tss: Adds RSA Threshold signatures

tss/rsa/README.md

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+# RSA Threshold Signatures
+
+This is an implementation of ["Practical Threshold Signatures" by Victor Shoup](https://www.iacr.org/archive/eurocrypt2000/1807/18070209-new.pdf).
+Protocol 1 is implemented.
+
+## Threshold Primer
+
+Let *l* be the total number of players, *t* be the number of corrupted players, and *k* be the threshold.
+The idea of threshold signatures is that at least *k* players need to participate to form a valid signature.
+
+Setup consists of a dealer generating *l* key shares from a key pair and "dealing" them to the players. In this implementation the dealer is trusted.
+
+During the signing phase, at least *k* players use their key share and the message to generate a signature share.
+Finally, the *k* signature shares are combined to form a valid signature for the message.
+
+## Modifications
+
+1. Our implementation is not robust. That is, the corrupted players can prevent a valid signature from being formed by the non-corrupted players. As such, we remove all verification.
+2. The paper requires p and q to be safe primes. We do not.

tss/rsa/internal/pkcs1v15.go

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+// https://cs.opensource.google/go/go/+/refs/tags/go1.18.3:src/crypto/rsa/pkcs1v15.go
+
+// Copyright (c) 2009 The Go Authors. All rights reserved.
+//
+// Redistribution and use in source and binary forms, with or without
+// modification, are permitted provided that the following conditions are
+// met:
+//
+//    * Redistributions of source code must retain the above copyright
+// notice, this list of conditions and the following disclaimer.
+//    * Redistributions in binary form must reproduce the above
+// copyright notice, this list of conditions and the following disclaimer
+// in the documentation and/or other materials provided with the
+// distribution.
+//    * Neither the name of Google Inc. nor the names of its
+// contributors may be used to endorse or promote products derived from
+// this software without specific prior written permission.
+//
+// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+// "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+// LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
+// A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT
+// OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
+// SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
+// LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
+// DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
+// THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
+// (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
+// OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+
+// Copyright 2009 The Go Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package internal
+
+import (
+	"crypto"
+	"crypto/rsa"
+	"errors"
+	"fmt"
+)
+
+var hashPrefixes = map[crypto.Hash][]byte{
+	crypto.MD5: {
+		0x30, 0x20, 0x30, 0x0c, 0x06, 0x08, 0x2a, 0x86, 0x48, 0x86, 0xf7, 0x0d, 0x02, 0x05, 0x05,
+		0x00, 0x04, 0x10,
+	},
+	crypto.SHA1: {0x30, 0x21, 0x30, 0x09, 0x06, 0x05, 0x2b, 0x0e, 0x03, 0x02, 0x1a, 0x05, 0x00, 0x04, 0x14},
+	crypto.SHA224: {
+		0x30, 0x2d, 0x30, 0x0d, 0x06, 0x09, 0x60, 0x86, 0x48, 0x01, 0x65, 0x03, 0x04, 0x02, 0x04,
+		0x05, 0x00, 0x04, 0x1c,
+	},
+	crypto.SHA256: {
+		0x30, 0x31, 0x30, 0x0d, 0x06, 0x09, 0x60, 0x86, 0x48, 0x01, 0x65, 0x03, 0x04, 0x02, 0x01,
+		0x05, 0x00, 0x04, 0x20,
+	},
+	crypto.SHA384: {
+		0x30, 0x41, 0x30, 0x0d, 0x06, 0x09, 0x60, 0x86, 0x48, 0x01, 0x65, 0x03, 0x04, 0x02, 0x02,
+		0x05, 0x00, 0x04, 0x30,
+	},
+	crypto.SHA512: {
+		0x30, 0x51, 0x30, 0x0d, 0x06, 0x09, 0x60, 0x86, 0x48, 0x01, 0x65, 0x03, 0x04, 0x02, 0x03,
+		0x05, 0x00, 0x04, 0x40,
+	},
+	crypto.MD5SHA1:   {}, // A special TLS case which doesn't use an ASN1 prefix.
+	crypto.RIPEMD160: {0x30, 0x20, 0x30, 0x08, 0x06, 0x06, 0x28, 0xcf, 0x06, 0x03, 0x00, 0x31, 0x04, 0x14},
+}
+
+func PadPKCS1v15(pub *rsa.PublicKey, hash crypto.Hash, hashed []byte) ([]byte, error) {
+	hashLen, prefix, err := pkcs1v15HashInfo(hash, len(hashed))
+	if err != nil {
+		return nil, err
+	}
+
+	tLen := len(prefix) + hashLen
+	k := pub.Size()
+	if k < tLen+11 {
+		return nil, fmt.Errorf("message too long")
+	}
+
+	// EM = 0x00 || 0x01 || PS || 0x00 || T
+	em := make([]byte, k)
+	em[1] = 1
+	for i := 2; i < k-tLen-1; i++ {
+		em[i] = 0xff
+	}
+	copy(em[k-tLen:k-hashLen], prefix)
+	copy(em[k-hashLen:k], hashed)
+
+	return em, nil
+}
+
+func pkcs1v15HashInfo(hash crypto.Hash, inLen int) (hashLen int, prefix []byte, err error) {
+	// Special case: crypto.Hash(0) is used to indicate that the data is
+	// signed directly.
+	if hash == 0 {
+		return inLen, nil, nil
+	}
+
+	hashLen = hash.Size()
+	if inLen != hashLen {
+		return 0, nil, errors.New("threshold_internal: crypto/rsa: input must be hashed message")
+	}
+	prefix, ok := hashPrefixes[hash]
+	if !ok {
+		return 0, nil, errors.New("threshold_internal: crypto/rsa: unsupported hash function")
+	}
+	return
+}

tss/rsa/internal/pss/pss.go

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+// https://cs.opensource.google/go/go/+/refs/tags/go1.18.3:src/crypto/rsa/pss.go
+
+// Copyright (c) 2009 The Go Authors. All rights reserved.
+//
+// Redistribution and use in source and binary forms, with or without
+// modification, are permitted provided that the following conditions are
+// met:
+//
+//    * Redistributions of source code must retain the above copyright
+// notice, this list of conditions and the following disclaimer.
+//    * Redistributions in binary form must reproduce the above
+// copyright notice, this list of conditions and the following disclaimer
+// in the documentation and/or other materials provided with the
+// distribution.
+//    * Neither the name of Google Inc. nor the names of its
+// contributors may be used to endorse or promote products derived from
+// this software without specific prior written permission.
+//
+// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+// "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+// LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
+// A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT
+// OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
+// SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
+// LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
+// DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
+// THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
+// (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
+// OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+
+// Copyright 2013 The Go Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package pss
+
+// This file implements the RSASSA-PSS signature scheme according to RFC 8017.
+
+import (
+	"crypto"
+	"crypto/rsa"
+	"errors"
+	"hash"
+	"io"
+)
+
+// Per RFC 8017, Section 9.1
+//
+//     EM = MGF1 xor DB || H( 8*0x00 || mHash || salt ) || 0xbc
+//
+// where
+//
+//     DB = PS || 0x01 || salt
+//
+// and PS can be empty so
+//
+//     emLen = dbLen + hLen + 1 = psLen + sLen + hLen + 2
+//
+
+func emsaPSSEncode(mHash []byte, emBits int, salt []byte, hash hash.Hash) ([]byte, error) {
+	// See RFC 8017, Section 9.1.1.
+
+	hLen := hash.Size()
+	sLen := len(salt)
+	emLen := (emBits + 7) / 8
+
+	// 1.  If the length of M is greater than the input limitation for the
+	//     hash function (2^61 - 1 octets for SHA-1), output "message too
+	//     long" and stop.
+	//
+	// 2.  Let mHash = Hash(M), an octet string of length hLen.
+
+	if len(mHash) != hLen {
+		return nil, errors.New("crypto/rsa: input must be hashed with given hash")
+	}
+
+	// 3.  If emLen < hLen + sLen + 2, output "encoding error" and stop.
+
+	if emLen < hLen+sLen+2 {
+		return nil, errors.New("crypto/rsa: key size too small for PSS signature")
+	}
+
+	em := make([]byte, emLen)
+	psLen := emLen - sLen - hLen - 2
+	db := em[:psLen+1+sLen]
+	h := em[psLen+1+sLen : emLen-1]
+
+	// 4.  Generate a random octet string salt of length sLen; if sLen = 0,
+	//     then salt is the empty string.
+	//
+	// 5.  Let
+	//       M' = (0x)00 00 00 00 00 00 00 00 || mHash || salt;
+	//
+	//     M' is an octet string of length 8 + hLen + sLen with eight
+	//     initial zero octets.
+	//
+	// 6.  Let H = Hash(M'), an octet string of length hLen.
+
+	var prefix [8]byte
+
+	hash.Write(prefix[:])
+	hash.Write(mHash)
+	hash.Write(salt)
+
+	h = hash.Sum(h[:0])
+	hash.Reset()
+
+	// 7.  Generate an octet string PS consisting of emLen - sLen - hLen - 2
+	//     zero octets. The length of PS may be 0.
+	//
+	// 8.  Let DB = PS || 0x01 || salt; DB is an octet string of length
+	//     emLen - hLen - 1.
+
+	db[psLen] = 0x01
+	copy(db[psLen+1:], salt)
+
+	// 9.  Let dbMask = MGF(H, emLen - hLen - 1).
+	//
+	// 10. Let maskedDB = DB \xor dbMask.
+
+	mgf1XOR(db, hash, h)
+
+	// 11. Set the leftmost 8 * emLen - emBits bits of the leftmost octet in
+	//     maskedDB to zero.
+
+	db[0] &= 0xff >> (8*emLen - emBits)
+
+	// 12. Let EM = maskedDB || H || 0xbc.
+	em[emLen-1] = 0xbc
+
+	// 13. Output EM.
+	return em, nil
+}
+
+func padPSSWithSalt(pub *rsa.PublicKey, hash crypto.Hash, hashed, salt []byte) ([]byte, error) {
+	emBits := pub.N.BitLen() - 1
+	em, err := emsaPSSEncode(hashed, emBits, salt, hash.New())
+	if err != nil {
+		return nil, err
+	}
+	return em, nil
+}
+
+func saltLength(opts *rsa.PSSOptions) int {
+	if opts == nil {
+		return rsa.PSSSaltLengthAuto
+	}
+	return opts.SaltLength
+}
+
+func PadPSS(rand io.Reader, pub *rsa.PublicKey, hash crypto.Hash, digest []byte, opts *rsa.PSSOptions) ([]byte, error) {
+	if opts != nil && opts.Hash != 0 {
+		hash = opts.Hash
+	}
+
+	saltLength := saltLength(opts)
+	switch saltLength {
+	case rsa.PSSSaltLengthAuto:
+		saltLength = (pub.N.BitLen()-1+7)/8 - 2 - hash.Size()
+	case rsa.PSSSaltLengthEqualsHash:
+		saltLength = hash.Size()
+	}
+
+	salt := make([]byte, saltLength)
+	if _, err := io.ReadFull(rand, salt); err != nil {
+		return nil, err
+	}
+	return padPSSWithSalt(pub, hash, digest, salt)
+}

tss/rsa/internal/pss/rsa.go

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+// https://cs.opensource.google/go/go/+/refs/tags/go1.18.3:src/crypto/rsa/rsa.go
+
+// Copyright (c) 2009 The Go Authors. All rights reserved.
+//
+// Redistribution and use in source and binary forms, with or without
+// modification, are permitted provided that the following conditions are
+// met:
+//
+//    * Redistributions of source code must retain the above copyright
+// notice, this list of conditions and the following disclaimer.
+//    * Redistributions in binary form must reproduce the above
+// copyright notice, this list of conditions and the following disclaimer
+// in the documentation and/or other materials provided with the
+// distribution.
+//    * Neither the name of Google Inc. nor the names of its
+// contributors may be used to endorse or promote products derived from
+// this software without specific prior written permission.
+//
+// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+// "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+// LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
+// A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT
+// OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
+// SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
+// LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
+// DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
+// THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
+// (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
+// OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+
+package pss
+
+import (
+	"hash"
+)
+
+// incCounter increments a four byte, big-endian counter.
+func incCounter(c *[4]byte) {
+	if c[3]++; c[3] != 0 {
+		return
+	}
+	if c[2]++; c[2] != 0 {
+		return
+	}
+	if c[1]++; c[1] != 0 {
+		return
+	}
+	c[0]++
+}
+
+// mgf1XOR XORs the bytes in out with a mask generated using the MGF1 function
+// specified in PKCS #1 v2.1.
+func mgf1XOR(out []byte, hash hash.Hash, seed []byte) {
+	var counter [4]byte
+	var digest []byte
+
+	done := 0
+	for done < len(out) {
+		hash.Write(seed)
+		hash.Write(counter[0:4])
+		digest = hash.Sum(digest[:0])
+		hash.Reset()
+
+		for i := 0; i < len(digest) && done < len(out); i++ {
+			out[done] ^= digest[i]
+			done++
+		}
+		incCounter(&counter)
+	}
+}