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Rabindra Moirangthem avatar Crypto

computation time of pairing operations and their securities

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Rabindra Moirangthem

Suppose G1 is an elliptic group and G2 be a multiplicative group and they are of same prime order p and e is a bilinear pairing, e: G1 X G1 -> G2. The operations e(p,q)r and e(pr,q) gives equal result where p, q $\in$ G1 and r $\in$ Z*p.

The computation time of different cryptographic operations are given below source:

Operation Computation time (in ms)
Scalar multiplication in G1 0.24
Bilinear pairing 3.24
Multiplication operation in G2 1.46

The first operation e(p,q)r has a computation time of 3.24 + 1.46 = 4.7 ms while the second operation e(pr,q) has a computation time of 3.24 + 0.24 = 3.48 ms, even though both operations have the same result. Is there a compromise in the security aspect while using the less computation time operation.

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poncho avatar Crypto
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poncho

Is there a compromise in the security aspect while using the less computation time operation.

Given two algorithms that, given the same inputs, give identical outputs, the cryptographical security of those two algorithms are identical; after all, unless the attacker can measure the time, he can't tell which algorithm you used.

The one exception is if the attacker is assumed to have some sort of side channel available to him (because, if the side channel is considered an 'output', the two algorithms no longer generate identical outputs, and hence the above logic does not apply). However, unless we know what sort of side channel (and the vulnerabilities that the two implementations may have), we cannot say which is actually stronger.

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