From 57dc4c21f4880e359fc3c85d7d85bdf3a8950220 Mon Sep 17 00:00:00 2001
From: siddharth ravikumar <s@ricketyspace.net>
Date: Fri, 25 Nov 2022 12:50:50 -0500
Subject: challenge: do challenge 40

---
 challenge/c40.go | 82 ++++++++++++++++++++++++++++++++++++++++++++++++++++++++
 cryptopals.go    |  2 ++
 2 files changed, 84 insertions(+)
 create mode 100644 challenge/c40.go

diff --git a/challenge/c40.go b/challenge/c40.go
new file mode 100644
index 0000000..ec16059
--- /dev/null
+++ b/challenge/c40.go
@@ -0,0 +1,82 @@
+// Copyright © 2022 siddharth ravikumar <s@ricketyspace.net>
+// SPDX-License-Identifier: ISC
+
+package challenge
+
+import (
+	"fmt"
+	"math/big"
+
+	"ricketyspace.net/cryptopals/lib"
+)
+
+func C40() {
+	msg := []byte("42 is the answer.")
+
+	// Generate 3 rsa key pairs and capture the their public keys.
+	var rsaPubs []*lib.RSAPub
+	for i := 0; i < 3; i++ {
+		rsa, err := lib.RSAGenKey()
+		if err != nil {
+			fmt.Printf("gen key failed: %v", err)
+			return
+		}
+		rsaPubs = append(rsaPubs, rsa.Public)
+	}
+
+	// Encrypt message with the 3 rsa public keys.
+	var ciphers [][]byte
+	for i := 0; i < 3; i++ {
+		enc := rsaPubs[i].Encrypt(msg)
+		if len(enc) < 1 {
+			fmt.Printf("encrypt failed: %v", enc)
+			return
+		}
+		ciphers = append(ciphers, enc)
+	}
+
+	// Compute m_s_n
+	var msn []*big.Int
+	for i := 0; i < 3; i++ {
+		msn = append(msn, big.NewInt(0).Mul(
+			rsaPubs[(i+1)%3].N(), rsaPubs[(i+2)%3].N(),
+		))
+	}
+
+	// Compute N_012
+	n012 := big.NewInt(1)
+	for _, rpub := range rsaPubs {
+		n012 = n012.Mul(n012, rpub.N())
+	}
+
+	// Compute combination of residues.
+	result := big.NewInt(0)
+	for i := 0; i < 3; i++ {
+		r := big.NewInt(0).Mul(
+			big.NewInt(0).SetBytes(ciphers[i]),
+			msn[i],
+		) // c_i * m_s_i
+
+		// invmod(m_s_i, n_i)
+		im, err := lib.InvMod(msn[i], rsaPubs[i].N())
+		if err != nil {
+			fmt.Printf("invmod: invmod(m_s_%d, n_%d): %v",
+				i, i, err,
+			)
+			return
+		}
+
+		// c_i * m_s_i * invmod(m_s_i, n_i)
+		r = r.Mul(r, im)
+
+		// Add to result.
+		result.Add(result, r)
+	}
+
+	// result mod N_012
+	result = result.Mod(result, n012)
+
+	// Cube root the result.
+	deci := lib.BigIntCubeRoot(result)
+	fmt.Printf("Decrypted message: %s\n", deci.Bytes())
+}
diff --git a/cryptopals.go b/cryptopals.go
index 8ff0d6c..0452433 100644
--- a/cryptopals.go
+++ b/cryptopals.go
@@ -98,5 +98,7 @@ func main() {
 		challenge.C38(flag.Args())
 	case 39:
 		challenge.C39()
+	case 40:
+		challenge.C40()
 	}
 }
-- 
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