| /** |
| * @license |
| * Copyright 2016 Google Inc. All rights reserved. |
| * 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. |
| */ |
| |
| // TODO(bleichen): |
| // - add tests for SHA1WithDSA with wrong key |
| // - add tests for "alternative" algorithm names |
| // - convert tests for deterministic DSA variants. |
| // Deterministic DSA has a few new drawbacks: |
| // * implementations flaws that generate k incorrectly can leak |
| // the key if multiple implementations (e.g. one correct one incorrect) |
| // is used. |
| // * timing attacks are more serious if the attacker can ask for the same |
| // signature multiple times, since this allows to get more accurate timings. |
| package com.google.security.wycheproof; |
| |
| import com.google.security.wycheproof.WycheproofRunner.ExcludedTest; |
| import com.google.security.wycheproof.WycheproofRunner.ProviderType; |
| import com.google.security.wycheproof.WycheproofRunner.SlowTest; |
| // Android-removed: Android doesn't support JMX |
| // import java.lang.management.ManagementFactory; |
| // import java.lang.management.ThreadMXBean; |
| import java.math.BigInteger; |
| import java.security.GeneralSecurityException; |
| import java.security.KeyFactory; |
| import java.security.KeyPair; |
| import java.security.KeyPairGenerator; |
| import java.security.MessageDigest; |
| import java.security.NoSuchAlgorithmException; |
| import java.security.PublicKey; |
| import java.security.Signature; |
| import java.security.SignatureException; |
| import java.security.interfaces.DSAParams; |
| import java.security.interfaces.DSAPrivateKey; |
| import java.security.interfaces.DSAPublicKey; |
| import java.security.spec.DSAPrivateKeySpec; |
| import java.security.spec.DSAPublicKeySpec; |
| import java.util.Arrays; |
| import javax.crypto.Cipher; |
| import junit.framework.TestCase; |
| |
| /** |
| * Tests DSA against invalid signatures. The motivation for this test is the DSA implementation in |
| * gpg4browsers. This implementation accepts signatures with r=1 and s=0 as valid. |
| * |
| * @author bleichen@google.com (Daniel Bleichenbacher) |
| */ |
| public class DsaTest extends TestCase { |
| static final String MESSAGE = "Hello"; |
| |
| static final DSAPrivateKeySpec privateKey1 = |
| new DSAPrivateKeySpec( |
| // x |
| new BigInteger("15382583218386677486843706921635237927801862255437148328980464126979"), |
| // p |
| new BigInteger( |
| "181118486631420055711787706248812146965913392568235070235446058914" |
| + "1170708161715231951918020125044061516370042605439640379530343556" |
| + "4101919053459832890139496933938670005799610981765220283775567361" |
| + "4836626483403394052203488713085936276470766894079318754834062443" |
| + "1033792580942743268186462355159813630244169054658542719322425431" |
| + "4088256212718983105131138772434658820375111735710449331518776858" |
| + "7867938758654181244292694091187568128410190746310049564097068770" |
| + "8161261634790060655580211122402292101772553741704724263582994973" |
| + "9109274666495826205002104010355456981211025738812433088757102520" |
| + "562459649777989718122219159982614304359"), |
| // q |
| new BigInteger("19689526866605154788513693571065914024068069442724893395618704484701"), |
| // g |
| new BigInteger( |
| "2859278237642201956931085611015389087970918161297522023542900348" |
| + "0877180630984239764282523693409675060100542360520959501692726128" |
| + "3149190229583566074777557293475747419473934711587072321756053067" |
| + "2532404847508798651915566434553729839971841903983916294692452760" |
| + "2490198571084091890169933809199002313226100830607842692992570749" |
| + "0504363602970812128803790973955960534785317485341020833424202774" |
| + "0275688698461842637641566056165699733710043802697192696426360843" |
| + "1736206792141319514001488556117408586108219135730880594044593648" |
| + "9237302749293603778933701187571075920849848690861126195402696457" |
| + "4111219599568903257472567764789616958430")); |
| |
| static final DSAPublicKeySpec publicKey1 = |
| new DSAPublicKeySpec( |
| new BigInteger( |
| "3846308446317351758462473207111709291533523711306097971550086650" |
| + "2577333637930103311673872185522385807498738696446063139653693222" |
| + "3528823234976869516765207838304932337200968476150071617737755913" |
| + "3181601169463467065599372409821150709457431511200322947508290005" |
| + "1780020974429072640276810306302799924668893998032630777409440831" |
| + "4314588994475223696460940116068336991199969153649625334724122468" |
| + "7497038281983541563359385775312520539189474547346202842754393945" |
| + "8755803223951078082197762886933401284142487322057236814878262166" |
| + "5072306622943221607031324846468109901964841479558565694763440972" |
| + "5447389416166053148132419345627682740529"), |
| privateKey1.getP(), |
| privateKey1.getQ(), |
| privateKey1.getG()); |
| |
| // Signatures for Key1. |
| static final String[] VALID_SIGNATURES = { |
| "303d021c1e41b479ad576905b960fe14eadb91b0ccf34843dab916173bb8c9cd" |
| + "021d00ade65988d237d30f9ef41dd424a4e1c8f16967cf3365813fe8786236", |
| }; |
| |
| /** |
| * The following test vectos are derived from a valid signature by |
| * using alternative BER encoding as well as legacy formats. |
| * Accepting such signatures is in many cases benign. Hence the tests |
| * below will pass if such signatures are accepted as valid. |
| * The test vectors could be used to check for signature malleability. |
| * An example where this kind of signature malleability was a problem is |
| * https://en.bitcoin.it/wiki/Transaction_Malleability |
| */ |
| static final String[] MODIFIED_SIGNATURES = { |
| // BER:long form encoding of length |
| "30813d021c1e41b479ad576905b960fe14eadb91b0ccf34843dab916173bb8c9" |
| + "cd021d00ade65988d237d30f9ef41dd424a4e1c8f16967cf3365813fe8786236", |
| "303e02811c1e41b479ad576905b960fe14eadb91b0ccf34843dab916173bb8c9" |
| + "cd021d00ade65988d237d30f9ef41dd424a4e1c8f16967cf3365813fe8786236", |
| "303e021c1e41b479ad576905b960fe14eadb91b0ccf34843dab916173bb8c9cd" |
| + "02811d00ade65988d237d30f9ef41dd424a4e1c8f16967cf3365813fe8786236", |
| // BER:length contains leading 0 |
| "3082003d021c1e41b479ad576905b960fe14eadb91b0ccf34843dab916173bb8" |
| + "c9cd021d00ade65988d237d30f9ef41dd424a4e1c8f16967cf3365813fe87862" |
| + "36", |
| "303f0282001c1e41b479ad576905b960fe14eadb91b0ccf34843dab916173bb8" |
| + "c9cd021d00ade65988d237d30f9ef41dd424a4e1c8f16967cf3365813fe87862" |
| + "36", |
| "303f021c1e41b479ad576905b960fe14eadb91b0ccf34843dab916173bb8c9cd" |
| + "0282001d00ade65988d237d30f9ef41dd424a4e1c8f16967cf3365813fe87862" |
| + "36", |
| // BER:prepending 0's to integer |
| "303f021e00001e41b479ad576905b960fe14eadb91b0ccf34843dab916173bb8" |
| + "c9cd021d00ade65988d237d30f9ef41dd424a4e1c8f16967cf3365813fe87862" |
| + "36", |
| "303f021c1e41b479ad576905b960fe14eadb91b0ccf34843dab916173bb8c9cd" |
| + "021f000000ade65988d237d30f9ef41dd424a4e1c8f16967cf3365813fe87862" |
| + "36", |
| // The Sun provider accepts DSA signatures where a leading 00 has |
| // been omitted in the ASN encoding. |
| "303c021c1e41b479ad576905b960fe14eadb91b0ccf34843dab916173bb8c9cd" |
| + "021cade65988d237d30f9ef41dd424a4e1c8f16967cf3365813fe8786236", |
| }; |
| |
| /** |
| * The following test vectors are invalid DSA signatures. |
| * According to {@link java.security.Signature#verify(byte[])} verifying an invalid |
| * signature may either return false or throw a SignatureException. |
| * We expect that a correct implementation of DSA signatures satisfies this contract. |
| * Throwing a RuntimeException instead of a SignatureException could for example |
| * result in a denial of service attack. |
| * |
| * <p>A list of problems that are caught by these signatures: |
| * <li> CVE-2016-5546: OpenJDK8 throwed java.lang.ArrayIndexOutOfBoundsException for |
| * some invalid DSA signatures. |
| * </ul> |
| */ |
| static final String[] INVALID_SIGNATURES = { |
| // wrong length |
| "303e021c1e41b479ad576905b960fe14eadb91b0ccf34843dab916173bb8c9cd" |
| + "021d00ade65988d237d30f9ef41dd424a4e1c8f16967cf3365813fe8786236", |
| "303c021c1e41b479ad576905b960fe14eadb91b0ccf34843dab916173bb8c9cd" |
| + "021d00ade65988d237d30f9ef41dd424a4e1c8f16967cf3365813fe8786236", |
| "303d021d1e41b479ad576905b960fe14eadb91b0ccf34843dab916173bb8c9cd" |
| + "021d00ade65988d237d30f9ef41dd424a4e1c8f16967cf3365813fe8786236", |
| "303d021b1e41b479ad576905b960fe14eadb91b0ccf34843dab916173bb8c9cd" |
| + "021d00ade65988d237d30f9ef41dd424a4e1c8f16967cf3365813fe8786236", |
| "303d021c1e41b479ad576905b960fe14eadb91b0ccf34843dab916173bb8c9cd" |
| + "021e00ade65988d237d30f9ef41dd424a4e1c8f16967cf3365813fe8786236", |
| "303d021c1e41b479ad576905b960fe14eadb91b0ccf34843dab916173bb8c9cd" |
| + "021c00ade65988d237d30f9ef41dd424a4e1c8f16967cf3365813fe8786236", |
| // uint32 overflow in length |
| "3085010000003d021c1e41b479ad576905b960fe14eadb91b0ccf34843dab916" |
| + "173bb8c9cd021d00ade65988d237d30f9ef41dd424a4e1c8f16967cf3365813f" |
| + "e8786236", |
| "30420285010000001c1e41b479ad576905b960fe14eadb91b0ccf34843dab916" |
| + "173bb8c9cd021d00ade65988d237d30f9ef41dd424a4e1c8f16967cf3365813f" |
| + "e8786236", |
| "3042021c1e41b479ad576905b960fe14eadb91b0ccf34843dab916173bb8c9cd" |
| + "0285010000001d00ade65988d237d30f9ef41dd424a4e1c8f16967cf3365813f" |
| + "e8786236", |
| // uint64 overflow in length |
| "308901000000000000003d021c1e41b479ad576905b960fe14eadb91b0ccf348" |
| + "43dab916173bb8c9cd021d00ade65988d237d30f9ef41dd424a4e1c8f16967cf" |
| + "3365813fe8786236", |
| "3046028901000000000000001c1e41b479ad576905b960fe14eadb91b0ccf348" |
| + "43dab916173bb8c9cd021d00ade65988d237d30f9ef41dd424a4e1c8f16967cf" |
| + "3365813fe8786236", |
| "3046021c1e41b479ad576905b960fe14eadb91b0ccf34843dab916173bb8c9cd" |
| + "028901000000000000001d00ade65988d237d30f9ef41dd424a4e1c8f16967cf" |
| + "3365813fe8786236", |
| // length = 2**31 - 1 |
| "30847fffffff021c1e41b479ad576905b960fe14eadb91b0ccf34843dab91617" |
| + "3bb8c9cd021d00ade65988d237d30f9ef41dd424a4e1c8f16967cf3365813fe8" |
| + "786236", |
| "304102847fffffff1e41b479ad576905b960fe14eadb91b0ccf34843dab91617" |
| + "3bb8c9cd021d00ade65988d237d30f9ef41dd424a4e1c8f16967cf3365813fe8" |
| + "786236", |
| "3041021c1e41b479ad576905b960fe14eadb91b0ccf34843dab916173bb8c9cd" |
| + "02847fffffff00ade65988d237d30f9ef41dd424a4e1c8f16967cf3365813fe8" |
| + "786236", |
| // length = 2**32 - 1 |
| "3084ffffffff021c1e41b479ad576905b960fe14eadb91b0ccf34843dab91617" |
| + "3bb8c9cd021d00ade65988d237d30f9ef41dd424a4e1c8f16967cf3365813fe8" |
| + "786236", |
| "30410284ffffffff1e41b479ad576905b960fe14eadb91b0ccf34843dab91617" |
| + "3bb8c9cd021d00ade65988d237d30f9ef41dd424a4e1c8f16967cf3365813fe8" |
| + "786236", |
| "3041021c1e41b479ad576905b960fe14eadb91b0ccf34843dab916173bb8c9cd" |
| + "0284ffffffff00ade65988d237d30f9ef41dd424a4e1c8f16967cf3365813fe8" |
| + "786236", |
| // length = 2**64 - 1 |
| "3088ffffffffffffffff021c1e41b479ad576905b960fe14eadb91b0ccf34843" |
| + "dab916173bb8c9cd021d00ade65988d237d30f9ef41dd424a4e1c8f16967cf33" |
| + "65813fe8786236", |
| "30450288ffffffffffffffff1e41b479ad576905b960fe14eadb91b0ccf34843" |
| + "dab916173bb8c9cd021d00ade65988d237d30f9ef41dd424a4e1c8f16967cf33" |
| + "65813fe8786236", |
| "3045021c1e41b479ad576905b960fe14eadb91b0ccf34843dab916173bb8c9cd" |
| + "0288ffffffffffffffff00ade65988d237d30f9ef41dd424a4e1c8f16967cf33" |
| + "65813fe8786236", |
| // removing sequence |
| "", |
| // appending 0's to sequence |
| "303f021c1e41b479ad576905b960fe14eadb91b0ccf34843dab916173bb8c9cd" |
| + "021d00ade65988d237d30f9ef41dd424a4e1c8f16967cf3365813fe878623600" |
| + "00", |
| // prepending 0's to sequence |
| "303f0000021c1e41b479ad576905b960fe14eadb91b0ccf34843dab916173bb8" |
| + "c9cd021d00ade65988d237d30f9ef41dd424a4e1c8f16967cf3365813fe87862" |
| + "36", |
| // appending unused 0's |
| "303f021c1e41b479ad576905b960fe14eadb91b0ccf34843dab916173bb8c9cd" |
| + "0000021d00ade65988d237d30f9ef41dd424a4e1c8f16967cf3365813fe87862" |
| + "36", |
| // appending null value |
| "303f021c1e41b479ad576905b960fe14eadb91b0ccf34843dab916173bb8c9cd" |
| + "021d00ade65988d237d30f9ef41dd424a4e1c8f16967cf3365813fe878623605" |
| + "00", |
| "303f021e1e41b479ad576905b960fe14eadb91b0ccf34843dab916173bb8c9cd" |
| + "0500021d00ade65988d237d30f9ef41dd424a4e1c8f16967cf3365813fe87862" |
| + "36", |
| "303f021c1e41b479ad576905b960fe14eadb91b0ccf34843dab916173bb8c9cd" |
| + "021f00ade65988d237d30f9ef41dd424a4e1c8f16967cf3365813fe878623605" |
| + "00", |
| // including garbage |
| "3042498177303d021c1e41b479ad576905b960fe14eadb91b0ccf34843dab916" |
| + "173bb8c9cd021d00ade65988d237d30f9ef41dd424a4e1c8f16967cf3365813f" |
| + "e8786236", |
| "30412500303d021c1e41b479ad576905b960fe14eadb91b0ccf34843dab91617" |
| + "3bb8c9cd021d00ade65988d237d30f9ef41dd424a4e1c8f16967cf3365813fe8" |
| + "786236", |
| "303f303d021c1e41b479ad576905b960fe14eadb91b0ccf34843dab916173bb8" |
| + "c9cd021d00ade65988d237d30f9ef41dd424a4e1c8f16967cf3365813fe87862" |
| + "360004deadbeef", |
| "30422221498177021c1e41b479ad576905b960fe14eadb91b0ccf34843dab916" |
| + "173bb8c9cd021d00ade65988d237d30f9ef41dd424a4e1c8f16967cf3365813f" |
| + "e8786236", |
| "304122202500021c1e41b479ad576905b960fe14eadb91b0ccf34843dab91617" |
| + "3bb8c9cd021d00ade65988d237d30f9ef41dd424a4e1c8f16967cf3365813fe8" |
| + "786236", |
| "3045221e021c1e41b479ad576905b960fe14eadb91b0ccf34843dab916173bb8" |
| + "c9cd0004deadbeef021d00ade65988d237d30f9ef41dd424a4e1c8f16967cf33" |
| + "65813fe8786236", |
| "3042021c1e41b479ad576905b960fe14eadb91b0ccf34843dab916173bb8c9cd" |
| + "2222498177021d00ade65988d237d30f9ef41dd424a4e1c8f16967cf3365813f" |
| + "e8786236", |
| "3041021c1e41b479ad576905b960fe14eadb91b0ccf34843dab916173bb8c9cd" |
| + "22212500021d00ade65988d237d30f9ef41dd424a4e1c8f16967cf3365813fe8" |
| + "786236", |
| "3045021c1e41b479ad576905b960fe14eadb91b0ccf34843dab916173bb8c9cd" |
| + "221f021d00ade65988d237d30f9ef41dd424a4e1c8f16967cf3365813fe87862" |
| + "360004deadbeef", |
| // including undefined tags |
| "3045aa00bb00cd00303d021c1e41b479ad576905b960fe14eadb91b0ccf34843" |
| + "dab916173bb8c9cd021d00ade65988d237d30f9ef41dd424a4e1c8f16967cf33" |
| + "65813fe8786236", |
| "3043aa02aabb303d021c1e41b479ad576905b960fe14eadb91b0ccf34843dab9" |
| + "16173bb8c9cd021d00ade65988d237d30f9ef41dd424a4e1c8f16967cf336581" |
| + "3fe8786236", |
| "30452224aa00bb00cd00021c1e41b479ad576905b960fe14eadb91b0ccf34843" |
| + "dab916173bb8c9cd021d00ade65988d237d30f9ef41dd424a4e1c8f16967cf33" |
| + "65813fe8786236", |
| "30432222aa02aabb021c1e41b479ad576905b960fe14eadb91b0ccf34843dab9" |
| + "16173bb8c9cd021d00ade65988d237d30f9ef41dd424a4e1c8f16967cf336581" |
| + "3fe8786236", |
| "3045021c1e41b479ad576905b960fe14eadb91b0ccf34843dab916173bb8c9cd" |
| + "2225aa00bb00cd00021d00ade65988d237d30f9ef41dd424a4e1c8f16967cf33" |
| + "65813fe8786236", |
| "3043021c1e41b479ad576905b960fe14eadb91b0ccf34843dab916173bb8c9cd" |
| + "2223aa02aabb021d00ade65988d237d30f9ef41dd424a4e1c8f16967cf336581" |
| + "3fe8786236", |
| // changing tag value |
| "2e3d021c1e41b479ad576905b960fe14eadb91b0ccf34843dab916173bb8c9cd" |
| + "021d00ade65988d237d30f9ef41dd424a4e1c8f16967cf3365813fe8786236", |
| "323d021c1e41b479ad576905b960fe14eadb91b0ccf34843dab916173bb8c9cd" |
| + "021d00ade65988d237d30f9ef41dd424a4e1c8f16967cf3365813fe8786236", |
| "ff3d021c1e41b479ad576905b960fe14eadb91b0ccf34843dab916173bb8c9cd" |
| + "021d00ade65988d237d30f9ef41dd424a4e1c8f16967cf3365813fe8786236", |
| "303d001c1e41b479ad576905b960fe14eadb91b0ccf34843dab916173bb8c9cd" |
| + "021d00ade65988d237d30f9ef41dd424a4e1c8f16967cf3365813fe8786236", |
| "303d041c1e41b479ad576905b960fe14eadb91b0ccf34843dab916173bb8c9cd" |
| + "021d00ade65988d237d30f9ef41dd424a4e1c8f16967cf3365813fe8786236", |
| "303dff1c1e41b479ad576905b960fe14eadb91b0ccf34843dab916173bb8c9cd" |
| + "021d00ade65988d237d30f9ef41dd424a4e1c8f16967cf3365813fe8786236", |
| "303d021c1e41b479ad576905b960fe14eadb91b0ccf34843dab916173bb8c9cd" |
| + "001d00ade65988d237d30f9ef41dd424a4e1c8f16967cf3365813fe8786236", |
| "303d021c1e41b479ad576905b960fe14eadb91b0ccf34843dab916173bb8c9cd" |
| + "041d00ade65988d237d30f9ef41dd424a4e1c8f16967cf3365813fe8786236", |
| "303d021c1e41b479ad576905b960fe14eadb91b0ccf34843dab916173bb8c9cd" |
| + "ff1d00ade65988d237d30f9ef41dd424a4e1c8f16967cf3365813fe8786236", |
| // dropping value of sequence |
| "3000", |
| // using composition |
| "3041300102303c1c1e41b479ad576905b960fe14eadb91b0ccf34843dab91617" |
| + "3bb8c9cd021d00ade65988d237d30f9ef41dd424a4e1c8f16967cf3365813fe8" |
| + "786236", |
| "3041222002011e021b41b479ad576905b960fe14eadb91b0ccf34843dab91617" |
| + "3bb8c9cd021d00ade65988d237d30f9ef41dd424a4e1c8f16967cf3365813fe8" |
| + "786236", |
| "3041021c1e41b479ad576905b960fe14eadb91b0ccf34843dab916173bb8c9cd" |
| + "2221020100021cade65988d237d30f9ef41dd424a4e1c8f16967cf3365813fe8" |
| + "786236", |
| // truncate sequence |
| "303c021c1e41b479ad576905b960fe14eadb91b0ccf34843dab916173bb8c9cd" |
| + "021d00ade65988d237d30f9ef41dd424a4e1c8f16967cf3365813fe87862", |
| "303c1c1e41b479ad576905b960fe14eadb91b0ccf34843dab916173bb8c9cd02" |
| + "1d00ade65988d237d30f9ef41dd424a4e1c8f16967cf3365813fe8786236", |
| // indefinite length with no delimiter |
| "3080021c1e41b479ad576905b960fe14eadb91b0ccf34843dab916173bb8c9cd" |
| + "021d00ade65988d237d30f9ef41dd424a4e1c8f16967cf3365813fe8786236", |
| // prepend empty sequence |
| "303f3000021c1e41b479ad576905b960fe14eadb91b0ccf34843dab916173bb8" |
| + "c9cd021d00ade65988d237d30f9ef41dd424a4e1c8f16967cf3365813fe87862" |
| + "36", |
| // append empty sequence |
| "303f021c1e41b479ad576905b960fe14eadb91b0ccf34843dab916173bb8c9cd" |
| + "021d00ade65988d237d30f9ef41dd424a4e1c8f16967cf3365813fe878623630" |
| + "00", |
| // sequence of sequence |
| "303f303d021c1e41b479ad576905b960fe14eadb91b0ccf34843dab916173bb8" |
| + "c9cd021d00ade65988d237d30f9ef41dd424a4e1c8f16967cf3365813fe87862" |
| + "36", |
| // truncated sequence |
| "301e021c1e41b479ad576905b960fe14eadb91b0ccf34843dab916173bb8c9cd", |
| // repeat element in sequence |
| "305c021c1e41b479ad576905b960fe14eadb91b0ccf34843dab916173bb8c9cd" |
| + "021d00ade65988d237d30f9ef41dd424a4e1c8f16967cf3365813fe878623602" |
| + "1d00ade65988d237d30f9ef41dd424a4e1c8f16967cf3365813fe8786236", |
| // removing integer |
| "301f021d00ade65988d237d30f9ef41dd424a4e1c8f16967cf3365813fe8786236", |
| // appending 0's to integer |
| "303f021e1e41b479ad576905b960fe14eadb91b0ccf34843dab916173bb8c9cd" |
| + "0000021d00ade65988d237d30f9ef41dd424a4e1c8f16967cf3365813fe87862" |
| + "36", |
| "303f021c1e41b479ad576905b960fe14eadb91b0ccf34843dab916173bb8c9cd" |
| + "021f00ade65988d237d30f9ef41dd424a4e1c8f16967cf3365813fe878623600" |
| + "00", |
| // dropping value of integer |
| "30210200021d00ade65988d237d30f9ef41dd424a4e1c8f16967cf3365813fe8786236", |
| "3020021c1e41b479ad576905b960fe14eadb91b0ccf34843dab916173bb8c9cd0200", |
| // modify first byte of integer |
| "303d021c1f41b479ad576905b960fe14eadb91b0ccf34843dab916173bb8c9cd" |
| + "021d00ade65988d237d30f9ef41dd424a4e1c8f16967cf3365813fe8786236", |
| "303d021c1e41b479ad576905b960fe14eadb91b0ccf34843dab916173bb8c9cd" |
| + "021d01ade65988d237d30f9ef41dd424a4e1c8f16967cf3365813fe8786236", |
| // modify last byte of integer |
| "303d021c1e41b479ad576905b960fe14eadb91b0ccf34843dab916173bb8c9cc" |
| + "021d00ade65988d237d30f9ef41dd424a4e1c8f16967cf3365813fe8786236", |
| "303d021c1e41b479ad576905b960fe14eadb91b0ccf34843dab916173bb8c9cd" |
| + "021d00ade65988d237d30f9ef41dd424a4e1c8f16967cf3365813fe8786237", |
| // truncate integer |
| "303c021b1e41b479ad576905b960fe14eadb91b0ccf34843dab916173bb8c902" |
| + "1d00ade65988d237d30f9ef41dd424a4e1c8f16967cf3365813fe8786236", |
| "303c021b41b479ad576905b960fe14eadb91b0ccf34843dab916173bb8c9cd02" |
| + "1d00ade65988d237d30f9ef41dd424a4e1c8f16967cf3365813fe8786236", |
| "303c021c1e41b479ad576905b960fe14eadb91b0ccf34843dab916173bb8c9cd" |
| + "021c00ade65988d237d30f9ef41dd424a4e1c8f16967cf3365813fe87862", |
| // leading ff in integer |
| "303e021dff1e41b479ad576905b960fe14eadb91b0ccf34843dab916173bb8c9" |
| + "cd021d00ade65988d237d30f9ef41dd424a4e1c8f16967cf3365813fe8786236", |
| "303e021c1e41b479ad576905b960fe14eadb91b0ccf34843dab916173bb8c9cd" |
| + "021eff00ade65988d237d30f9ef41dd424a4e1c8f16967cf3365813fe8786236", |
| // infinity |
| "3022090180021d00ade65988d237d30f9ef41dd424a4e1c8f16967cf3365813fe8786236", |
| "3021021c1e41b479ad576905b960fe14eadb91b0ccf34843dab916173bb8c9cd090180", |
| // Vectors where r or s have been modified e.g. by adding or subtracting the order of the |
| // group and hence violate the range check for r and s required by DSA. |
| "303d021c1e41b479ad576905b960fe14eadb91b0ccf34843dab916173bb8c9cd" |
| + "021d0168dcf02f57b0caef7ddc183bee1ca94ee09c1a02ee4b0200a54dcb93", |
| "303c021c1e41b479ad576905b960fe14eadb91b0ccf34843dab916173bb8c9cd" |
| + "021cf2efc2e24cbedb2fc00c236c5b2d1a430236b59b7880007f2ba2f8d9", |
| "303d021c1e41b479ad576905b960fe14eadb91b0ccf34843dab916173bb8c9cd" |
| + "021dff5219a6772dc82cf0610be22bdb5b1e370e969830cc9a7ec017879dca", |
| "303d021c1e41b479ad576905b960fe14eadb91b0ccf34843dab916173bb8c9cd" |
| + "021d01ade65988d237d30f9ef41dd424a4e1c8f16967cf3365813fe8786236", |
| "303e021d00d9384b2032d060e59848f87cb4535936bc25fa77959e96d7f88e33" |
| + "2a021d00ade65988d237d30f9ef41dd424a4e1c8f16967cf3365813fe8786236", |
| "303e021d00d9384b2032d060e59848f87cb4535936bc25fa77959e96d7f88e33" |
| + "2a021d0168dcf02f57b0caef7ddc183bee1ca94ee09c1a02ee4b0200a54dcb93", |
| "303d021d00d9384b2032d060e59848f87cb4535936bc25fa77959e96d7f88e33" |
| + "2a021cf2efc2e24cbedb2fc00c236c5b2d1a430236b59b7880007f2ba2f8d9", |
| "303e021d00d9384b2032d060e59848f87cb4535936bc25fa77959e96d7f88e33" |
| + "2a021dff5219a6772dc82cf0610be22bdb5b1e370e969830cc9a7ec017879dca", |
| "303e021d00d9384b2032d060e59848f87cb4535936bc25fa77959e96d7f88e33" |
| + "2a021d01ade65988d237d30f9ef41dd424a4e1c8f16967cf3365813fe8786236", |
| "303e021dff634b1dd327de7125da7903ad2163ca2addc096101fd395567ee360" |
| + "70021d00ade65988d237d30f9ef41dd424a4e1c8f16967cf3365813fe8786236", |
| "303e021dff634b1dd327de7125da7903ad2163ca2addc096101fd395567ee360" |
| + "70021d0168dcf02f57b0caef7ddc183bee1ca94ee09c1a02ee4b0200a54dcb93", |
| "303d021dff634b1dd327de7125da7903ad2163ca2addc096101fd395567ee360" |
| + "70021cf2efc2e24cbedb2fc00c236c5b2d1a430236b59b7880007f2ba2f8d9", |
| "303e021dff634b1dd327de7125da7903ad2163ca2addc096101fd395567ee360" |
| + "70021dff5219a6772dc82cf0610be22bdb5b1e370e969830cc9a7ec017879dca", |
| "303e021dff634b1dd327de7125da7903ad2163ca2addc096101fd395567ee360" |
| + "70021d01ade65988d237d30f9ef41dd424a4e1c8f16967cf3365813fe8786236", |
| "303d021ce1be4b8652a896fa469f01eb15246e4f330cb7bc2546e9e8c4473633" |
| + "021d00ade65988d237d30f9ef41dd424a4e1c8f16967cf3365813fe8786236", |
| "303d021ce1be4b8652a896fa469f01eb15246e4f330cb7bc2546e9e8c4473633" |
| + "021d0168dcf02f57b0caef7ddc183bee1ca94ee09c1a02ee4b0200a54dcb93", |
| "303c021ce1be4b8652a896fa469f01eb15246e4f330cb7bc2546e9e8c4473633" |
| + "021cf2efc2e24cbedb2fc00c236c5b2d1a430236b59b7880007f2ba2f8d9", |
| "303d021ce1be4b8652a896fa469f01eb15246e4f330cb7bc2546e9e8c4473633" |
| + "021dff5219a6772dc82cf0610be22bdb5b1e370e969830cc9a7ec017879dca", |
| "303d021ce1be4b8652a896fa469f01eb15246e4f330cb7bc2546e9e8c4473633" |
| + "021d01ade65988d237d30f9ef41dd424a4e1c8f16967cf3365813fe8786236", |
| "303e021d011e41b479ad576905b960fe14eadb91b0ccf34843dab916173bb8c9" |
| + "cd021d00ade65988d237d30f9ef41dd424a4e1c8f16967cf3365813fe8786236", |
| "303e021d011e41b479ad576905b960fe14eadb91b0ccf34843dab916173bb8c9" |
| + "cd021d0168dcf02f57b0caef7ddc183bee1ca94ee09c1a02ee4b0200a54dcb93", |
| "303d021d011e41b479ad576905b960fe14eadb91b0ccf34843dab916173bb8c9" |
| + "cd021cf2efc2e24cbedb2fc00c236c5b2d1a430236b59b7880007f2ba2f8d9", |
| "303e021d011e41b479ad576905b960fe14eadb91b0ccf34843dab916173bb8c9" |
| + "cd021dff5219a6772dc82cf0610be22bdb5b1e370e969830cc9a7ec017879dca", |
| "303e021d011e41b479ad576905b960fe14eadb91b0ccf34843dab916173bb8c9" |
| + "cd021d01ade65988d237d30f9ef41dd424a4e1c8f16967cf3365813fe8786236", |
| // Signatures with special case values for r and s. E.g. r=1, s=0 are values that can lead to |
| // forgeries if the DSA implementation does not check boundaries and computes s^(-1) == 0. |
| "3022020100021dff450969597a870820211805983688387a10cd4dcc451a7f3f432a96a3", |
| "3006020100020101", |
| "30060201000201ff", |
| "3022020100021d00baf696a68578f7dfdee7fa67c977c785ef32b233bae580c0bcd5695d", |
| "3022020100021d00baf696a68578f7dfdee7fa67c977c785ef32b233bae580c0bcd5695e", |
| "3022020100021d0100000000000000000000000000000000000000000000000000000000", |
| "3082010802010002820101008f7935d9b9aae9bfabed887acf4951b6f32ec59e" |
| + "3baf3718e8eac4961f3efd3606e74351a9c4183339b809e7c2ae1c539ba7475b" |
| + "85d011adb8b47987754984695cac0e8f14b3360828a22ffa27110a3d62a99345" |
| + "3409a0fe696c4658f84bdd20819c3709a01057b195adcd00233dba5484b6291f" |
| + "9d648ef883448677979cec04b434a6ac2e75e9985de23db0292fc1118c9ffa9d" |
| + "8181e7338db792b730d7b9e349592f68099872153915ea3d6b8b4653c633458f" |
| + "803b32a4c2e0f27290256e4e3f8a3b0838a1c450e4e18c1a29a37ddf5ea143de" |
| + "4b66ff04903ed5cf1623e158d487c608e97f211cd81dca23cb6e380765f822e3" |
| + "42be484c05763939601cd667", |
| "3008020100090380fe01", |
| "3022020101021dff450969597a870820211805983688387a10cd4dcc451a7f3f432a96a3", |
| "3006020101020101", |
| "30060201010201ff", |
| "3022020101021d00baf696a68578f7dfdee7fa67c977c785ef32b233bae580c0bcd5695d", |
| "3022020101021d00baf696a68578f7dfdee7fa67c977c785ef32b233bae580c0bcd5695e", |
| "3022020101021d0100000000000000000000000000000000000000000000000000000000", |
| "3082010802010102820101008f7935d9b9aae9bfabed887acf4951b6f32ec59e" |
| + "3baf3718e8eac4961f3efd3606e74351a9c4183339b809e7c2ae1c539ba7475b" |
| + "85d011adb8b47987754984695cac0e8f14b3360828a22ffa27110a3d62a99345" |
| + "3409a0fe696c4658f84bdd20819c3709a01057b195adcd00233dba5484b6291f" |
| + "9d648ef883448677979cec04b434a6ac2e75e9985de23db0292fc1118c9ffa9d" |
| + "8181e7338db792b730d7b9e349592f68099872153915ea3d6b8b4653c633458f" |
| + "803b32a4c2e0f27290256e4e3f8a3b0838a1c450e4e18c1a29a37ddf5ea143de" |
| + "4b66ff04903ed5cf1623e158d487c608e97f211cd81dca23cb6e380765f822e3" |
| + "42be484c05763939601cd667", |
| "3008020101090380fe01", |
| "30220201ff021dff450969597a870820211805983688387a10cd4dcc451a7f3f432a96a3", |
| "30060201ff020101", |
| "30060201ff0201ff", |
| "30220201ff021d00baf696a68578f7dfdee7fa67c977c785ef32b233bae580c0bcd5695d", |
| "30220201ff021d00baf696a68578f7dfdee7fa67c977c785ef32b233bae580c0bcd5695e", |
| "30220201ff021d0100000000000000000000000000000000000000000000000000000000", |
| "308201080201ff02820101008f7935d9b9aae9bfabed887acf4951b6f32ec59e" |
| + "3baf3718e8eac4961f3efd3606e74351a9c4183339b809e7c2ae1c539ba7475b" |
| + "85d011adb8b47987754984695cac0e8f14b3360828a22ffa27110a3d62a99345" |
| + "3409a0fe696c4658f84bdd20819c3709a01057b195adcd00233dba5484b6291f" |
| + "9d648ef883448677979cec04b434a6ac2e75e9985de23db0292fc1118c9ffa9d" |
| + "8181e7338db792b730d7b9e349592f68099872153915ea3d6b8b4653c633458f" |
| + "803b32a4c2e0f27290256e4e3f8a3b0838a1c450e4e18c1a29a37ddf5ea143de" |
| + "4b66ff04903ed5cf1623e158d487c608e97f211cd81dca23cb6e380765f822e3" |
| + "42be484c05763939601cd667", |
| "30080201ff090380fe01", |
| "303e021d00baf696a68578f7dfdee7fa67c977c785ef32b233bae580c0bcd569" |
| + "5d021dff450969597a870820211805983688387a10cd4dcc451a7f3f432a96a3", |
| "3022021d00baf696a68578f7dfdee7fa67c977c785ef32b233bae580c0bcd5695d020100", |
| "3022021d00baf696a68578f7dfdee7fa67c977c785ef32b233bae580c0bcd5695d020101", |
| "3022021d00baf696a68578f7dfdee7fa67c977c785ef32b233bae580c0bcd5695d0201ff", |
| "303e021d00baf696a68578f7dfdee7fa67c977c785ef32b233bae580c0bcd569" |
| + "5d021d00baf696a68578f7dfdee7fa67c977c785ef32b233bae580c0bcd5695d", |
| "303e021d00baf696a68578f7dfdee7fa67c977c785ef32b233bae580c0bcd569" |
| + "5d021d00baf696a68578f7dfdee7fa67c977c785ef32b233bae580c0bcd5695e", |
| "303e021d00baf696a68578f7dfdee7fa67c977c785ef32b233bae580c0bcd569" |
| + "5d021d0100000000000000000000000000000000000000000000000000000000", |
| "30820124021d00baf696a68578f7dfdee7fa67c977c785ef32b233bae580c0bc" |
| + "d5695d02820101008f7935d9b9aae9bfabed887acf4951b6f32ec59e3baf3718" |
| + "e8eac4961f3efd3606e74351a9c4183339b809e7c2ae1c539ba7475b85d011ad" |
| + "b8b47987754984695cac0e8f14b3360828a22ffa27110a3d62a993453409a0fe" |
| + "696c4658f84bdd20819c3709a01057b195adcd00233dba5484b6291f9d648ef8" |
| + "83448677979cec04b434a6ac2e75e9985de23db0292fc1118c9ffa9d8181e733" |
| + "8db792b730d7b9e349592f68099872153915ea3d6b8b4653c633458f803b32a4" |
| + "c2e0f27290256e4e3f8a3b0838a1c450e4e18c1a29a37ddf5ea143de4b66ff04" |
| + "903ed5cf1623e158d487c608e97f211cd81dca23cb6e380765f822e342be484c" |
| + "05763939601cd667", |
| "3024021d00baf696a68578f7dfdee7fa67c977c785ef32b233bae580c0bcd5695d090380fe01", |
| "303e021d00baf696a68578f7dfdee7fa67c977c785ef32b233bae580c0bcd569" |
| + "5e021dff450969597a870820211805983688387a10cd4dcc451a7f3f432a96a3", |
| "3022021d00baf696a68578f7dfdee7fa67c977c785ef32b233bae580c0bcd5695e020100", |
| "3022021d00baf696a68578f7dfdee7fa67c977c785ef32b233bae580c0bcd5695e020101", |
| "3022021d00baf696a68578f7dfdee7fa67c977c785ef32b233bae580c0bcd5695e0201ff", |
| "303e021d00baf696a68578f7dfdee7fa67c977c785ef32b233bae580c0bcd569" |
| + "5e021d00baf696a68578f7dfdee7fa67c977c785ef32b233bae580c0bcd5695d", |
| "303e021d00baf696a68578f7dfdee7fa67c977c785ef32b233bae580c0bcd569" |
| + "5e021d00baf696a68578f7dfdee7fa67c977c785ef32b233bae580c0bcd5695e", |
| "303e021d00baf696a68578f7dfdee7fa67c977c785ef32b233bae580c0bcd569" |
| + "5e021d0100000000000000000000000000000000000000000000000000000000", |
| "30820124021d00baf696a68578f7dfdee7fa67c977c785ef32b233bae580c0bc" |
| + "d5695e02820101008f7935d9b9aae9bfabed887acf4951b6f32ec59e3baf3718" |
| + "e8eac4961f3efd3606e74351a9c4183339b809e7c2ae1c539ba7475b85d011ad" |
| + "b8b47987754984695cac0e8f14b3360828a22ffa27110a3d62a993453409a0fe" |
| + "696c4658f84bdd20819c3709a01057b195adcd00233dba5484b6291f9d648ef8" |
| + "83448677979cec04b434a6ac2e75e9985de23db0292fc1118c9ffa9d8181e733" |
| + "8db792b730d7b9e349592f68099872153915ea3d6b8b4653c633458f803b32a4" |
| + "c2e0f27290256e4e3f8a3b0838a1c450e4e18c1a29a37ddf5ea143de4b66ff04" |
| + "903ed5cf1623e158d487c608e97f211cd81dca23cb6e380765f822e342be484c" |
| + "05763939601cd667", |
| "3024021d00baf696a68578f7dfdee7fa67c977c785ef32b233bae580c0bcd5695e090380fe01", |
| "303e021d01000000000000000000000000000000000000000000000000000000" |
| + "00021dff450969597a870820211805983688387a10cd4dcc451a7f3f432a96a3", |
| "3022021d0100000000000000000000000000000000000000000000000000000000020100", |
| "3022021d0100000000000000000000000000000000000000000000000000000000020101", |
| "3022021d01000000000000000000000000000000000000000000000000000000000201ff", |
| "303e021d01000000000000000000000000000000000000000000000000000000" |
| + "00021d00baf696a68578f7dfdee7fa67c977c785ef32b233bae580c0bcd5695d", |
| "303e021d01000000000000000000000000000000000000000000000000000000" |
| + "00021d00baf696a68578f7dfdee7fa67c977c785ef32b233bae580c0bcd5695e", |
| "303e021d01000000000000000000000000000000000000000000000000000000" |
| + "00021d0100000000000000000000000000000000000000000000000000000000", |
| "30820124021d0100000000000000000000000000000000000000000000000000" |
| + "00000002820101008f7935d9b9aae9bfabed887acf4951b6f32ec59e3baf3718" |
| + "e8eac4961f3efd3606e74351a9c4183339b809e7c2ae1c539ba7475b85d011ad" |
| + "b8b47987754984695cac0e8f14b3360828a22ffa27110a3d62a993453409a0fe" |
| + "696c4658f84bdd20819c3709a01057b195adcd00233dba5484b6291f9d648ef8" |
| + "83448677979cec04b434a6ac2e75e9985de23db0292fc1118c9ffa9d8181e733" |
| + "8db792b730d7b9e349592f68099872153915ea3d6b8b4653c633458f803b32a4" |
| + "c2e0f27290256e4e3f8a3b0838a1c450e4e18c1a29a37ddf5ea143de4b66ff04" |
| + "903ed5cf1623e158d487c608e97f211cd81dca23cb6e380765f822e342be484c" |
| + "05763939601cd667", |
| "3024021d0100000000000000000000000000000000000000000000000000000000090380fe01", |
| "3082012402820101008f7935d9b9aae9bfabed887acf4951b6f32ec59e3baf37" |
| + "18e8eac4961f3efd3606e74351a9c4183339b809e7c2ae1c539ba7475b85d011" |
| + "adb8b47987754984695cac0e8f14b3360828a22ffa27110a3d62a993453409a0" |
| + "fe696c4658f84bdd20819c3709a01057b195adcd00233dba5484b6291f9d648e" |
| + "f883448677979cec04b434a6ac2e75e9985de23db0292fc1118c9ffa9d8181e7" |
| + "338db792b730d7b9e349592f68099872153915ea3d6b8b4653c633458f803b32" |
| + "a4c2e0f27290256e4e3f8a3b0838a1c450e4e18c1a29a37ddf5ea143de4b66ff" |
| + "04903ed5cf1623e158d487c608e97f211cd81dca23cb6e380765f822e342be48" |
| + "4c05763939601cd667021dff450969597a870820211805983688387a10cd4dcc" |
| + "451a7f3f432a96a3", |
| "3082010802820101008f7935d9b9aae9bfabed887acf4951b6f32ec59e3baf37" |
| + "18e8eac4961f3efd3606e74351a9c4183339b809e7c2ae1c539ba7475b85d011" |
| + "adb8b47987754984695cac0e8f14b3360828a22ffa27110a3d62a993453409a0" |
| + "fe696c4658f84bdd20819c3709a01057b195adcd00233dba5484b6291f9d648e" |
| + "f883448677979cec04b434a6ac2e75e9985de23db0292fc1118c9ffa9d8181e7" |
| + "338db792b730d7b9e349592f68099872153915ea3d6b8b4653c633458f803b32" |
| + "a4c2e0f27290256e4e3f8a3b0838a1c450e4e18c1a29a37ddf5ea143de4b66ff" |
| + "04903ed5cf1623e158d487c608e97f211cd81dca23cb6e380765f822e342be48" |
| + "4c05763939601cd667020100", |
| "3082010802820101008f7935d9b9aae9bfabed887acf4951b6f32ec59e3baf37" |
| + "18e8eac4961f3efd3606e74351a9c4183339b809e7c2ae1c539ba7475b85d011" |
| + "adb8b47987754984695cac0e8f14b3360828a22ffa27110a3d62a993453409a0" |
| + "fe696c4658f84bdd20819c3709a01057b195adcd00233dba5484b6291f9d648e" |
| + "f883448677979cec04b434a6ac2e75e9985de23db0292fc1118c9ffa9d8181e7" |
| + "338db792b730d7b9e349592f68099872153915ea3d6b8b4653c633458f803b32" |
| + "a4c2e0f27290256e4e3f8a3b0838a1c450e4e18c1a29a37ddf5ea143de4b66ff" |
| + "04903ed5cf1623e158d487c608e97f211cd81dca23cb6e380765f822e342be48" |
| + "4c05763939601cd667020101", |
| "3082010802820101008f7935d9b9aae9bfabed887acf4951b6f32ec59e3baf37" |
| + "18e8eac4961f3efd3606e74351a9c4183339b809e7c2ae1c539ba7475b85d011" |
| + "adb8b47987754984695cac0e8f14b3360828a22ffa27110a3d62a993453409a0" |
| + "fe696c4658f84bdd20819c3709a01057b195adcd00233dba5484b6291f9d648e" |
| + "f883448677979cec04b434a6ac2e75e9985de23db0292fc1118c9ffa9d8181e7" |
| + "338db792b730d7b9e349592f68099872153915ea3d6b8b4653c633458f803b32" |
| + "a4c2e0f27290256e4e3f8a3b0838a1c450e4e18c1a29a37ddf5ea143de4b66ff" |
| + "04903ed5cf1623e158d487c608e97f211cd81dca23cb6e380765f822e342be48" |
| + "4c05763939601cd6670201ff", |
| "3082012402820101008f7935d9b9aae9bfabed887acf4951b6f32ec59e3baf37" |
| + "18e8eac4961f3efd3606e74351a9c4183339b809e7c2ae1c539ba7475b85d011" |
| + "adb8b47987754984695cac0e8f14b3360828a22ffa27110a3d62a993453409a0" |
| + "fe696c4658f84bdd20819c3709a01057b195adcd00233dba5484b6291f9d648e" |
| + "f883448677979cec04b434a6ac2e75e9985de23db0292fc1118c9ffa9d8181e7" |
| + "338db792b730d7b9e349592f68099872153915ea3d6b8b4653c633458f803b32" |
| + "a4c2e0f27290256e4e3f8a3b0838a1c450e4e18c1a29a37ddf5ea143de4b66ff" |
| + "04903ed5cf1623e158d487c608e97f211cd81dca23cb6e380765f822e342be48" |
| + "4c05763939601cd667021d00baf696a68578f7dfdee7fa67c977c785ef32b233" |
| + "bae580c0bcd5695d", |
| "3082012402820101008f7935d9b9aae9bfabed887acf4951b6f32ec59e3baf37" |
| + "18e8eac4961f3efd3606e74351a9c4183339b809e7c2ae1c539ba7475b85d011" |
| + "adb8b47987754984695cac0e8f14b3360828a22ffa27110a3d62a993453409a0" |
| + "fe696c4658f84bdd20819c3709a01057b195adcd00233dba5484b6291f9d648e" |
| + "f883448677979cec04b434a6ac2e75e9985de23db0292fc1118c9ffa9d8181e7" |
| + "338db792b730d7b9e349592f68099872153915ea3d6b8b4653c633458f803b32" |
| + "a4c2e0f27290256e4e3f8a3b0838a1c450e4e18c1a29a37ddf5ea143de4b66ff" |
| + "04903ed5cf1623e158d487c608e97f211cd81dca23cb6e380765f822e342be48" |
| + "4c05763939601cd667021d00baf696a68578f7dfdee7fa67c977c785ef32b233" |
| + "bae580c0bcd5695e", |
| "3082012402820101008f7935d9b9aae9bfabed887acf4951b6f32ec59e3baf37" |
| + "18e8eac4961f3efd3606e74351a9c4183339b809e7c2ae1c539ba7475b85d011" |
| + "adb8b47987754984695cac0e8f14b3360828a22ffa27110a3d62a993453409a0" |
| + "fe696c4658f84bdd20819c3709a01057b195adcd00233dba5484b6291f9d648e" |
| + "f883448677979cec04b434a6ac2e75e9985de23db0292fc1118c9ffa9d8181e7" |
| + "338db792b730d7b9e349592f68099872153915ea3d6b8b4653c633458f803b32" |
| + "a4c2e0f27290256e4e3f8a3b0838a1c450e4e18c1a29a37ddf5ea143de4b66ff" |
| + "04903ed5cf1623e158d487c608e97f211cd81dca23cb6e380765f822e342be48" |
| + "4c05763939601cd667021d010000000000000000000000000000000000000000" |
| + "0000000000000000", |
| "3082020a02820101008f7935d9b9aae9bfabed887acf4951b6f32ec59e3baf37" |
| + "18e8eac4961f3efd3606e74351a9c4183339b809e7c2ae1c539ba7475b85d011" |
| + "adb8b47987754984695cac0e8f14b3360828a22ffa27110a3d62a993453409a0" |
| + "fe696c4658f84bdd20819c3709a01057b195adcd00233dba5484b6291f9d648e" |
| + "f883448677979cec04b434a6ac2e75e9985de23db0292fc1118c9ffa9d8181e7" |
| + "338db792b730d7b9e349592f68099872153915ea3d6b8b4653c633458f803b32" |
| + "a4c2e0f27290256e4e3f8a3b0838a1c450e4e18c1a29a37ddf5ea143de4b66ff" |
| + "04903ed5cf1623e158d487c608e97f211cd81dca23cb6e380765f822e342be48" |
| + "4c05763939601cd66702820101008f7935d9b9aae9bfabed887acf4951b6f32e" |
| + "c59e3baf3718e8eac4961f3efd3606e74351a9c4183339b809e7c2ae1c539ba7" |
| + "475b85d011adb8b47987754984695cac0e8f14b3360828a22ffa27110a3d62a9" |
| + "93453409a0fe696c4658f84bdd20819c3709a01057b195adcd00233dba5484b6" |
| + "291f9d648ef883448677979cec04b434a6ac2e75e9985de23db0292fc1118c9f" |
| + "fa9d8181e7338db792b730d7b9e349592f68099872153915ea3d6b8b4653c633" |
| + "458f803b32a4c2e0f27290256e4e3f8a3b0838a1c450e4e18c1a29a37ddf5ea1" |
| + "43de4b66ff04903ed5cf1623e158d487c608e97f211cd81dca23cb6e380765f8" |
| + "22e342be484c05763939601cd667", |
| "3082010a02820101008f7935d9b9aae9bfabed887acf4951b6f32ec59e3baf37" |
| + "18e8eac4961f3efd3606e74351a9c4183339b809e7c2ae1c539ba7475b85d011" |
| + "adb8b47987754984695cac0e8f14b3360828a22ffa27110a3d62a993453409a0" |
| + "fe696c4658f84bdd20819c3709a01057b195adcd00233dba5484b6291f9d648e" |
| + "f883448677979cec04b434a6ac2e75e9985de23db0292fc1118c9ffa9d8181e7" |
| + "338db792b730d7b9e349592f68099872153915ea3d6b8b4653c633458f803b32" |
| + "a4c2e0f27290256e4e3f8a3b0838a1c450e4e18c1a29a37ddf5ea143de4b66ff" |
| + "04903ed5cf1623e158d487c608e97f211cd81dca23cb6e380765f822e342be48" |
| + "4c05763939601cd667090380fe01", |
| "3024090380fe01021dff450969597a870820211805983688387a10cd4dcc451a7f3f432a96a3", |
| "3008090380fe01020100", |
| "3008090380fe01020101", |
| "3008090380fe010201ff", |
| "3024090380fe01021d00baf696a68578f7dfdee7fa67c977c785ef32b233bae580c0bcd5695d", |
| "3024090380fe01021d00baf696a68578f7dfdee7fa67c977c785ef32b233bae580c0bcd5695e", |
| "3024090380fe01021d0100000000000000000000000000000000000000000000000000000000", |
| "3082010a090380fe0102820101008f7935d9b9aae9bfabed887acf4951b6f32e" |
| + "c59e3baf3718e8eac4961f3efd3606e74351a9c4183339b809e7c2ae1c539ba7" |
| + "475b85d011adb8b47987754984695cac0e8f14b3360828a22ffa27110a3d62a9" |
| + "93453409a0fe696c4658f84bdd20819c3709a01057b195adcd00233dba5484b6" |
| + "291f9d648ef883448677979cec04b434a6ac2e75e9985de23db0292fc1118c9f" |
| + "fa9d8181e7338db792b730d7b9e349592f68099872153915ea3d6b8b4653c633" |
| + "458f803b32a4c2e0f27290256e4e3f8a3b0838a1c450e4e18c1a29a37ddf5ea1" |
| + "43de4b66ff04903ed5cf1623e158d487c608e97f211cd81dca23cb6e380765f8" |
| + "22e342be484c05763939601cd667", |
| "300a090380fe01090380fe01", |
| }; |
| |
| @SuppressWarnings("InsecureCryptoUsage") |
| public void testVectors( |
| String[] signatures, |
| DSAPublicKeySpec key, |
| String message, |
| String algorithm, |
| String signatureType, |
| boolean isValidDER, |
| boolean isValidBER) |
| throws Exception { |
| byte[] messageBytes = message.getBytes("UTF-8"); |
| Signature verifier = Signature.getInstance(algorithm); |
| KeyFactory kf = KeyFactory.getInstance("DSA"); |
| PublicKey pub = kf.generatePublic(key); |
| int errors = 0; |
| for (String signature : signatures) { |
| byte[] signatureBytes = TestUtil.hexToBytes(signature); |
| verifier.initVerify(pub); |
| verifier.update(messageBytes); |
| boolean verified = false; |
| try { |
| verified = verifier.verify(signatureBytes); |
| } catch (SignatureException ex) { |
| // verify can throw SignatureExceptions if the signature is malformed. |
| // We don't flag these cases and simply consider the signature as invalid. |
| verified = false; |
| } catch (Exception ex) { |
| // Other exceptions indicate some internal error, e.g. careless ASN parsing. |
| // We count these as errors. |
| System.out.println(signatureType + ":" + signature + " throws:" + ex.toString()); |
| errors++; |
| continue; |
| } |
| if (isValidDER && !verified) { |
| System.out.println(signatureType + " was not verified:" + signature); |
| errors++; |
| } else if (!isValidBER && verified) { |
| System.out.println(signatureType + " was verified:" + signature); |
| errors++; |
| } |
| } |
| assertEquals(0, errors); |
| } |
| |
| public void testValidSignatures() throws Exception { |
| testVectors( |
| VALID_SIGNATURES, publicKey1, "Hello", "SHA224WithDSA", "Valid DSA signature", true, true); |
| } |
| |
| public void testModifiedSignatures() throws Exception { |
| testVectors( |
| MODIFIED_SIGNATURES, publicKey1, "Hello", "SHA224WithDSA", "Modified DSA signature", |
| false, true); |
| } |
| |
| public void testInvalidSignatures() throws Exception { |
| testVectors( |
| INVALID_SIGNATURES, publicKey1, "Hello", "SHA224WithDSA", "Invalid DSA signature", |
| false, false); |
| } |
| |
| // Extract the integer r from a DSA signature. |
| // This method implicitely assumes that the DSA signature is DER encoded. |
| BigInteger extractR(byte[] signature) throws Exception { |
| int lengthR = signature[3]; |
| return new BigInteger(Arrays.copyOfRange(signature, 4, 4 + lengthR)); |
| } |
| |
| BigInteger extractS(byte[] signature) throws Exception { |
| int lengthR = signature[3]; |
| int startS = 4 + lengthR; |
| int lengthS = signature[startS + 1]; |
| return new BigInteger(Arrays.copyOfRange(signature, startS + 2, startS + 2 + lengthS)); |
| } |
| |
| /** Extract the k that was used to sign the signature. Validates the k if check == true. */ |
| BigInteger extractK(byte[] signature, BigInteger h, DSAPrivateKey priv, boolean check) |
| throws Exception { |
| BigInteger x = priv.getX(); |
| BigInteger q = priv.getParams().getQ(); |
| BigInteger r = extractR(signature); |
| BigInteger s = extractS(signature); |
| BigInteger k = x.multiply(r).add(h).multiply(s.modInverse(q)).mod(q); |
| if (check) { |
| BigInteger p = priv.getParams().getP(); |
| BigInteger g = priv.getParams().getG(); |
| BigInteger r2 = g.modPow(k, p).mod(q); |
| assertEquals(r.toString(), r2.toString()); |
| } |
| return k; |
| } |
| |
| /** |
| * Providers that implement SHA1WithDSA but not at least SHA256WithDSA are outdated and should be |
| * avoided even if DSA is currently not used in a project. Such providers promote using a weak |
| * signature scheme. It can also "inspire" developers to use invalid schemes such as SHA1WithDSA |
| * together with 2048-bit key. Such invalid use cases are often untested and can have serious |
| * flaws. For example the SUN provider leaked the private keys with 3 to 5 signatures in such |
| * instances. |
| */ |
| public void testOutdatedProvider() throws Exception { |
| try { |
| Signature sig = Signature.getInstance("SHA1WithDSA"); |
| try { |
| Signature.getInstance("SHA256WithDSA"); |
| } catch (NoSuchAlgorithmException ex) { |
| fail("Provider " + sig.getProvider().getName() + " is outdated and should not be used."); |
| } |
| } catch (NoSuchAlgorithmException ex) { |
| System.out.println("SHA1WithDSA is not supported"); |
| } |
| } |
| |
| /** |
| * This is just a test for basic functionality of DSA. The test generates a public and private |
| * key, generates a signature, verifies it and prints the whole thing out. This test is useful |
| * when an implementation is seriously broken. |
| */ |
| @SlowTest(providers = {ProviderType.BOUNCY_CASTLE, ProviderType.SPONGY_CASTLE}) |
| @SuppressWarnings("InsecureCryptoUsage") |
| public void testBasic() throws Exception { |
| int keySize = 2048; |
| String algorithm = "SHA256WithDSA"; |
| String hashAlgorithm = "SHA-256"; |
| String message = "Hello"; |
| |
| byte[] messageBytes = message.getBytes("UTF-8"); |
| KeyPairGenerator generator = java.security.KeyPairGenerator.getInstance("DSA"); |
| generator.initialize(keySize); |
| KeyPair keyPair = generator.generateKeyPair(); |
| DSAPublicKey pub = (DSAPublicKey) keyPair.getPublic(); |
| DSAPrivateKey priv = (DSAPrivateKey) keyPair.getPrivate(); |
| Signature signer = Signature.getInstance(algorithm); |
| Signature verifier = Signature.getInstance(algorithm); |
| signer.initSign(priv); |
| signer.update(messageBytes); |
| byte[] signature = signer.sign(); |
| verifier.initVerify(pub); |
| verifier.update(messageBytes); |
| assertTrue(verifier.verify(signature)); |
| |
| // Extract some parameters. |
| byte[] rawHash = MessageDigest.getInstance(hashAlgorithm).digest(messageBytes); |
| DSAParams params = priv.getParams(); |
| |
| // Print keys and signature, so that it can be used to generate new test vectors. |
| System.out.println("Message:" + message); |
| System.out.println("Hash:" + TestUtil.bytesToHex(rawHash)); |
| System.out.println("Params:"); |
| System.out.println("p:" + params.getP().toString()); |
| System.out.println("q:" + params.getQ().toString()); |
| System.out.println("g:" + params.getG().toString()); |
| System.out.println("Private key:"); |
| System.out.println("X:" + priv.getX().toString()); |
| System.out.println("encoded:" + TestUtil.bytesToHex(priv.getEncoded())); |
| System.out.println("Public key:"); |
| System.out.println("Y:" + pub.getY().toString()); |
| System.out.println("encoded:" + TestUtil.bytesToHex(pub.getEncoded())); |
| System.out.println("Signature:" + TestUtil.bytesToHex(signature)); |
| System.out.println("r:" + extractR(signature).toString()); |
| System.out.println("s:" + extractS(signature).toString()); |
| } |
| |
| @SuppressWarnings("InsecureCryptoUsage") |
| public void testKeyGeneration(int keysize) throws Exception { |
| KeyPairGenerator generator = KeyPairGenerator.getInstance("DSA"); |
| generator.initialize(keysize); |
| KeyPair keyPair = generator.generateKeyPair(); |
| DSAPrivateKey priv = (DSAPrivateKey) keyPair.getPrivate(); |
| DSAParams params = priv.getParams(); |
| assertEquals(keysize, params.getP().bitLength()); |
| // The NIST standard does not fully specify the size of q that |
| // must be used for a given key size. Hence there are differences. |
| // For example if keysize = 2048, then OpenSSL uses 256 bit q's by default, |
| // but the SUN provider uses 224 bits. Both are acceptable sizes. |
| // The tests below simply asserts that the size of q does not decrease the |
| // overall security of the DSA. |
| int qsize = params.getQ().bitLength(); |
| switch (keysize) { |
| case 1024: |
| assertTrue("Invalid qsize for 1024 bit key:" + qsize, qsize >= 160); |
| break; |
| case 2048: |
| assertTrue("Invalid qsize for 2048 bit key:" + qsize, qsize >= 224); |
| break; |
| case 3072: |
| assertTrue("Invalid qsize for 3072 bit key:" + qsize, qsize >= 256); |
| break; |
| default: |
| fail("Invalid key size:" + keysize); |
| } |
| // Check the length of the private key. |
| // For example GPG4Browsers or the KJUR library derived from it use |
| // q.bitCount() instead of q.bitLength() to determine the size of the private key |
| // and hence would generate keys that are much too small. |
| assertTrue(priv.getX().bitLength() >= qsize - 32); |
| } |
| |
| /** |
| * Tests the key generation for DSA. |
| * |
| * <p>Problems found: |
| * <ul> |
| * <li> CVE-2016-1000343 BouncyCastle before v.1.56 always generated DSA keys with |
| * a 160-bit q. |
| * </ul> |
| */ |
| @SlowTest(providers = {ProviderType.BOUNCY_CASTLE, ProviderType.SPONGY_CASTLE}) |
| public void testKeyGenerationAll() throws Exception { |
| testKeyGeneration(1024); |
| testKeyGeneration(2048); |
| } |
| |
| /** |
| * Checks whether the one time key k in DSA is biased. For example the SUN provider fell for this |
| * test until April 2016. |
| */ |
| @SuppressWarnings("InsecureCryptoUsage") |
| @ExcludedTest( |
| providers = {ProviderType.BOUNCY_CASTLE}, |
| comment = "Signature.SHA1WithDSA is removed") |
| public void testDsaBias() throws Exception { |
| // q is close to 2/3 * 2^160. |
| BigInteger q = new BigInteger("974317976835659416858874959372334979171063697271"); |
| BigInteger p = |
| new BigInteger( |
| "1106803511314772711673172950296693567629309594518393175860816428" |
| + "6658764043763662129010863568011543182924292444458455864283745070" |
| + "9908516713302345161980412667892373845670780253725557376379049862" |
| + "4062950082444499320797079243439689601679418602390654466821968220" |
| + "32212146727497041502702331623782703855119908989712161"); |
| BigInteger g = |
| new BigInteger( |
| "1057342118316953575810387190942009018497979302261477972033090351" |
| + "7561815639397594841480480197745063606756857212792356354588585967" |
| + "3837265237205154744016475608524531648654928648461175919672511710" |
| + "4878976887505840764543501512668232945506391524642105449699321960" |
| + "32410302985148400531470153936516167243072120845392903"); |
| BigInteger x = new BigInteger("13706102843888006547723575730792302382646994436"); |
| |
| KeyFactory kf = KeyFactory.getInstance("DSA"); |
| DSAPrivateKey priv = (DSAPrivateKey) kf.generatePrivate(new DSAPrivateKeySpec(x, p, q, g)); |
| |
| // If we make TESTS tests with a fair coin then the probability that |
| // either heads or tails appears less than MINCOUNT times is less than |
| // 2^{-32}. |
| // I.e. 2*sum(binomial(tests,i) for i in range(mincount))*2**32 < 2**tests |
| // Therefore the test below is not expected to fail unless the generation |
| // of the one time keys is indeed biased. |
| final int tests = 1024; |
| final int mincount = 410; |
| |
| String hashAlgorithm = "SHA"; |
| String message = "Hello"; |
| byte[] messageBytes = message.getBytes("UTF-8"); |
| byte[] digest = MessageDigest.getInstance(hashAlgorithm).digest(messageBytes); |
| BigInteger h = new BigInteger(1, digest); |
| |
| final BigInteger qHalf = q.shiftRight(1); |
| Signature signer = Signature.getInstance("SHA1WithDSA"); |
| signer.initSign(priv); |
| int countLsb = 0; // count the number of k's with msb set |
| int countMsb = 0; // count the number of k's with lsb set |
| for (int i = 0; i < tests; i++) { |
| signer.update(messageBytes); |
| byte[] signature = signer.sign(); |
| BigInteger k = extractK(signature, h, priv, i < 10); |
| if (k.testBit(0)) { |
| countLsb++; |
| } |
| if (k.compareTo(qHalf) == 1) { |
| countMsb++; |
| } |
| } |
| if (countLsb < mincount || countLsb > tests - mincount) { |
| fail("Bias detected in the least significant bit of k:" + countLsb); |
| } |
| if (countMsb < mincount || countMsb > tests - mincount) { |
| fail("Bias detected in the most significant bit of k:" + countMsb); |
| } |
| } |
| |
| /** |
| * Checks whether CVE-2016-0695 has been fixed. Before the April 2016 security update, the SUN |
| * provider had a serious flaw that leaked the private key with about 3-5 signatures. In |
| * particular, "Sha1WithDSA" always generated 160 bit k's independently of q. Unfortunately, it is |
| * easily possible to use 2048 and 3072 bit DSA keys together with SHA1WithDSA. All a user has to |
| * do is to use the algorithm name "DSA" instead of "SHA256WithDSA" rsp. "SHA224WithDSA". |
| * |
| * <p>An algorithm to extract the key from the signatures has been described for example in the |
| * paper <a href="http://www.hpl.hp.com/techreports/1999/HPL-1999-90.pdf">Lattice Attacks on |
| * Digital Signature Schemes</a> by N.A. Howgrave-Graham, N.P. Smart. |
| * |
| * <p>This bug is the same as US-CERT: VU # 940388: GnuPG generated ElGamal signatures that leaked |
| * the private key. |
| */ |
| @SlowTest(providers = {ProviderType.BOUNCY_CASTLE, ProviderType.SPONGY_CASTLE}) |
| @SuppressWarnings("InsecureCryptoUsage") |
| public void testBiasSha1WithDSA() throws Exception { |
| String hashAlgorithm = "SHA"; |
| String message = "Hello"; |
| byte[] messageBytes = message.getBytes("UTF-8"); |
| byte[] digest = MessageDigest.getInstance(hashAlgorithm).digest(messageBytes); |
| BigInteger h = new BigInteger(1, digest); |
| |
| KeyPairGenerator generator = java.security.KeyPairGenerator.getInstance("DSA"); |
| generator.initialize(2048); |
| KeyPair keyPair = generator.generateKeyPair(); |
| DSAPrivateKey priv = (DSAPrivateKey) keyPair.getPrivate(); |
| Signature signer = Signature.getInstance("DSA"); |
| try { |
| // Private key and selected algorithm by signer do not match. |
| // Hence throwing an exception at this point would be the reasonable. |
| signer.initSign(priv); |
| signer.update(messageBytes); |
| byte[] signature = signer.sign(); |
| BigInteger q = priv.getParams().getQ(); |
| BigInteger k = extractK(signature, h, priv, true); |
| |
| // Now check if k is heavily biased. |
| int lengthDiff = q.bitLength() - k.bitLength(); |
| if (lengthDiff > 32) { |
| fail( |
| "Severly biased DSA signature:" |
| + " len(q)=" |
| + q.bitLength() |
| + " len(k)=" |
| + k.bitLength()); |
| } |
| } catch (GeneralSecurityException ex) { |
| // The key is invalid, hence getting here is reasonable. |
| return; |
| } |
| } |
| |
| /** |
| * This test checks for potential of a timing attack. The test generates a number of signatures, |
| * selects a fraction of them with a small timing and then compares the values k for the selected |
| * signatures with a normal distribution. The test fails if these ks are much smaller than |
| * expected. An implementation flaw that can lead to a test failure is to compute the signature |
| * with a modular exponentiation with a runtime that depend on the length of the exponent. |
| * |
| * <p>A failing test simply means that the timing can be used to get information about k. Further |
| * analysis is necessary to determine if the bias is exploitable and how many timings are |
| * necessary for an attack. A passing test does not mean that the implementation is secure against |
| * timing attacks. The test only catches relatively big timing differences. It requires high |
| * confidence to fail. Noise on the test machine can prevent that a relation between timing and k |
| * can be detected. |
| * |
| * <p>Claims of what is exploitable: http://www.hpl.hp.com/techreports/1999/HPL-1999-90.pdf 30 |
| * signatures are sufficient to find the private key if the attacker knows 8 bits of each k. |
| * http://eprint.iacr.org/2004/277.pdf 27 signatures are sufficient if 8 bits of each k is known. |
| * Our own old experiments (using 1GB memory on a Pentium-4? CPU): 2^11 signatures are sufficient |
| * with a 3 bit leakage. 2^15 signatures are sufficient with a 2 bit leakage. 2^24 signatures are |
| * sufficient with a 1 bit leakage. Estimate for biased generation in the NIST standard: e.g. 2^22 |
| * signatures, 2^40 memory, 2^64 time |
| * |
| * <p><b>Sample output for the SUN provider:</b> <code> |
| * count:50000 cutoff:4629300 relative average:0.9992225872624547 sigmas:0.3010906585642381 |
| * count:25000 cutoff:733961 relative average:0.976146066585879 sigmas:6.532668708070148 |
| * count:12500 cutoff:688305 relative average:0.9070352192339134 sigmas:18.00255238454385 |
| * count:6251 cutoff:673971 relative average:0.7747148791368986 sigmas:30.850903417893825 |
| * count:3125 cutoff:667045 relative average:0.5901994097874541 sigmas:39.67877152897901 |
| * count:1563 cutoff:662088 relative average:0.4060286694971057 sigmas:40.67294313795137 |
| * count:782 cutoff:657921 relative average:0.2577955312387898 sigmas:35.94906247333319 |
| * count:391 cutoff:653608 relative average:0.1453438859272699 sigmas:29.271192100879457 |
| * count:196 cutoff:649280 relative average:0.08035497211567771 sigmas:22.300206785132406 |
| * count:98 cutoff:645122 relative average:0.05063589092661368 sigmas:16.27820353139225 |
| * count:49 cutoff:641582 relative average:0.018255560447883384 sigmas:11.903018745467488 |
| * count:25 cutoff:638235 relative average:0.009082660721102722 sigmas:8.581595888660086 |
| * count:13 cutoff:633975 relative average:0.0067892346039088326 sigmas:6.20259924188633 |
| * </code> |
| * |
| * <p><b>What this shows:</b> The first line uses all 50'000 signatures. The average k of these |
| * signatures is close to the expected value q/2. Being more selective gives us signatures with a |
| * more biased k. For example, the 196 signatures with the fastest timing have about a 3-bit bias. |
| * From this we expect that 2^19 signatures and timings are sufficient to find the private key. |
| * |
| * <p>A list of problems caught by this test: |
| * <ul> |
| * <li> CVE-2016-5548 OpenJDK8's DSA is vulnerable to timing attacks. |
| * <li> CVE-2016-1000341 BouncyCastle before v 1.56 is vulnernerable to timing attacks. |
| * </ul> |
| */ |
| @SlowTest(providers = {ProviderType.BOUNCY_CASTLE, ProviderType.OPENJDK, |
| ProviderType.SPONGY_CASTLE}) |
| @SuppressWarnings("InsecureCryptoUsage") |
| public void testTiming() throws Exception { |
| // BEGIN Android-removed: Android doesn't support JMX |
| /* |
| ThreadMXBean bean = ManagementFactory.getThreadMXBean(); |
| if (!bean.isCurrentThreadCpuTimeSupported()) { |
| System.out.println("getCurrentThreadCpuTime is not supported. Skipping"); |
| return; |
| } |
| String hashAlgorithm = "SHA-1"; |
| String message = "Hello"; |
| byte[] messageBytes = message.getBytes("UTF-8"); |
| byte[] digest = MessageDigest.getInstance(hashAlgorithm).digest(messageBytes); |
| BigInteger h = new BigInteger(1, digest); |
| KeyPairGenerator generator = java.security.KeyPairGenerator.getInstance("DSA"); |
| generator.initialize(1024); |
| KeyPair keyPair = generator.generateKeyPair(); |
| DSAPrivateKey priv = (DSAPrivateKey) keyPair.getPrivate(); |
| Signature signer = Signature.getInstance("SHA1WITHDSA"); |
| signer.initSign(priv); |
| // The timings below are quite noisy. Thus we need a large number of samples. |
| int samples = 50000; |
| long[] timing = new long[samples]; |
| BigInteger[] k = new BigInteger[samples]; |
| for (int i = 0; i < samples; i++) { |
| long start = bean.getCurrentThreadCpuTime(); |
| signer.update(messageBytes); |
| byte[] signature = signer.sign(); |
| timing[i] = bean.getCurrentThreadCpuTime() - start; |
| k[i] = extractK(signature, h, priv, false); |
| } |
| long[] sorted = Arrays.copyOf(timing, timing.length); |
| Arrays.sort(sorted); |
| // Here we are only interested in roughly the 8 most significant bits of the ks. |
| // Hence, using double is sufficiently precise. |
| double q = priv.getParams().getQ().doubleValue(); |
| double expectedAverage = q / 2; |
| double maxSigmas = 0; |
| System.out.println("testTiming: SHA1WITHDSA"); |
| for (int idx = samples - 1; idx > 10; idx /= 2) { |
| long cutoff = sorted[idx]; |
| int count = 0; |
| double total = 0; |
| for (int i = 0; i < samples; i++) { |
| if (timing[i] <= cutoff) { |
| total += k[i].doubleValue(); |
| count += 1; |
| } |
| } |
| double expectedStdDev = q / Math.sqrt(12 * count); |
| double average = total / count; |
| // Number of standard deviations that the average is away from |
| // the expected value: |
| double sigmas = (expectedAverage - average) / expectedStdDev; |
| if (sigmas > maxSigmas) { |
| maxSigmas = sigmas; |
| } |
| System.out.println( |
| "count:" |
| + count |
| + " cutoff:" |
| + cutoff |
| + " relative average:" |
| + (average / expectedAverage) |
| + " sigmas:" |
| + sigmas); |
| } |
| // Checks if the signatures with a small timing have a biased k. |
| // We use 7 standard deviations, so that the probability of a false positive is smaller |
| // than 10^{-10}. |
| if (maxSigmas >= 7) { |
| fail("Signatures with short timing have a biased k"); |
| } |
| */ |
| // END Android-removed: Android doesn't support JMX |
| } |
| |
| /** |
| * DSA does not allow encryption. This test verifies that a provider does not implement an ad hoc |
| * scheme that attempts to turn DSA into a public key encryption scheme. |
| */ |
| @SuppressWarnings("InsecureCryptoUsage") |
| public void testEncryptionWithDsa() throws Exception { |
| try { |
| Cipher cipher = Cipher.getInstance("DSA"); |
| fail("DSA must not be used as a cipher:" + cipher.getProvider().toString()); |
| } catch (NoSuchAlgorithmException ex) { |
| // This is expected |
| } |
| } |
| } |
