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PKCS ( Public-key cryptography standards )

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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 to perform some action

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

Symetric Keys

Both parties share the same secret key

A major problem is securely distributing the key

DES - 56 bit key considered unsafe for financial purposes since 1998

3 DES uses three DES keys

Public/Private keys

One key is the mathematical inverse of the other

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 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 particular short block, called a message digest. It is not random: digesting the same unit of data with the same digest algorithm will always produce the same short 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 to generate 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.

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 the same output

Used to

Produce fixed-length fingerprint of arbitrary-length data

Produce data checksums to enable detection of modifications

Distill passwords down to fixed-length encryption keys

Also called message digests or fingerprints

Hash algorithm + key to make hash value dependant 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

MD51 HMAC-MD5

SHA-11 HMAC-SHA (recommended)

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

- A data string associating a message with an originating entity
- Signature generation algorithm
- Signature verification algorithm
- Signature scheme

- Used for authentication, integrity, and nonrepudiation
- Public key certification is one of the most significant applications

Diffie-Hellman protocol

Diffie-Hellman protocol

Diffie-Hellman protocol

Machine A

MachineB

1.Picks a GF(p)at random

2.Computes TA = ga mod p

3.Sends TA

4. Receives TB

5. Computes KA = TBamod p

1.Picks b GF(p) at random

2.Computes TB = gb mod p

3.Receives TA

4. Sends TB

5. Computes KB = TAbmod p

Where K = KA =KB, Because:

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

Querida Anita de mi corazón:

Quisiera pedirte que nuestro número primo sea 128903289023 y nuestra g23489.

Te quiere

Betito.

- Consider the following scenario:
AnitaMiddlepersonBetito

ga = 8389 gx = 5876 gb = 9267

8389 5876

58769267

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.

I am A, R1

A

B

R2, KAB {R1}

KAB{R2}

I am A, R1

T

B

R2, KAB{R1}

B

- I am A, R2

B

T

R3, KAB{R2}

Certificate Authorities (CA)

OpenSSL, Netscape, Verisign, Entrust, RSA Keon

Public/Private Key Pairs - Key management

x.509 Identity Certificates - Certificate management

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

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

PKCS User Functions:PKCS1_OAEP_Encrypt, PKCS1_OAEP_Decrypt, PKCS1_v15_Sign,

PKCS Primitives: PKCS1_OAEP_Encode, PKCS1_OAEP_Decode, etc

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

FPfinite field operations : Addition, Squaring, multiplication, inversion and exponentiation

RSA Cryptography Standard

Version 2.0 onwards (1998)

RSA Encryption Standard

Version 1.5 (1993)

Specifies how to use the RSA algorithm securely for encryption and signature

Why do we need this?

Padding for encryption

Different schemes for signature

Chosen ciphertext attack based on multiplicative property of RSA

Attacker wishes to decrypt c

Choose 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

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

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!

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!

Decryption oracle

ciphertext C

d

Information based on C,d

- 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.
- Decryption oracle computes B = Ad mod n and send B back to the attacker.
- 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

Algorithm 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

c2and 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];

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

M = Cd mod n

n

dq = d mod (q-1)

Mq =Cdq mod q

v = (Mq – Mp) p-1 mod q,

dp = d mod (p-1)

Mp = Cdp mod p

p

q

M = Mp + pv mod n.

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.

PGP dose not encrypt the key file which includes n.

Decryption oracle

integer X

d, n’

Xd mod 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

Decryption oracle

any integer C mod n

d

Cd∈ PKCS-format or not

PKCS-Format for a message m

most significant byte

least significant byte

00

02

random padding

00

message m

at least 8 bytes

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 with reasonable probability of success (chosen ciphertext)

Uses Optimal asymmetric encryption protocol (OAEP) by Bellare-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 able to break RSA

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

PKCS 1 version 1.5 padding continues to be allowed for backward compatibility

Accommodation for multi-prime RSA

Speed up private key operations

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 vice versa

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 named inputs!!

Encryption scheme

Combines encryption primitive with an encryption encoding method

message encoded message integer message representative encrypted message

Decryption scheme

Combines decryption primitive with a decryption decoding method

encrypted message integer message representative encoded message message

Original version 1.5 scheme and new version 2.0 scheme

Encryption scheme

Combines signature primitive with a signature encoding method.

message encoded message integer message representative signature

Decryption scheme

Combines verification primitive with a verification decoding method

signature integer message representative encoded

message message

Original version 1.5 scheme

Signature with appendix

The data is an octet string D, where ||D|| ≤ k-11. BT is a single octet whose hex representation is either 00 or 01. PS is an octet 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.

The formatted data block (called the encryption block) is:

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

PKCS-Format for a message m

most significant byte

least significant byte

00

02

random padding

00

message m

at least 8 bytes

The leading 00 block ensures that the octet string EB, when interpreted as an integer, is less than the modulus n.

If the block type is BT = 00, then either D must begin with a non-zero octet or its legth must be known, in order to permit unambiguous parsing of EB.

If BT = 01, then unambiguous parsing is always possible.

For the reason given in (iii), and to thwart certain potential attacks on the signature mechanism, BT = 01 is recommended.

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

Message Hashing. Hash the message M using the selected message-digest algorithm to get the octet string MD.

Message Digest Encoding. MD and the hash algorithm identifier are combined into an ASN.1 (Abstract Syntax Notation) value and then BER-encoded (Basic Encoded Rules) to give an octec data string D.

Data block formatting. With data string input D, use the data formatting discussed previously to form octet string EB.

Octet-string2integer conversion. Let the octets ob EB be EB1|| EB1|| EB2||… ||EBk. Define EB’i to be the integer whose binary representation is the octet EBi (LSB bit is on the right).

RSA Computation. Compute s = md mod n.

Integer2octet-string conversion. Convert s to an octet string. The signature is S = ED.

1. Message Hashing

2. Message Digest Encoding

3. Data block formatting

4. OctetString2integer conversion

5. RSA COmputation

6. Integer2octetString conversion

MESSAGE

SIGNATURE

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

RSA Computation. Compute m = se mod n.

Integer2octet-string conversion. Convert m to an octet string as in step 6 of the signature process.

Parsing. Parse EB into a block type BT, a padding 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.

Data Decoding.

BER-decode D to get a message digest MD and a hash algorithm identifier.

Reject if the hashing algorithm does not identify one of MD2 or MD5.

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

1. OctetString2integer conversion

2. RSA Computation

3. Integer2octetString conversion

4. Parsing

5. Data Encoding

6. Message digesting and comparison

Signature and message

SIGNATURE

Probabilistic signature scheme (PSS)

Provably secure in random oracle model

Natural extension to message recovery