Reductions of an elliptic curve with almost prime orders
نویسندگان
چکیده
منابع مشابه
Reductions of an elliptic curve with almost prime orders
1 Let E be an elliptic curve over Q. For a prime p of good reduction, let Ep be the reduction of E modulo p. We investigate Koblitz’s Conjecture about the number of primes p for which Ep(Fp) has prime order. More precisely, our main result is that if E is with Complex Multiplication, then there exist infinitely many primes p for which #Ep(Fp) has at most 5 prime factors. We also obtain upper bo...
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Let E/Q be an elliptic curve over the rationals and, for any prime p, let us denote by |E(Fp)| the number of Fp points of the reduced curve modulo p. Consider the function ΠE,s(x) = #{p ≤ x : |E(Fp)| = Ps}, where Ps denotes a squarefree number with at most s prime divisors. In particular P1 denotes a prime number. In 1988 Koblitz, motivated by criptographic applications, (see [1]), conjectured ...
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Public key cryptosystem has many uses, such as to sign digitally, to realize electronic commerce. Especially, RSA public key cryptosystem has been the most widely used, but its key for ensuring sufficient security reaches about 2000 bits long. On the other hand, elliptic curve cryptosystem(ECC) has the same security level with about 7-fold smaller length key. Accordingly, ECC has been received ...
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ژورنال
عنوان ژورنال: Acta Arithmetica
سال: 2005
ISSN: 0065-1036,1730-6264
DOI: 10.4064/aa119-3-3