pkcs (public-key cryptography standards) -...

Códigos y Criptografía Francisco Rodríguez Henríquez

PKCS (Public-key cryptographystandards)


Network Access Security Model


Security Levels

• Confidentiality

– Protection from disclosure to unauthorized persons• Integrity

– Maintaining data consistency• Authentication

– Assurance of identity of person or originator of data• Non-repudiation

– Originator of communications can't deny it later• Authorization

– Identity combined with an access policy grants the rights toperform some action


Security Building Blocks

• Encryption provides– confidentiality, can provide authentication and

integrity protection

• Checksums/hash algorithms provide– integrity protection, can provide authentication

• Digital signatures provide– authentication, integrity protection, and non-

repudiation


Keys

• Symetric Keys

– Both parties share the same secret key

– A major problem is securely distributing thekey

– DES - 56 bit key considered unsafe forfinancial purposes since 1998

– 3 DES uses three DES keys


Keys

• Public/Private keys

– One key is the mathematical inverse of theother

– Private keys are known only to the owner– Public key are stored in public servers,

usually in a X.509 certificate.– RSA (patent expires Sept 2000), Diffie-

Hellman, DSA


A Simplified Model of ConventionalEncryption


Public-Key Cryptography


Message Digest• A message digest, also known as a one-way hash function, is a fixed

length computionally unique identifier corresponding to a set of data.That is, each unit of data (a file, a buffer, etc.) will map to a particularshort block, called a message digest. It is not random: digesting the sameunit of data with the same digest algorithm will always produce the sameshort block.

• A good message digest algorithm possesses the following qualities– The algorithm accepts any input data length.– The algorithm produces a fixed length output for any input data.

– The digest does not reveal anything about the input that was used togenerate it.

– It is computationally infeasible to produce data that has a specific digest.– It is computationally infeasible to produce two different unit of data that

produce the same digest.


Hash Algorithms

• Reduce variable-length input to fixed-length (128 or 160bit) output

• Requirements

– Can't deduce input from output

– Can't generate a given output

– Can't find two inputs which produce thesame output


Hash Algorithms

• Used to– Produce fixed-length fingerprint of arbitrary-

length data– Produce data checksums to enable detection

of modifications– Distil passwords down to fixed-length

encryption keys

• Also called message digests orfingerprints


Message AuthenticationCode MAC

• Hash algorithm + key to make hash valuedependant on the key

• Most common form is HMAC (hash MAC)– hash( key, hash( key, data ))

• Key affects both start and end of hashing process

• Naming: hash + key = HMAC-hash– MD5 1 HMAC-MD5– SHA-1 1 HMAC-SHA (recommended)


RSA: An Example


Digital Signatures• Combines a hash with a digital signature

algorithm• To sign

– hash the data– encrypt the hash with the sender's private key– send data signer’s name and signature

• To verify– hash the data– decrypt the signature with the sender's public key– the result of which should match the hash


Digital Signatures

• A data string associating a message with anoriginating entity– Signature generation algorithm– Signature verification algorithm– Signature scheme

• Used for authentication, integrity, andnonrepudiation

• Public key certification is one of the mostsignificant applications


Digital Signature/VerificationSchemes


Diffie-Hellman protocol


Key exchange: Diffie-Hellman protocol

1. Picks a ∈ GF(p) at random2. Computes TA = ga mod p3. Sends TA

4. Receives TB

5. Computes KA = TBa mod p

1. Picks b ∈ GF(p) at random2. Computes TB = gb mod p3. Receives TA

4. Sends TB

5. Computes KB = TAb mod p

Where K = KA = KB, Because:TB

a = (gb)a = gba = gab = (ga)b = TAb mod p

Machine A Machine B


Mensaje para Anita en La Jornada

Querida Anita de mi corazón: Quisiera pedirte que nuestro número primo

sea 128903289023 y nuestra g 23489. Te quiere

Betito.


Middle-person attack.• Consider the following scenario:

Anita Middleperson Betitoga = 8389 gx = 5876 gb = 9267

8389 58765876 9267

Shared key KAX: Shared key KBX

5876a = 8389x 9267x = 5876b

• After this exchange, the middle-person attacker simply decrypts any messages sent out by A or B, and then reads any possibly modifies them before re-encrypting with the appropriate key and transmitting them to the correct party.• Middle-person attack is possible due to the fact that DHC does not authenticate the participants. Possible solutions are digital signatures and other protocol variants.


Solution: Mutual authentication

BA

I am A, R1

R2, KAB {R1}

KAB{R2}


Reflection attack

T

BBT

B

I am A,R1R2, KAB{R1}

I am A, R2

R3, KAB{R2}


Encryption across apacket-switching network


Elements of PKI

• Certificate Authorities (CA)– OpenSSL, Netscape, Verisign, Entrust, RSA Keon

• Public/Private Key Pairs - Key management

• x.509 Identity Certificates - Certificatemanagement

• LDAP servers


• Public-key cryptography standards (PKCS)• Owned by RSA and motivated to promote RSA• Created in early 1990’s• Numbered from PKCS1 to PKCS15• Some along the way have

– lost interest– folded into other PKCS– taken over by other standards bodies

• Continue to evolve

PKCS


RSA cryptosystem by layers

FP finite field operations : Addition, Squaring,

multiplication, inversion and exponentiation

RSA primitive Operations: Encryption: C = Me mod n,Decryption M = Cd mod n.

PKCS Primitives: PKCS1_OAEP_Encode,PKCS1_OAEP_Decode, etc

PKCS User Functions:PKCS1_OAEP_Encrypt,PKCS1_OAEP_Decrypt, PKCS1_v15_Sign,

Protocols and Applications: SSL, TLS, WTLS, WAP,etc.


• RSA Cryptography Standard

Version 2.0 onwards (1998)

RSA Encryption Standard

Version 1.5 (1993)

PKCS 1


• Specifies how to use the RSA algorithmsecurely for encryption and signature

• Why do we need this?

– Padding for encryption

– Different schemes for signature

PKCS 1


• Chosen ciphertext attack based onmultiplicative property of RSA

• Attacker wishes to decrypt cChoose r, compute c’ = c⋅ re mod n

Get victim to decrypt c’ giving cd ⋅ r mod n

cd ⋅ r ⋅ r-1 mod n = cd mod n

• Padding destroys multiplicative property

PKCS 1


RSA: Key Generation


RSA: Encryption, Decryption


RSA: An Example


RSA encryption isdeterministic

Attack example: C = (PIN)e mod n, where PIN is 4-digit number.We can find M by a brute force attack within several 10 seconds.

=> We need a semantically secure cryptosystem!

We can check whether M is the message of C by C=Me mod n.

Semantically secure: For two messages M0, M1, and C = Mb2 mod n,

attackers can not guess whether C is encryption of Mb (b=0,1).

An easy way is to pad M with random integer R like M||R, but no security proof!


Chosen Ciphertext Attack (CCA)

Decryption oracle

ciphertext C

Information based on C,dd

An attack example:(0) We assume the decryption oracle computes Ad mod n for a request.(1) Attacker computes A = ReC mod n for a random R in Zn, and sends A to

the decryption oracle.(2) Decryption oracle computes B = Ad mod n and send B back to the

attacker.(3) The attacker computes B/R = M mod n and get the message M.

There are several models, which are secure against the chosen ciphertext attack


Side Channel AttacksAlgorithm Binary exponentiation Input: a in G, exponent d = (dk,dk-1,…,d0)

(dk is the most significant bit) Output: c = ad in G 1. c = a; 2. For i = k-1 down to 0; 3. c = c2; 4. If di =1 then c = c*a; 5. Return c;

The time or the power to execute c2 and c*a are different

(side channel information).

Algorithm Coron’s exponentiation Input: a in G, exponent d = (dk,dk-1,…,dl0) Output: c = ad in G 1. c[0] = 1; 2. For i = k-1 down to 0; 3. c[0] = c[0]2; 4. c[1] = c[0]*a; 5. c[0] = c[di]; 6. Return c[0];


Differential Fault Attack(DFA)

An attacker obtains a decryption which is computed in a wrong way.

nM = Cd mod n

p dp = d mod (p-1)

Mp = Cdp mod p

dq = d mod (q-1)

Mq =Cdq mod q v = (Mq – Mp) p-1 mod q,

q

n M = Mp + pv mod n.

In the RSA using the CRT, if an attacker can break the computation of v (as v=0), then he/she can factor n by computing gcd(M-Mp,n)=p.


Klima-Rosa attack againstPGP

Decryption oracle

integer X

Xd mod n’d, n’

An attacker can change the public key n to n’

The attacker can obtain Xd mod n’ for changed n’.He/she can recover d by Silver-Pohlig-Hellman algorithm

PGP dose not encrypt the key file which includes n.


Bleichenbacher’s CCADecryption oracle

any integer C mod n

Cd PKCS-format or notd

PKCS-Format for a message m

00 02 random padding 00 message mat least 8 bytes

most significant byte least significant byte

Theorem (Bleichenbacher): Let n be a 1024-bit RSA modus. For a given C, the value Cd mod n can be computed by about 220 accesses to the decryption oracle, where d is the secret key.


• Version 1.5, 1993– Encryption padding was found defective in

1998 by Bleichenbacher– Possible to generate valid ciphertext without

knowing corresponding plaintext withreasonable probability of success (chosenciphertext)

PKCS 1


• Uses Optimal asymmetric encryption protocol (OAEP) byBellare-Rogoway 1994– provably secure in the random oracle model.– Informally, if hash functions are truly random, then an

adversary who can recover such a message must be ableto break RSA

– plaintext-awareness: to construct a valid OAEP encodedmessage, an adversary must know the original plaintext

• PKCS 1 version 1.5 padding continues to be allowed forbackward compatibility

• Accommodation for multi-prime RSA– Speed up private key operations

PKCS 1


• Cryptographic primitives• Cryptographic scheme

– Encryption scheme– Signature scheme

• Signature with appendix: supported• Signature with message recovery: not supported

• Encoding and decoding– Converting an integer message into an octet string

for use in encryption or signature scheme and viceversa

PKCS 1


• Cryptographic primitives

• Encrypt RSAEP((n,e),m)

• Decrypt RSADP((n,d),c)

• Sign RSASP1((n,d),m)

• Verify RSAVP1((n,e),s)

Basically exponentiation with differently namedinputs!!

PKCS 1


Encryption scheme• Combines encryption primitive with an encryption

encoding method• message → encoded message → integer message

representative → encrypted messageDecryption scheme• Combines decryption primitive with a decryption

decoding method• encrypted message → integer message representative →

encoded message → messageOriginal version 1.5 scheme and new version 2.0 scheme

PKCS 1


Encryption scheme• Combines signature primitive with a signature encoding

method.• message → encoded message → integer message

representative → signatureDecryption scheme• Combines verification primitive with a verification

decoding method• signature → integer message representative → encoded• message → messageOriginal version 1.5 scheme

Signature with appendix

PKCS 1


PKCS 1

Comp. mess. digestMD’Message digestMD

Length of X in octets||X||MessageMsignatureSpriv exp.dPadding stringPSpublic exp.eBlock typeBTPrime factors of np, q

Encrypted dataEDThe modulus, 28(k-

1)≤ n<28kn

Encryption blockEBLength of n in octetskMeaningSymbolMeaningSymbol


The data is an octet string D, where ||D|| ≤ k-11. BT is a single octet whose hexrepresentation is either 00 or 01. PS is anoctet string with ||PS|| = k -3-||D||. If BT =00, then all octets in PS are 00; if BT=01,then all octets in PS are FF.

PKCS Data formatting


PKCS-Format for a message m

00 02 random padding 00 message mat least 8 bytes

most significant byte least significant byte

PKCS Data formattingThe formatted data block (called the encryption block) is:

EB = 00||BT||PS||00||D.


i. The leading 00 block ensures that the octetstring EB, when interpreted as an integer, isless than the modulus n.

ii. If the block type is BT = 00, then either D mustbegin with a non-zero octet or its length mustbe known, in order to permit unambiguousparsing of EB.



iii. If BT = 01, then unambiguous parsing isalways possible.

iv. For the reason given in (iii), and tothwart certain potential attacks on thesignature mechanism, BT = 01 isrecommended.



Example: Suppose that n is a 1024-bitmodulus (so k = 128). If ||D|| = 20 octets,then ||PS|| = 105 octets, so that ||EB|| =128 octets.



1. Message Hashing. Hash the message Musing the selected message-digest algorithmto get the octet string MD.

2. Message Digest Encoding. MD and thehash algorithm identifier are combined intoan ASN.1 (Abstract Syntax Notation) valueand then BER-encoded (Basic EncodedRules) to give an octec data string D.

Signature process for PKCS #1


3. Data block formatting. With data stringinput D, use the data formatting discussedpreviously to form octet string EB.

4. Octet-string2integer conversion. Let theoctets ob EB be EB1|| EB1|| EB2||… ||EBk.Define EB’i to be the integer whose binaryrepresentation is the octet EBi (LSB bit ison the right).



5. RSA Computation. Compute s = md mod n.

6. Integer2octet-string conversion. Convert s

to an octet string. The signature is S = ED.




5. RSA COmputation

4. OctetString2integer conversion3. Data block formatting

2. Message Digest Encoding

1. Message Hashing

6. Integer2octetString conversion

MESSAGE

SIGNATURE


1. Octet-string2integer conversion. Reject S ifthe bit-length of S is not a multiple of 8.Convert S to an integer s as in step 4 of thesignature process. Reject the signature is s >n.

2. RSA Computation. Compute m = se mod n.

Verification process forPKCS #1


3. Integer2octet-string conversion. Convert mto an octet string as in step 6 of thesignature process.

4. Parsing. Parse EB into a block type BT, apadding string PS, and the data D.

• Reject if EB cannot be parsed unambiguously.• Reject if BT is not one of 00 or 01.• Reject if PS consists of < 8 octets or is

inconsistent with BT.



5. Data Decoding.– BER-decode D to get a message digest MD and

a hash algorithm identifier.

– Reject if the hashing algorithm does not identifyone of MD2 or MD5.

6. Message Digest and Comparison. Hash themessage M using the selected message-digest algorithm to get the octet string MD’and compare it with MD obtained in (5).




5. Data Encoding

4. Parsing3. Integer2octetString conversion

2. RSA Computation

1. OctetString2integer conversion

6. Message digesting and comparison

Signature and message

SIGNATURE


Probabilistic signature scheme (PSS)

Provably secure in random oracle model

Natural extension to message recovery

PKCS 1: The Future

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