CryptoComputing with rationals
... recover rationals using the Paillier cryptosystem. In this section, we prove the unicity of the recovered solution (r, s) if the conditions of Theorem 1 are respected. Theorem 1. If t0 = rs−1 mod N , −R ≤ r ≤ R and 0 < s ≤ S, then the algorithm of Gauss uniquely recovers r and s provided 2RS < N . P ...
... recover rationals using the Paillier cryptosystem. In this section, we prove the unicity of the recovered solution (r, s) if the conditions of Theorem 1 are respected. Theorem 1. If t0 = rs−1 mod N , −R ≤ r ≤ R and 0 < s ≤ S, then the algorithm of Gauss uniquely recovers r and s provided 2RS < N . P ...
A practical Differential Power Analysis Attack against the Miller
... and Joye have shown in [4]. Let l ∈ N∗ , and G1 ⊂ E(Fq ), G2 ⊂ E(Fqk ), G3 ⊂ F∗qk be three groups of order l, and k be the smallest integer such that l divides (q k − 1), k is called the embedding degree. The most useful property in pairing based cryptography is bilinearity: e([n]P, [m]Q) = e(P, Q)n ...
... and Joye have shown in [4]. Let l ∈ N∗ , and G1 ⊂ E(Fq ), G2 ⊂ E(Fqk ), G3 ⊂ F∗qk be three groups of order l, and k be the smallest integer such that l divides (q k − 1), k is called the embedding degree. The most useful property in pairing based cryptography is bilinearity: e([n]P, [m]Q) = e(P, Q)n ...
![arXiv:math/9802122v1 [math.CO] 27 Feb 1998](http://s1.studyres.com/store/data/013469206_1-76e512f42e60a4643a93990b56cee184-300x300.png)
3.3 Factor Rings
... In the next section we will look at conditions on I under which R/I is an integral domain or a field, for a commutative ring R. Our final goal in this section is to prove the Fundamental Homomorphism Theorem for rings, which states that if φ : R −→ S is a ring homomorphism, then the image of φ is b ...
... In the next section we will look at conditions on I under which R/I is an integral domain or a field, for a commutative ring R. Our final goal in this section is to prove the Fundamental Homomorphism Theorem for rings, which states that if φ : R −→ S is a ring homomorphism, then the image of φ is b ...
