Subtraction?

[protosam]

Is subtraction just not possible due to the use of exponents in the Paillier system? When I was playing around with gaillier.go, for the life of me I couldn't figure out a way to plug subtraction in.

I noticed this when I ran this:

	k := new(big.Int).SetInt64(-10)
	c := new(big.Int).SetInt64(32)

	pub, priv, err := gaillier.GenerateKeyPair(rand.Reader, 256)
	if err != nil {
		log.Fatal(err)
	}

	//encrypt
	encC, err := gaillier.Encrypt(pub, c.Bytes())
	if err != nil {
		log.Fatal(err)
	}

	fmt.Println(encC)

	// 32 + -10
	res := gaillier.AddConstant(pub, encC, k.Bytes())

	// Decrypt
	decRes, err := gaillier.Decrypt(priv, res)
	if err != nil {
		log.Fatal(err)
	}

	// Get the result
	result := new(big.Int).SetBytes(decRes)

	fmt.Println(result)

[Deleted user]

Subtraction is the opposite of addition trying multiplying by -1 then adding.

…

On Mon, Sep 23, 2019, 05:43 Sam ***@***.***> wrote: Is subtraction just not possible due to the use of exponents in the Paillier system? When I was playing around with gaillier.go, for the life of me I couldn't figure out a way to plug subtraction in. I noticed this when I ran this: k := new(big.Int).SetInt64(-10) c := new(big.Int).SetInt64(32) pub, priv, err := gaillier.GenerateKeyPair(rand.Reader, 256) if err != nil { log.Fatal(err) } //encrypt encC, err := gaillier.Encrypt(pub, c.Bytes()) if err != nil { log.Fatal(err) } fmt.Println(encC) // 32 + -10 res := gaillier.AddConstant(pub, encC, k.Bytes()) // Decrypt decRes, err := gaillier.Decrypt(priv, res) if err != nil { log.Fatal(err) } // Get the result result := new(big.Int).SetBytes(decRes) fmt.Println(result) — You are receiving this because you are subscribed to this thread. Reply to this email directly, view it on GitHub <#1?email_source=notifications&email_token=AELDQNAUOBDMAT5IZIPSAM3QLBCNLA5CNFSM4IZGJIMKYY3PNVWWK3TUL52HS4DFUVEXG43VMWVGG33NNVSW45C7NFSM4HM56Z2Q>, or mute the thread <https://github.com/notifications/unsubscribe-auth/AELDQNG2PF36UGYL2FQ6QLDQLBCNLANCNFSM4IZGJIMA> .

[protosam]

I'm at a bit of a loss as to how to accomplish that because of this:
https://github.com/actuallyachraf/gomorph/blob/master/gaillier/gaillier.go#L161-L163

Specifically new(big.Int).Exp(pubkey.G, k, pubkey.Nsq) is causing any number to be positive, even though I'm making k negative.

I'm still trying to wrap my head around around the purpose of bit.Int.Exp(x, y, m int) and what it is actually doing.

[actuallyachraf]

The line you pointed to specifically the go Exp(x,y,m) does modular exponentiation.
As to your request, I am sorry I missed it but Paillier does modular arithmetic over n thus messages can't be negative (0 <= m <= n) is a required condition.