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language fixes
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@@ -46,9 +46,9 @@ and verifying that a given solution is correct.
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Pairing-based cryptography works by operating on mathematical functions that
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satisfy the property of 'bilinear mapping'. This property is satisfied for
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functions `e` with values `P`, `Q`, and `R` where `e(P, Q + R) = e(P, Q) + e(P, R)`
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functions `e` with values `P`, `Q`, and `R` where `e(P, Q + R) = e(P, Q) * e(P, R)`
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and `e(P + Q, R) = e(P, R) * e(Q, R)`. The most familiar example of this is
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exponentiation. Written in common notation, P^(Q+R) = P^Q * P^R.
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exponentiation. Written in common notation, `P^(Q+R) = P^Q * P^R`.
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Pairing-based elliptic-curve cryptography creates a bilinear mapping using
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an elliptic-curve. With some original curve, you can define two groups,
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@@ -75,7 +75,7 @@ decide which should be larger, the public keys or the signatures.
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BLS signatures rely on pairing-based elliptic-curve cryptography to produce
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various types of signatures. For a more in-depth but still high level discussion
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pairing-based elliptic-curve cryptography, see Vitalik Buterin's post on
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[Exploring Elliptic Curve Pairings][vitalik-curve-post]. For much more in
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[Exploring Elliptic Curve Pairings][vitalik-pairing-post]. For much more in
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depth discussion, see the specific paper on BLS12-381,
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[Compact Multi-Signatures for Smaller Blockchains][multi-signatures-smaller-blockchains].
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@@ -223,7 +223,7 @@ Below is a list of popular HSMs along with their support for BLS signatures.
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* Amazon Cloud HSM
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* [No support][cloud-hsm-support]
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* Ledger
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* [Lists support for the BLS12-381 curve][ledger-bls-announce],
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* [Lists support for the BLS12-381 curve][ledger-bls-announce]
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I cannot find support listed for Google Cloud, although perhaps it exists.
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