of developing cardiovascular diseases. No significant differences were found among non-indigenous and indigenous people in the carrierfrequency of theT allele. Associations of rs1801133C677T polymorphisms of the MTHFR gene with components of MS were studied. Among the non-indigenous male population with carriers of the homozygous TT genotype, a tendency has been established to reduce the chances of developing hypertriglyceridemia and an increase in LDL cholesterol levels. In men of the indigenous ethnic group of carriers of the TT genotype, there is a tendency to increase the chances of reducing the level of HDL cholesterol and increasing the chances of developing hyperglycemia. Among non-indigenous female carriers of the homozygous TT genotype, a tendency was established to reduce the likelihood of developing abdominal obesity. Among indigenous women, the carriage of a homozygous TT is associated with arterial hypertension.Целью работы явилось изучение ассоциации полиморфизма С677Т (($1801133) гена MTHFR с компонентами метаболического синдрома у молодых коренных и некоренных жителей северного региона. Обследовано 834 молодых человека в возрасте 18-44 года, из них 695 пациентов с проявлениями метаболического синдрома и 139 здоровых молодых людей. Выявлено, что 28,7% всех обследованных являлись носителями аллеля Т rs1801133 (С677Г) гена MTHFR, связанного с риском развития сердечно­сосудистых заболеваний. Среди некоренных и коренных жителей по частоте носительства аллеля Т достоверных различий не выявлено. Изучены ассоциации полиморфизмов rs1801133 С677Т гена MTHFR с компонентами МС. Среди некоренного мужского населения-носителей гомозиготного генотипа ТТ установлена тенденция к снижению шансов развития гипертритицеридемии, повышения уровня ХС ЛПНП. У мужчин коренной этнической группы носителей генотипа ТТ обнаружена тенденция к повышению шансов снижения уровня ХС ЛПВП и повышению шансов развития гипергликемии. Среди некоренных женщин носительниц гомозиготного генотипа ТТ была установлена тенденция к снижению вероятности развития абдоминального ожирения. У коренных представительниц носительство гомозиготного ТТ ассоциировано с артериальной гипертензией

Efficient Ephemeral Elliptic Curve Cryptographic Keys

We show how any pair of authenticated users can on-the-fly agree on an elliptic curve group that is unique to their communication session, unpredictable to outside observers, and secure against known attacks. Our proposal is suitable for deployment on constrained devices such as smartphones, allowing them to efficiently generate ephemeral parameters that are unique to any single cryptographic application such as symmetric key agreement. For such applications it thus offers an alternative to long term usage of standardized or otherwise pre-generated elliptic curve parameters, obtaining security against cryptographic attacks aimed at other users, and eliminating the need to trust elliptic curves generated by third parties

On the Static Diffie-Hellman Problem on Elliptic Curves over Extension Fields

We show that for any elliptic curve E(Fqn ), if an adversary has access to a Static Diffie-Hellman Problem (Static DHP) oracle, then by making O(q1− 1/n+1) Static DHP oracle queries during an initial learning phase, for fixed n > 1 and q → ∞ the adversary can solve any further instance of the Static DHP in heuristic time O˜(q1− 1/n+1). Our proposal also solves the Delayed Target DHP as defined by Freeman, and naturally extends to provide algorithms for solving the Delayed Target DLP, the One-More DHP and One-More DLP, as studied by Koblitz and Menezes in the context of Jacobians of hyperelliptic curves of small genus. We also argue that for any group in which index calculus can be effectively applied, the above problems have a natural relationship, and will always be easier than the DLP. While practical only for very small n, our algorithm reduces the security provided by the elliptic curves defined over Fp2 and Fp4 proposed by Galbraith, Lin and Scott at EUROCRYPT 2009, should they be used in any protocol where a user can be made to act as a proxy Static DHP oracle, or if used in protocols whose security is related to any of the above problems

Improved Agreeing-Gluing Algorithm

In this paper we study the asymptotical complexity of solving a system of sparse algebraic equations over finite fields. An equation is called sparse if it depends on a bounded number of variables. Finding efficiently solutions to the system of such equations is an underlying hard problem in the cryptanalysis of modern ciphers. New deterministic Improved Agreeing-Gluing Algorithm is introduced. The expected running time of the Algorithm on uniformly random instances of the problem is rigorously estimated. The estimate is at present the best theoretical bound on the complexity of solving average instances of the problem. In particular, this is a significant improvement over those in our earlier papers [20,21]. In sparse Boolean equations a gap between the present worst case and the average time complexity of the problem has significantly increased. Also we formulate Average Time Complexity Conjecture. If proved that will have far-reaching consequences in the field of cryptanalysis and in computing in general