verifier.cpp - android_bootable_recovery - Gitiles

 /*
  * Copyright (C) 2008 The Android Open Source Project
  *
  * Licensed under the Apache License, Version 2.0 (the "License");
  * you may not use this file except in compliance with the License.
  * You may obtain a copy of the License at
  *
  *      http://www.apache.org/licenses/LICENSE-2.0
  *
  * Unless required by applicable law or agreed to in writing, software
  * distributed under the License is distributed on an "AS IS" BASIS,
  * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
  * See the License for the specific language governing permissions and
  * limitations under the License.
  */

 #include "verifier.h"

 #include <errno.h>
 #include <stdio.h>
 #include <stdlib.h>
 #include <string.h>

 #include <algorithm>
 #include <memory>

 #include <android-base/logging.h>
 #include <openssl/bn.h>
 #include <openssl/ecdsa.h>
 #include <openssl/obj_mac.h>

 #include "asn1_decoder.h"
 #include "common.h"
 #include "print_sha1.h"
 #include "ui.h"

 static constexpr size_t MiB = 1024 * 1024;

 /*
  * Simple version of PKCS#7 SignedData extraction. This extracts the
  * signature OCTET STRING to be used for signature verification.
  *
  * For full details, see http://www.ietf.org/rfc/rfc3852.txt
  *
  * The PKCS#7 structure looks like:
  *
  *   SEQUENCE (ContentInfo)
  *     OID (ContentType)
  *     [0] (content)
  *       SEQUENCE (SignedData)
  *         INTEGER (version CMSVersion)
  *         SET (DigestAlgorithmIdentifiers)
  *         SEQUENCE (EncapsulatedContentInfo)
  *         [0] (CertificateSet OPTIONAL)
  *         [1] (RevocationInfoChoices OPTIONAL)
  *         SET (SignerInfos)
  *           SEQUENCE (SignerInfo)
  *             INTEGER (CMSVersion)
  *             SEQUENCE (SignerIdentifier)
  *             SEQUENCE (DigestAlgorithmIdentifier)
  *             SEQUENCE (SignatureAlgorithmIdentifier)
  *             OCTET STRING (SignatureValue)
  */
 static bool read_pkcs7(uint8_t* pkcs7_der, size_t pkcs7_der_len, uint8_t** sig_der,
         size_t* sig_der_length) {
     asn1_context_t* ctx = asn1_context_new(pkcs7_der, pkcs7_der_len);
     if (ctx == NULL) {
         return false;
     }

     asn1_context_t* pkcs7_seq = asn1_sequence_get(ctx);
     if (pkcs7_seq != NULL && asn1_sequence_next(pkcs7_seq)) {
         asn1_context_t *signed_data_app = asn1_constructed_get(pkcs7_seq);
         if (signed_data_app != NULL) {
             asn1_context_t* signed_data_seq = asn1_sequence_get(signed_data_app);
             if (signed_data_seq != NULL
                     && asn1_sequence_next(signed_data_seq)
                     && asn1_sequence_next(signed_data_seq)
                     && asn1_sequence_next(signed_data_seq)
                     && asn1_constructed_skip_all(signed_data_seq)) {
                 asn1_context_t *sig_set = asn1_set_get(signed_data_seq);
                 if (sig_set != NULL) {
                     asn1_context_t* sig_seq = asn1_sequence_get(sig_set);
                     if (sig_seq != NULL
                             && asn1_sequence_next(sig_seq)
                             && asn1_sequence_next(sig_seq)
                             && asn1_sequence_next(sig_seq)
                             && asn1_sequence_next(sig_seq)) {
                         uint8_t* sig_der_ptr;
                         if (asn1_octet_string_get(sig_seq, &sig_der_ptr, sig_der_length)) {
                             *sig_der = (uint8_t*) malloc(*sig_der_length);
                             if (*sig_der != NULL) {
                                 memcpy(*sig_der, sig_der_ptr, *sig_der_length);
                             }
                         }
                         asn1_context_free(sig_seq);
                     }
                     asn1_context_free(sig_set);
                 }
                 asn1_context_free(signed_data_seq);
             }
             asn1_context_free(signed_data_app);
         }
         asn1_context_free(pkcs7_seq);
     }
     asn1_context_free(ctx);

     return *sig_der != NULL;
 }

 // Look for an RSA signature embedded in the .ZIP file comment given
 // the path to the zip.  Verify it matches one of the given public
 // keys.
 //
 // Return VERIFY_SUCCESS, VERIFY_FAILURE (if any error is encountered
 // or no key matches the signature).

 int verify_file(unsigned char* addr, size_t length,
                 const std::vector<Certificate>& keys) {
     ui->SetProgress(0.0);

     // An archive with a whole-file signature will end in six bytes:
     //
     //   (2-byte signature start) $ff $ff (2-byte comment size)
     //
     // (As far as the ZIP format is concerned, these are part of the
     // archive comment.)  We start by reading this footer, this tells
     // us how far back from the end we have to start reading to find
     // the whole comment.

 #define FOOTER_SIZE 6

     if (length < FOOTER_SIZE) {
         LOG(ERROR) << "not big enough to contain footer";
         return VERIFY_FAILURE;
     }

     unsigned char* footer = addr + length - FOOTER_SIZE;

     if (footer[2] != 0xff || footer[3] != 0xff) {
         LOG(ERROR) << "footer is wrong";
         return VERIFY_FAILURE;
     }

     size_t comment_size = footer[4] + (footer[5] << 8);
     size_t signature_start = footer[0] + (footer[1] << 8);
     LOG(INFO) << "comment is " << comment_size << " bytes; signature is " << signature_start
               << " bytes from end";

     if (signature_start > comment_size) {
         LOGE("signature start: %zu is larger than comment size: %zu\n", signature_start,
              comment_size);
         return VERIFY_FAILURE;
     }

     if (signature_start <= FOOTER_SIZE) {
         LOG(ERROR) << "Signature start is in the footer";
         return VERIFY_FAILURE;
     }

 #define EOCD_HEADER_SIZE 22

     // The end-of-central-directory record is 22 bytes plus any
     // comment length.
     size_t eocd_size = comment_size + EOCD_HEADER_SIZE;

     if (length < eocd_size) {
         LOG(ERROR) << "not big enough to contain EOCD";
         return VERIFY_FAILURE;
     }

     // Determine how much of the file is covered by the signature.
     // This is everything except the signature data and length, which
     // includes all of the EOCD except for the comment length field (2
     // bytes) and the comment data.
     size_t signed_len = length - eocd_size + EOCD_HEADER_SIZE - 2;

     unsigned char* eocd = addr + length - eocd_size;

     // If this is really is the EOCD record, it will begin with the
     // magic number $50 $4b $05 $06.
     if (eocd[0] != 0x50 || eocd[1] != 0x4b ||
         eocd[2] != 0x05 || eocd[3] != 0x06) {
         LOG(ERROR) << "signature length doesn't match EOCD marker";
         return VERIFY_FAILURE;
     }

     for (size_t i = 4; i < eocd_size-3; ++i) {
         if (eocd[i  ] == 0x50 && eocd[i+1] == 0x4b &&
             eocd[i+2] == 0x05 && eocd[i+3] == 0x06) {
             // if the sequence $50 $4b $05 $06 appears anywhere after
             // the real one, libziparchive will find the later (wrong) one,
             // which could be exploitable.  Fail verification if
             // this sequence occurs anywhere after the real one.
             LOG(ERROR) << "EOCD marker occurs after start of EOCD";
             return VERIFY_FAILURE;
         }
     }

     bool need_sha1 = false;
     bool need_sha256 = false;
     for (const auto& key : keys) {
         switch (key.hash_len) {
             case SHA_DIGEST_LENGTH: need_sha1 = true; break;
             case SHA256_DIGEST_LENGTH: need_sha256 = true; break;
         }
     }

     SHA_CTX sha1_ctx;
     SHA256_CTX sha256_ctx;
     SHA1_Init(&sha1_ctx);
     SHA256_Init(&sha256_ctx);

     double frac = -1.0;
     size_t so_far = 0;
     while (so_far < signed_len) {
         // On a Nexus 5X, experiment showed 16MiB beat 1MiB by 6% faster for a
         // 1196MiB full OTA and 60% for an 89MiB incremental OTA.
         // http://b/28135231.
         size_t size = std::min(signed_len - so_far, 16 * MiB);

         if (need_sha1) SHA1_Update(&sha1_ctx, addr + so_far, size);
         if (need_sha256) SHA256_Update(&sha256_ctx, addr + so_far, size);
         so_far += size;

         double f = so_far / (double)signed_len;
         if (f > frac + 0.02 || size == so_far) {
             ui->SetProgress(f);
             frac = f;
         }
     }

     uint8_t sha1[SHA_DIGEST_LENGTH];
     SHA1_Final(sha1, &sha1_ctx);
     uint8_t sha256[SHA256_DIGEST_LENGTH];
     SHA256_Final(sha256, &sha256_ctx);

     uint8_t* sig_der = nullptr;
     size_t sig_der_length = 0;

     uint8_t* signature = eocd + eocd_size - signature_start;
     size_t signature_size = signature_start - FOOTER_SIZE;

     LOG(INFO) << "signature (offset: " << std::hex << (length - signature_start) << ", length: "
               << signature_size << "): " << print_hex(signature, signature_size);

     if (!read_pkcs7(signature, signature_size, &sig_der, &sig_der_length)) {
         LOG(ERROR) << "Could not find signature DER block";
         return VERIFY_FAILURE;
     }

     /*
      * Check to make sure at least one of the keys matches the signature. Since
      * any key can match, we need to try each before determining a verification
      * failure has happened.
      */
     size_t i = 0;
     for (const auto& key : keys) {
         const uint8_t* hash;
         int hash_nid;
         switch (key.hash_len) {
             case SHA_DIGEST_LENGTH:
                 hash = sha1;
                 hash_nid = NID_sha1;
                 break;
             case SHA256_DIGEST_LENGTH:
                 hash = sha256;
                 hash_nid = NID_sha256;
                 break;
             default:
                 continue;
         }

         // The 6 bytes is the "(signature_start) $ff $ff (comment_size)" that
         // the signing tool appends after the signature itself.
         if (key.key_type == Certificate::KEY_TYPE_RSA) {
             if (!RSA_verify(hash_nid, hash, key.hash_len, sig_der,
                             sig_der_length, key.rsa.get())) {
                 LOG(INFO) << "failed to verify against RSA key " << i;
                 continue;
             }

             LOG(INFO) << "whole-file signature verified against RSA key " << i;
             free(sig_der);
             return VERIFY_SUCCESS;
         } else if (key.key_type == Certificate::KEY_TYPE_EC
                 && key.hash_len == SHA256_DIGEST_LENGTH) {
             if (!ECDSA_verify(0, hash, key.hash_len, sig_der,
                               sig_der_length, key.ec.get())) {
                 LOG(INFO) << "failed to verify against EC key " << i;
                 continue;
             }

             LOG(INFO) << "whole-file signature verified against EC key " << i;
             free(sig_der);
             return VERIFY_SUCCESS;
         } else {
             LOG(INFO) << "Unknown key type " << key.key_type;
         }
         i++;
     }

     if (need_sha1) {
         LOG(INFO) << "SHA-1 digest: " << print_hex(sha1, SHA_DIGEST_LENGTH);
     }
     if (need_sha256) {
         LOG(INFO) << "SHA-256 digest: " << print_hex(sha256, SHA256_DIGEST_LENGTH);
     }
     free(sig_der);
     LOG(ERROR) << "failed to verify whole-file signature";
     return VERIFY_FAILURE;
 }

 std::unique_ptr<RSA, RSADeleter> parse_rsa_key(FILE* file, uint32_t exponent) {
     // Read key length in words and n0inv. n0inv is a precomputed montgomery
     // parameter derived from the modulus and can be used to speed up
     // verification. n0inv is 32 bits wide here, assuming the verification logic
     // uses 32 bit arithmetic. However, BoringSSL may use a word size of 64 bits
     // internally, in which case we don't have a valid n0inv. Thus, we just
     // ignore the montgomery parameters and have BoringSSL recompute them
     // internally. If/When the speedup from using the montgomery parameters
     // becomes relevant, we can add more sophisticated code here to obtain a
     // 64-bit n0inv and initialize the montgomery parameters in the key object.
     uint32_t key_len_words = 0;
     uint32_t n0inv = 0;
     if (fscanf(file, " %i , 0x%x", &key_len_words, &n0inv) != 2) {
         return nullptr;
     }

     if (key_len_words > 8192 / 32) {
         LOG(ERROR) << "key length (" << key_len_words << ") too large";
         return nullptr;
     }

     // Read the modulus.
     std::unique_ptr<uint32_t[]> modulus(new uint32_t[key_len_words]);
     if (fscanf(file, " , { %u", &modulus[0]) != 1) {
         return nullptr;
     }
     for (uint32_t i = 1; i < key_len_words; ++i) {
         if (fscanf(file, " , %u", &modulus[i]) != 1) {
             return nullptr;
         }
     }

     // Cconvert from little-endian array of little-endian words to big-endian
     // byte array suitable as input for BN_bin2bn.
     std::reverse((uint8_t*)modulus.get(),
                  (uint8_t*)(modulus.get() + key_len_words));

     // The next sequence of values is the montgomery parameter R^2. Since we
     // generally don't have a valid |n0inv|, we ignore this (see comment above).
     uint32_t rr_value;
     if (fscanf(file, " } , { %u", &rr_value) != 1) {
         return nullptr;
     }
     for (uint32_t i = 1; i < key_len_words; ++i) {
         if (fscanf(file, " , %u", &rr_value) != 1) {
             return nullptr;
         }
     }
     if (fscanf(file, " } } ") != 0) {
         return nullptr;
     }

     // Initialize the key.
     std::unique_ptr<RSA, RSADeleter> key(RSA_new());
     if (!key) {
       return nullptr;
     }

     key->n = BN_bin2bn((uint8_t*)modulus.get(),
                        key_len_words * sizeof(uint32_t), NULL);
     if (!key->n) {
       return nullptr;
     }

     key->e = BN_new();
     if (!key->e || !BN_set_word(key->e, exponent)) {
       return nullptr;
     }

     return key;
 }

 struct BNDeleter {
   void operator()(BIGNUM* bn) {
     BN_free(bn);
   }
 };

 std::unique_ptr<EC_KEY, ECKEYDeleter> parse_ec_key(FILE* file) {
     uint32_t key_len_bytes = 0;
     if (fscanf(file, " %i", &key_len_bytes) != 1) {
         return nullptr;
     }

     std::unique_ptr<EC_GROUP, void (*)(EC_GROUP*)> group(
         EC_GROUP_new_by_curve_name(NID_X9_62_prime256v1), EC_GROUP_free);
     if (!group) {
         return nullptr;
     }

     // Verify that |key_len| matches the group order.
     if (key_len_bytes != BN_num_bytes(EC_GROUP_get0_order(group.get()))) {
         return nullptr;
     }

     // Read the public key coordinates. Note that the byte order in the file is
     // little-endian, so we convert to big-endian here.
     std::unique_ptr<uint8_t[]> bytes(new uint8_t[key_len_bytes]);
     std::unique_ptr<BIGNUM, BNDeleter> point[2];
     for (int i = 0; i < 2; ++i) {
         unsigned int byte = 0;
         if (fscanf(file, " , { %u", &byte) != 1) {
             return nullptr;
         }
         bytes[key_len_bytes - 1] = byte;

         for (size_t i = 1; i < key_len_bytes; ++i) {
             if (fscanf(file, " , %u", &byte) != 1) {
                 return nullptr;
             }
             bytes[key_len_bytes - i - 1] = byte;
         }

         point[i].reset(BN_bin2bn(bytes.get(), key_len_bytes, nullptr));
         if (!point[i]) {
             return nullptr;
         }

         if (fscanf(file, " }") != 0) {
             return nullptr;
         }
     }

     if (fscanf(file, " } ") != 0) {
         return nullptr;
     }

     // Create and initialize the key.
     std::unique_ptr<EC_KEY, ECKEYDeleter> key(EC_KEY_new());
     if (!key || !EC_KEY_set_group(key.get(), group.get()) ||
         !EC_KEY_set_public_key_affine_coordinates(key.get(), point[0].get(),
                                                   point[1].get())) {
         return nullptr;
     }

     return key;
 }

 // Reads a file containing one or more public keys as produced by
 // DumpPublicKey:  this is an RSAPublicKey struct as it would appear
 // as a C source literal, eg:
 //
 //  "{64,0xc926ad21,{1795090719,...,-695002876},{-857949815,...,1175080310}}"
 //
 // For key versions newer than the original 2048-bit e=3 keys
 // supported by Android, the string is preceded by a version
 // identifier, eg:
 //
 //  "v2 {64,0xc926ad21,{1795090719,...,-695002876},{-857949815,...,1175080310}}"
 //
 // (Note that the braces and commas in this example are actual
 // characters the parser expects to find in the file; the ellipses
 // indicate more numbers omitted from this example.)
 //
 // The file may contain multiple keys in this format, separated by
 // commas.  The last key must not be followed by a comma.
 //
 // A Certificate is a pair of an RSAPublicKey and a particular hash
 // (we support SHA-1 and SHA-256; we store the hash length to signify
 // which is being used).  The hash used is implied by the version number.
 //
 //       1: 2048-bit RSA key with e=3 and SHA-1 hash
 //       2: 2048-bit RSA key with e=65537 and SHA-1 hash
 //       3: 2048-bit RSA key with e=3 and SHA-256 hash
 //       4: 2048-bit RSA key with e=65537 and SHA-256 hash
 //       5: 256-bit EC key using the NIST P-256 curve parameters and SHA-256 hash
 //
 // Returns true on success, and appends the found keys (at least one) to certs.
 // Otherwise returns false if the file failed to parse, or if it contains zero
 // keys. The contents in certs would be unspecified on failure.
 bool load_keys(const char* filename, std::vector<Certificate>& certs) {
     std::unique_ptr<FILE, decltype(&fclose)> f(fopen(filename, "r"), fclose);
     if (!f) {
         PLOG(ERROR) << "error opening " << filename;
         return false;
     }

     while (true) {
         certs.emplace_back(0, Certificate::KEY_TYPE_RSA, nullptr, nullptr);
         Certificate& cert = certs.back();
         uint32_t exponent = 0;

         char start_char;
         if (fscanf(f.get(), " %c", &start_char) != 1) return false;
         if (start_char == '{') {
             // a version 1 key has no version specifier.
             cert.key_type = Certificate::KEY_TYPE_RSA;
             exponent = 3;
             cert.hash_len = SHA_DIGEST_LENGTH;
         } else if (start_char == 'v') {
             int version;
             if (fscanf(f.get(), "%d {", &version) != 1) return false;
             switch (version) {
                 case 2:
                     cert.key_type = Certificate::KEY_TYPE_RSA;
                     exponent = 65537;
                     cert.hash_len = SHA_DIGEST_LENGTH;
                     break;
                 case 3:
                     cert.key_type = Certificate::KEY_TYPE_RSA;
                     exponent = 3;
                     cert.hash_len = SHA256_DIGEST_LENGTH;
                     break;
                 case 4:
                     cert.key_type = Certificate::KEY_TYPE_RSA;
                     exponent = 65537;
                     cert.hash_len = SHA256_DIGEST_LENGTH;
                     break;
                 case 5:
                     cert.key_type = Certificate::KEY_TYPE_EC;
                     cert.hash_len = SHA256_DIGEST_LENGTH;
                     break;
                 default:
                     return false;
             }
         }

         if (cert.key_type == Certificate::KEY_TYPE_RSA) {
             cert.rsa = parse_rsa_key(f.get(), exponent);
             if (!cert.rsa) {
               return false;
             }

             LOG(INFO) << "read key e=" << exponent << " hash=" << cert.hash_len;
         } else if (cert.key_type == Certificate::KEY_TYPE_EC) {
             cert.ec = parse_ec_key(f.get());
             if (!cert.ec) {
               return false;
             }
         } else {
             LOG(ERROR) << "Unknown key type " << cert.key_type;
             return false;
         }

         // if the line ends in a comma, this file has more keys.
         int ch = fgetc(f.get());
         if (ch == ',') {
             // more keys to come.
             continue;
         } else if (ch == EOF) {
             break;
         } else {
             LOG(ERROR) << "unexpected character between keys";
             return false;
         }
     }

     return true;
 }
	/*
	* Copyright (C) 2008 The Android Open Source Project
	*
	* Licensed under the Apache License, Version 2.0 (the "License");
	* you may not use this file except in compliance with the License.
	* You may obtain a copy of the License at
	*
	* http://www.apache.org/licenses/LICENSE-2.0
	*
	* Unless required by applicable law or agreed to in writing, software
	* distributed under the License is distributed on an "AS IS" BASIS,
	* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
	* See the License for the specific language governing permissions and
	* limitations under the License.
	*/

	#include "verifier.h"

	#include <errno.h>
	#include <stdio.h>
	#include <stdlib.h>
	#include <string.h>

	#include <algorithm>
	#include <memory>

	#include <android-base/logging.h>
	#include <openssl/bn.h>
	#include <openssl/ecdsa.h>
	#include <openssl/obj_mac.h>

	#include "asn1_decoder.h"
	#include "common.h"
	#include "print_sha1.h"
	#include "ui.h"

	static constexpr size_t MiB = 1024 * 1024;

	/*
	* Simple version of PKCS#7 SignedData extraction. This extracts the
	* signature OCTET STRING to be used for signature verification.
	*
	* For full details, see http://www.ietf.org/rfc/rfc3852.txt
	*
	* The PKCS#7 structure looks like:
	*
	* SEQUENCE (ContentInfo)
	* OID (ContentType)
	* [0] (content)
	* SEQUENCE (SignedData)
	* INTEGER (version CMSVersion)
	* SET (DigestAlgorithmIdentifiers)
	* SEQUENCE (EncapsulatedContentInfo)
	* [0] (CertificateSet OPTIONAL)
	* [1] (RevocationInfoChoices OPTIONAL)
	* SET (SignerInfos)
	* SEQUENCE (SignerInfo)
	* INTEGER (CMSVersion)
	* SEQUENCE (SignerIdentifier)
	* SEQUENCE (DigestAlgorithmIdentifier)
	* SEQUENCE (SignatureAlgorithmIdentifier)
	* OCTET STRING (SignatureValue)
	*/
	static bool read_pkcs7(uint8_t* pkcs7_der, size_t pkcs7_der_len, uint8_t** sig_der,
	size_t* sig_der_length) {
	asn1_context_t* ctx = asn1_context_new(pkcs7_der, pkcs7_der_len);
	if (ctx == NULL) {
	return false;
	}

	asn1_context_t* pkcs7_seq = asn1_sequence_get(ctx);
	if (pkcs7_seq != NULL && asn1_sequence_next(pkcs7_seq)) {
	asn1_context_t *signed_data_app = asn1_constructed_get(pkcs7_seq);
	if (signed_data_app != NULL) {
	asn1_context_t* signed_data_seq = asn1_sequence_get(signed_data_app);
	if (signed_data_seq != NULL
	&& asn1_sequence_next(signed_data_seq)
	&& asn1_sequence_next(signed_data_seq)
	&& asn1_sequence_next(signed_data_seq)
	&& asn1_constructed_skip_all(signed_data_seq)) {
	asn1_context_t *sig_set = asn1_set_get(signed_data_seq);
	if (sig_set != NULL) {
	asn1_context_t* sig_seq = asn1_sequence_get(sig_set);
	if (sig_seq != NULL
	&& asn1_sequence_next(sig_seq)
	&& asn1_sequence_next(sig_seq)
	&& asn1_sequence_next(sig_seq)
	&& asn1_sequence_next(sig_seq)) {
	uint8_t* sig_der_ptr;
	if (asn1_octet_string_get(sig_seq, &sig_der_ptr, sig_der_length)) {
	sig_der = (uint8_t) malloc(*sig_der_length);
	if (*sig_der != NULL) {
	memcpy(sig_der, sig_der_ptr, sig_der_length);
	}
	}
	asn1_context_free(sig_seq);
	}
	asn1_context_free(sig_set);
	}
	asn1_context_free(signed_data_seq);
	}
	asn1_context_free(signed_data_app);
	}
	asn1_context_free(pkcs7_seq);
	}
	asn1_context_free(ctx);

	return *sig_der != NULL;
	}

	// Look for an RSA signature embedded in the .ZIP file comment given
	// the path to the zip. Verify it matches one of the given public
	// keys.
	//
	// Return VERIFY_SUCCESS, VERIFY_FAILURE (if any error is encountered
	// or no key matches the signature).

	int verify_file(unsigned char* addr, size_t length,
	const std::vector<Certificate>& keys) {
	ui->SetProgress(0.0);

	// An archive with a whole-file signature will end in six bytes:
	//
	// (2-byte signature start) $ff $ff (2-byte comment size)
	//
	// (As far as the ZIP format is concerned, these are part of the
	// archive comment.) We start by reading this footer, this tells
	// us how far back from the end we have to start reading to find
	// the whole comment.

	#define FOOTER_SIZE 6

	if (length < FOOTER_SIZE) {
	LOG(ERROR) << "not big enough to contain footer";
	return VERIFY_FAILURE;
	}

	unsigned char* footer = addr + length - FOOTER_SIZE;

	if (footer[2] != 0xff \|\| footer[3] != 0xff) {
	LOG(ERROR) << "footer is wrong";
	return VERIFY_FAILURE;
	}

	size_t comment_size = footer[4] + (footer[5] << 8);
	size_t signature_start = footer[0] + (footer[1] << 8);
	LOG(INFO) << "comment is " << comment_size << " bytes; signature is " << signature_start
	<< " bytes from end";

	if (signature_start > comment_size) {
	LOGE("signature start: %zu is larger than comment size: %zu\n", signature_start,
	comment_size);
	return VERIFY_FAILURE;
	}

	if (signature_start <= FOOTER_SIZE) {
	LOG(ERROR) << "Signature start is in the footer";
	return VERIFY_FAILURE;
	}

	#define EOCD_HEADER_SIZE 22

	// The end-of-central-directory record is 22 bytes plus any
	// comment length.
	size_t eocd_size = comment_size + EOCD_HEADER_SIZE;

	if (length < eocd_size) {
	LOG(ERROR) << "not big enough to contain EOCD";
	return VERIFY_FAILURE;
	}

	// Determine how much of the file is covered by the signature.
	// This is everything except the signature data and length, which
	// includes all of the EOCD except for the comment length field (2
	// bytes) and the comment data.
	size_t signed_len = length - eocd_size + EOCD_HEADER_SIZE - 2;

	unsigned char* eocd = addr + length - eocd_size;

	// If this is really is the EOCD record, it will begin with the
	// magic number $50 $4b $05 $06.
	if (eocd[0] != 0x50 \|\| eocd[1] != 0x4b \|\|
	eocd[2] != 0x05 \|\| eocd[3] != 0x06) {
	LOG(ERROR) << "signature length doesn't match EOCD marker";
	return VERIFY_FAILURE;
	}

	for (size_t i = 4; i < eocd_size-3; ++i) {
	if (eocd[i ] == 0x50 && eocd[i+1] == 0x4b &&
	eocd[i+2] == 0x05 && eocd[i+3] == 0x06) {
	// if the sequence $50 $4b $05 $06 appears anywhere after
	// the real one, libziparchive will find the later (wrong) one,
	// which could be exploitable. Fail verification if
	// this sequence occurs anywhere after the real one.
	LOG(ERROR) << "EOCD marker occurs after start of EOCD";
	return VERIFY_FAILURE;
	}
	}

	bool need_sha1 = false;
	bool need_sha256 = false;
	for (const auto& key : keys) {
	switch (key.hash_len) {
	case SHA_DIGEST_LENGTH: need_sha1 = true; break;
	case SHA256_DIGEST_LENGTH: need_sha256 = true; break;
	}
	}

	SHA_CTX sha1_ctx;
	SHA256_CTX sha256_ctx;
	SHA1_Init(&sha1_ctx);
	SHA256_Init(&sha256_ctx);

	double frac = -1.0;
	size_t so_far = 0;
	while (so_far < signed_len) {
	// On a Nexus 5X, experiment showed 16MiB beat 1MiB by 6% faster for a
	// 1196MiB full OTA and 60% for an 89MiB incremental OTA.
	// http://b/28135231.
	size_t size = std::min(signed_len - so_far, 16 * MiB);

	if (need_sha1) SHA1_Update(&sha1_ctx, addr + so_far, size);
	if (need_sha256) SHA256_Update(&sha256_ctx, addr + so_far, size);
	so_far += size;

	double f = so_far / (double)signed_len;
	if (f > frac + 0.02 \|\| size == so_far) {
	ui->SetProgress(f);
	frac = f;
	}
	}

	uint8_t sha1[SHA_DIGEST_LENGTH];
	SHA1_Final(sha1, &sha1_ctx);
	uint8_t sha256[SHA256_DIGEST_LENGTH];
	SHA256_Final(sha256, &sha256_ctx);

	uint8_t* sig_der = nullptr;
	size_t sig_der_length = 0;

	uint8_t* signature = eocd + eocd_size - signature_start;
	size_t signature_size = signature_start - FOOTER_SIZE;

	LOG(INFO) << "signature (offset: " << std::hex << (length - signature_start) << ", length: "
	<< signature_size << "): " << print_hex(signature, signature_size);

	if (!read_pkcs7(signature, signature_size, &sig_der, &sig_der_length)) {
	LOG(ERROR) << "Could not find signature DER block";
	return VERIFY_FAILURE;
	}

	/*
	* Check to make sure at least one of the keys matches the signature. Since
	* any key can match, we need to try each before determining a verification
	* failure has happened.
	*/
	size_t i = 0;
	for (const auto& key : keys) {
	const uint8_t* hash;
	int hash_nid;
	switch (key.hash_len) {
	case SHA_DIGEST_LENGTH:
	hash = sha1;
	hash_nid = NID_sha1;
	break;
	case SHA256_DIGEST_LENGTH:
	hash = sha256;
	hash_nid = NID_sha256;
	break;
	default:
	continue;
	}

	// The 6 bytes is the "(signature_start) $ff $ff (comment_size)" that
	// the signing tool appends after the signature itself.
	if (key.key_type == Certificate::KEY_TYPE_RSA) {
	if (!RSA_verify(hash_nid, hash, key.hash_len, sig_der,
	sig_der_length, key.rsa.get())) {
	LOG(INFO) << "failed to verify against RSA key " << i;
	continue;
	}

	LOG(INFO) << "whole-file signature verified against RSA key " << i;
	free(sig_der);
	return VERIFY_SUCCESS;
	} else if (key.key_type == Certificate::KEY_TYPE_EC
	&& key.hash_len == SHA256_DIGEST_LENGTH) {
	if (!ECDSA_verify(0, hash, key.hash_len, sig_der,
	sig_der_length, key.ec.get())) {
	LOG(INFO) << "failed to verify against EC key " << i;
	continue;
	}

	LOG(INFO) << "whole-file signature verified against EC key " << i;
	free(sig_der);
	return VERIFY_SUCCESS;
	} else {
	LOG(INFO) << "Unknown key type " << key.key_type;
	}
	i++;
	}

	if (need_sha1) {
	LOG(INFO) << "SHA-1 digest: " << print_hex(sha1, SHA_DIGEST_LENGTH);
	}
	if (need_sha256) {
	LOG(INFO) << "SHA-256 digest: " << print_hex(sha256, SHA256_DIGEST_LENGTH);
	}
	free(sig_der);
	LOG(ERROR) << "failed to verify whole-file signature";
	return VERIFY_FAILURE;
	}

	std::unique_ptr<RSA, RSADeleter> parse_rsa_key(FILE* file, uint32_t exponent) {
	// Read key length in words and n0inv. n0inv is a precomputed montgomery
	// parameter derived from the modulus and can be used to speed up
	// verification. n0inv is 32 bits wide here, assuming the verification logic
	// uses 32 bit arithmetic. However, BoringSSL may use a word size of 64 bits
	// internally, in which case we don't have a valid n0inv. Thus, we just
	// ignore the montgomery parameters and have BoringSSL recompute them
	// internally. If/When the speedup from using the montgomery parameters
	// becomes relevant, we can add more sophisticated code here to obtain a
	// 64-bit n0inv and initialize the montgomery parameters in the key object.
	uint32_t key_len_words = 0;
	uint32_t n0inv = 0;
	if (fscanf(file, " %i , 0x%x", &key_len_words, &n0inv) != 2) {
	return nullptr;
	}

	if (key_len_words > 8192 / 32) {
	LOG(ERROR) << "key length (" << key_len_words << ") too large";
	return nullptr;
	}

	// Read the modulus.
	std::unique_ptr<uint32_t[]> modulus(new uint32_t[key_len_words]);
	if (fscanf(file, " , { %u", &modulus[0]) != 1) {
	return nullptr;
	}
	for (uint32_t i = 1; i < key_len_words; ++i) {
	if (fscanf(file, " , %u", &modulus[i]) != 1) {
	return nullptr;
	}
	}

	// Cconvert from little-endian array of little-endian words to big-endian
	// byte array suitable as input for BN_bin2bn.
	std::reverse((uint8_t*)modulus.get(),
	(uint8_t*)(modulus.get() + key_len_words));

	// The next sequence of values is the montgomery parameter R^2. Since we
	// generally don't have a valid \|n0inv\|, we ignore this (see comment above).
	uint32_t rr_value;
	if (fscanf(file, " } , { %u", &rr_value) != 1) {
	return nullptr;
	}
	for (uint32_t i = 1; i < key_len_words; ++i) {
	if (fscanf(file, " , %u", &rr_value) != 1) {
	return nullptr;
	}
	}
	if (fscanf(file, " } } ") != 0) {
	return nullptr;
	}

	// Initialize the key.
	std::unique_ptr<RSA, RSADeleter> key(RSA_new());
	if (!key) {
	return nullptr;
	}

	key->n = BN_bin2bn((uint8_t*)modulus.get(),
	key_len_words * sizeof(uint32_t), NULL);
	if (!key->n) {
	return nullptr;
	}

	key->e = BN_new();
	if (!key->e \|\| !BN_set_word(key->e, exponent)) {
	return nullptr;
	}

	return key;
	}

	struct BNDeleter {
	void operator()(BIGNUM* bn) {
	BN_free(bn);
	}
	};

	std::unique_ptr<EC_KEY, ECKEYDeleter> parse_ec_key(FILE* file) {
	uint32_t key_len_bytes = 0;
	if (fscanf(file, " %i", &key_len_bytes) != 1) {
	return nullptr;
	}

	std::unique_ptr<EC_GROUP, void ()(EC_GROUP)> group(
	EC_GROUP_new_by_curve_name(NID_X9_62_prime256v1), EC_GROUP_free);
	if (!group) {
	return nullptr;
	}

	// Verify that \|key_len\| matches the group order.
	if (key_len_bytes != BN_num_bytes(EC_GROUP_get0_order(group.get()))) {
	return nullptr;
	}

	// Read the public key coordinates. Note that the byte order in the file is
	// little-endian, so we convert to big-endian here.
	std::unique_ptr<uint8_t[]> bytes(new uint8_t[key_len_bytes]);
	std::unique_ptr<BIGNUM, BNDeleter> point[2];
	for (int i = 0; i < 2; ++i) {
	unsigned int byte = 0;
	if (fscanf(file, " , { %u", &byte) != 1) {
	return nullptr;
	}
	bytes[key_len_bytes - 1] = byte;

	for (size_t i = 1; i < key_len_bytes; ++i) {
	if (fscanf(file, " , %u", &byte) != 1) {
	return nullptr;
	}
	bytes[key_len_bytes - i - 1] = byte;
	}

	point[i].reset(BN_bin2bn(bytes.get(), key_len_bytes, nullptr));
	if (!point[i]) {
	return nullptr;
	}

	if (fscanf(file, " }") != 0) {
	return nullptr;
	}
	}

	if (fscanf(file, " } ") != 0) {
	return nullptr;
	}

	// Create and initialize the key.
	std::unique_ptr<EC_KEY, ECKEYDeleter> key(EC_KEY_new());
	if (!key \|\| !EC_KEY_set_group(key.get(), group.get()) \|\|
	!EC_KEY_set_public_key_affine_coordinates(key.get(), point[0].get(),
	point[1].get())) {
	return nullptr;
	}

	return key;
	}

	// Reads a file containing one or more public keys as produced by
	// DumpPublicKey: this is an RSAPublicKey struct as it would appear
	// as a C source literal, eg:
	//
	// "{64,0xc926ad21,{1795090719,...,-695002876},{-857949815,...,1175080310}}"
	//
	// For key versions newer than the original 2048-bit e=3 keys
	// supported by Android, the string is preceded by a version
	// identifier, eg:
	//
	// "v2 {64,0xc926ad21,{1795090719,...,-695002876},{-857949815,...,1175080310}}"
	//
	// (Note that the braces and commas in this example are actual
	// characters the parser expects to find in the file; the ellipses
	// indicate more numbers omitted from this example.)
	//
	// The file may contain multiple keys in this format, separated by
	// commas. The last key must not be followed by a comma.
	//
	// A Certificate is a pair of an RSAPublicKey and a particular hash
	// (we support SHA-1 and SHA-256; we store the hash length to signify
	// which is being used). The hash used is implied by the version number.
	//
	// 1: 2048-bit RSA key with e=3 and SHA-1 hash
	// 2: 2048-bit RSA key with e=65537 and SHA-1 hash
	// 3: 2048-bit RSA key with e=3 and SHA-256 hash
	// 4: 2048-bit RSA key with e=65537 and SHA-256 hash
	// 5: 256-bit EC key using the NIST P-256 curve parameters and SHA-256 hash
	//
	// Returns true on success, and appends the found keys (at least one) to certs.
	// Otherwise returns false if the file failed to parse, or if it contains zero
	// keys. The contents in certs would be unspecified on failure.
	bool load_keys(const char* filename, std::vector<Certificate>& certs) {
	std::unique_ptr<FILE, decltype(&fclose)> f(fopen(filename, "r"), fclose);
	if (!f) {
	PLOG(ERROR) << "error opening " << filename;
	return false;
	}

	while (true) {
	certs.emplace_back(0, Certificate::KEY_TYPE_RSA, nullptr, nullptr);
	Certificate& cert = certs.back();
	uint32_t exponent = 0;

	char start_char;
	if (fscanf(f.get(), " %c", &start_char) != 1) return false;
	if (start_char == '{') {
	// a version 1 key has no version specifier.
	cert.key_type = Certificate::KEY_TYPE_RSA;
	exponent = 3;
	cert.hash_len = SHA_DIGEST_LENGTH;
	} else if (start_char == 'v') {
	int version;
	if (fscanf(f.get(), "%d {", &version) != 1) return false;
	switch (version) {
	case 2:
	cert.key_type = Certificate::KEY_TYPE_RSA;
	exponent = 65537;
	cert.hash_len = SHA_DIGEST_LENGTH;
	break;
	case 3:
	cert.key_type = Certificate::KEY_TYPE_RSA;
	exponent = 3;
	cert.hash_len = SHA256_DIGEST_LENGTH;
	break;
	case 4:
	cert.key_type = Certificate::KEY_TYPE_RSA;
	exponent = 65537;
	cert.hash_len = SHA256_DIGEST_LENGTH;
	break;
	case 5:
	cert.key_type = Certificate::KEY_TYPE_EC;
	cert.hash_len = SHA256_DIGEST_LENGTH;
	break;
	default:
	return false;
	}
	}

	if (cert.key_type == Certificate::KEY_TYPE_RSA) {
	cert.rsa = parse_rsa_key(f.get(), exponent);
	if (!cert.rsa) {
	return false;
	}

	LOG(INFO) << "read key e=" << exponent << " hash=" << cert.hash_len;
	} else if (cert.key_type == Certificate::KEY_TYPE_EC) {
	cert.ec = parse_ec_key(f.get());
	if (!cert.ec) {
	return false;
	}
	} else {
	LOG(ERROR) << "Unknown key type " << cert.key_type;
	return false;
	}

	// if the line ends in a comma, this file has more keys.
	int ch = fgetc(f.get());
	if (ch == ',') {
	// more keys to come.
	continue;
	} else if (ch == EOF) {
	break;
	} else {
	LOG(ERROR) << "unexpected character between keys";
	return false;
	}
	}

	return true;
	}