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Has anyone written a constant-time BigInteger modular multiplication function in Java? I need to use modular multiplication for a cryptographic protocol, and I don't want to try to write it myself ...
#2: Post edited
by
skye
·
2026-02-03T02:21:59Z (8 months ago)
I forgot to include half the cryptographic protocol in the first revision.
- Has anyone written a constant-time `BigInteger` modular multiplication function in Java? I need to use modular multiplication for a cryptographic protocol, and I don't want to try to write it myself or rely on blinding.
For context, the reason I want to do this is to implement a cryptographic protocol to allow multiply peers peers, each of whom have a number $ a $ and a number $ b $, to decide whether the sum each peer's $ a $ value equals the sum of each peer's $ b $ value. My plan to implement this is to have each peer generate a random value $ r $, then publish $ g^{r+a} $ and $ g^{r+b} $. Since I assume $ a $ and $ b $ are high-entropy, this should not reveal a peer's value of $ a $ or $ b $.- I've also considered using ECC for this, but then I need to find a constant-time ECC implementation, and I'm more familiar with finite field arithmetic anyway.
- Has anyone written a constant-time `BigInteger` modular multiplication function in Java? I need to use modular multiplication for a cryptographic protocol, and I don't want to try to write it myself or rely on blinding.
- For context, the reason I want to do this is to implement a cryptographic protocol. The following arithmetic is in a finite field. Suppose a number of peers, each of whom have a number $ a $ and a number $ b $, want to decide whether the sum each peer's $ a $ value equals the sum of each peer's $ b $ value. My plan to implement this is to have each peer generate a random value $ r $ and compute $ g^r $, then publish $ g^rg^a $ and $ g^rg^b $. Then the product of every peer's $ g^rg^a $ value will equal the product of every peer's $ g^rg^b $ values, as long as the sum of every peer's $ a $ is equal to the sum of every peer's $ b $. Since I assume $ a $ and $ b $ are high-entropy, this should not reveal a peer's value of $ a $ or $ b $.
- In this protocol, I need a constant-time guarantee for multiplying $ g^r $ with $ g^a $ or $ g^b $, since I assume a or b are long-lived. The modular exponentiation doesn't need to be constant-time, since I only ever need to compute $ g^r $, $ g^a $, or $ g^b $ once.
- I've also considered using ECC for this, but then I need to find a constant-time ECC implementation, and I'm more familiar with finite field arithmetic anyway.
#1: Initial revision
by
skye
·
2026-02-03T02:07:51Z (8 months ago)
Constant-time modular multiplication library in Java?
Has anyone written a constant-time `BigInteger` modular multiplication function in Java? I need to use modular multiplication for a cryptographic protocol, and I don't want to try to write it myself or rely on blinding.
For context, the reason I want to do this is to implement a cryptographic protocol to allow multiply peers peers, each of whom have a number $ a $ and a number $ b $, to decide whether the sum each peer's $ a $ value equals the sum of each peer's $ b $ value. My plan to implement this is to have each peer generate a random value $ r $, then publish $ g^{r+a} $ and $ g^{r+b} $. Since I assume $ a $ and $ b $ are high-entropy, this should not reveal a peer's value of $ a $ or $ b $.
I've also considered using ECC for this, but then I need to find a constant-time ECC implementation, and I'm more familiar with finite field arithmetic anyway.