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miracl / MIRACL

MIRACL Cryptographic SDK: Multiprecision Integer and Rational Arithmetic Cryptographic Library is a C software library that is widely regarded by developers as the gold standard open source SDK for elliptic curve cryptography (ECC).
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Which one of the two fits supersingular curve in the paper? #52

Open SevenBruce opened 7 years ago

SevenBruce commented 7 years ago

I'm reading a paper, it says like following,

For the cryptographic schemes based on the bilinear pairing, we choose a Tate pairing e : G1 × G1 → GT defined on the super-singular elliptic curve E : y2 = x3 + 1 mod p‘ over the prime field Fp' with the prime order q', where p' and q' are 512-bit prime number and 160-bit prime number respectively.

I should use "ssp_pair.cpp" or "AKE2SST.CPP "? the paper is online with "Efficient and Privacy-Preserving Data Aggregation Scheme for Smart Grid against Internal Adversaries" with DOI:10.1109/TSG.2017.2720159

mcarrickscott commented 7 years ago

Hello,

You could use either ssp_pair.cpp or ake2sst.cpp.

Using ssp_pair.cpp should be much easier to implement this scheme. See for example wang.cpp in miracl distribution.

I can not access this paper.

In general pairing-based schemes are often described in the setting G1 x G1 -> GT. This is a Type-1 pairing.

But it is better if they can be moved to the setting G1 x G2 -> GT, which is a Type-3 pairing.

Type-3 pairing is more efficient and more secure. Unfortunately in the literature most schemes are described using Type-1 pairing, although they work just as well on Type-3.

Mike

On Fri, Sep 1, 2017 at 6:51 PM, SevenBruce notifications@github.com wrote:

I'm reading a paper, it says like following,

For the cryptographic schemes based on the bilinear pairing, we choose a Tate pairing e : G1 × G1 → GT defined on the super-singular elliptic curve E : y2 = x3 + 1 mod p‘ over the prime field Fp' with the prime order q', where p' and q' are 512-bit prime number and 160-bit prime number respectively.

I should use "ssp_pair.cpp" or "AKE2SST.CPP "? the paper is online with "Efficient and Privacy-Preserving Data Aggregation Scheme for Smart Grid against Internal Adversaries" with DOI:10.1109/TSG.2017.2720159

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SevenBruce commented 7 years ago

Hello, Mike,

How can I create a curve : y2 = x3 + 1, as now I know A = 0, B=1, n = 160, how can I found a p and q ?

Thanks

mcarrickscott commented 7 years ago

Hello,

See http://crypto.stanford.edu/~dabo/papers/bfibe.pdf

Page 20.

Mike

On Tue, Sep 5, 2017 at 5:08 PM, SevenBruce notifications@github.com wrote:

Hello, Mike,

How can I create a curve : y2 = x3 + 1, as now I know A = 0, B=1, n = 160, how can I found a p and q ?

Thanks

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SevenBruce commented 7 years ago

Hello，Mike, Thank you very much!!! Bruce