Crypto Pitfalls. or why cryptography is harder than it looks P. Veríssimo All rights reserved. Reproduction only by permission

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1 Crypto Pitfalls or why cryptography is harder than it looks 1 RECALL: Generic problems of symmetric crypto key is shared and secret, if lost/revealed at either end, the channel is compromised key distribution is a critical point, the chicken-and-egg problem: new key must get securely to both ends awkward if keys are to be changed frequently key management becomes worrying for large systems, since one key is needed for each pair of participants arbitrary communication among 10 participants requires 45 keys and this number goes up to almost 5000, for 100 participants in fact, (n(n-1)/2) keys are needed for n participants 2

2 RECALL: Generic problems of asymmetric crypto asymmetric crypto does not have the key distribution problem of symmetric crypto however, problem now lies on authenticity of a said public key suppose Bob sends his public key which is intersected and replaced or suppose the public key database (a.k.a. PKI or CA) is compromised: Bob s key can be replaced by a phony key known to intruder Trudy Certification Authority deployment thus requires great care 3 RECALL: Generic problems of crypto hashes Uniqueness of hashes is not guaranteed Collisions between x and x happen when there is: x x and h(x) = h(x ) There is a logical reason, the Pigeonhole principle: if there are n containers for n+1 objects, then at least one container will have 2 objects in it. Examples for hashes consider 3-bit hash function: 8 possible hash values consider 5-bit long files: 32 possible different files each hash value corresponds to at least 32/8=4 files 128-bit hashes, 1000-bit msgs: approx msgs map to same hash 4

3 Generic problems of Digital Signatures Key management is a crucial issue should foresee different types of keys (session vs. long-term) should foresee infrastructure to identify holders and allow revoking replay, re-utilization: a signed message sent more than once in a protocol a cheque can be copied and used twice repudiation Alice may lie, right after signing a bill, and say key was compromised before that countermeasures include non-reusable info use of sequence numbers (impractical for general use) time-related info e.g. time-stamps (needs synchronized clocks) challenge/response (using nonces) but there may always be a non-technical window of vulnerability 5 Digital Signatures with RSA (recap) equivalent to using the RSA private key to encrypt a message Some attacks may loom Attack #1 (smooth numbers): when Bob signs several messages without checking what, giving Alice a collection of small (smooth) signed messages remedies: check what you sign; always sign digests, not messages Attack #2 (key change): changing key to a certain value that matches a desired message allowed when Alice encrypted before signing remedies: all users use same exponent but vary module; but in fact, best is never to sign anything encrypted, please Attack #3 (same algorithm): should not use same algorithm for signing and encrypting in a protocol 6

4 Attack #1 smooth-numbers Example: Alice, Bob communicating n A = 95, e A = 59, d A = 11 n B = 77, e B = 53, d B = 17 suppose there are 26 contracts, 00 to 25 Alice has Bob sign 05 and 17 without Bob checking: c 05 = m db mod n B = mod 77 = 3 c 17 = m db mod n B = mod 77 = 19 Alice starts her game 05, 17 were rigged so that mod 77 = 08, a bad contract for Bob corresponding signature is c = c 05 c 17 = mod 77 = 57 Alice can compute c and claims Bob signed 08 Judge computes c e B mod nb = mod 77 = 08 Signature validated; Bob has a problem public key: (e, n); private key: (d, n); 7 Recall: Attack #2 key-change n A = 95, e A = 59, d A = 11 n B = 77, e B = 53, d B = 17 Bob, Alice agree to sign contract 06 Alice encrypts, then signs: (m e B mod nb ) d A mod na = (06 53 mod 77) 11 mod 95 = 63 Bob now changes his public key Computes r such that 13 r mod 77 = 6; say, r = 59 Computes re B mod (n B ) = mod 60 = 7 Replaces public key e B with 7, private key d B = 43 Bob claims contract was 13, a bad contract for Alice Judge computes c ea mod n B = (63 59 mod 95) 43 mod 77 = 13 Signature validated; Alice has a problem 8

5 Attack #3 - same-algorithm Delivery receipt of signed and confidential document: Alice signed, encrypted, and sent: Eb(Sa(M)) Bob receives and immediately produces receipt, i.e., signs, encrypts and sends: Ea (Sb (Eb (Sa(M)))) Bob now decrypts and verifies: Va( Db( Eb(Sa(M)))) = M Attack on mechanism above, when algorithm for encrypting and signing is the same: legitimate but malicious user with interception capability recall that Ea=Va e Da=Sa Mallory gets 1st message and resends as his: Eb(Da(M)) equiv: Eb(Sa(M)) Bob sends receipt automatically to Mallory: Em (Db [Eb (Da(M))]) equiv: (Sb (Eb (Sa(M)))) Mallory can read M, making Ea (Dm[Em (Db [Eb (Da(M))])] ) = M 9 Attacking a secure channel 1- Attacking ALGORITHMS best protection is making it public, tested by many 2- Attacking MESSAGES shows that a channel does not live only on good ciphers 3- Attacking PROTOCOL EXECUTION protocols need robust design (exception handling, bounds check) 4- Attacking KEYS shows that the best algorithms on the best protocols can still fail by the weakest link best protection is use good quality keys (long, random), and avoid exposure as much as possible 10

6 Attacking Algorithms Ciphertext-only attacker gathers as much encrypted material as possible e.g., statistical analysis: ciphertext may follow repetitions of plaintext Known-plaintext life gets easier if attacker has corresponding pairs clear/cipher-text Chosen-plaintext life gets even easier if attacker can choose the text that will be encrypted and then get corresponding pairs clear/cipher-text e.g., provoking the transmission of a given cleartext OBSERVATIONS: RSA, IDEA or AES have resisted the erosion of time w.r.t. cryptanalysis, but one can never guess the future forget about DES except some legacy app s, with triple DES safeguard crypto material from analysis: use temporary keys (K) encrypted by long-term (L) keys (key-encrypting keys) : EL(K)EK(M) 11 Statistical analysis example If plaintext repeats, ciphertext may too Example using DES: input (in hex): corresponding output (in hex): ef7c 4bb2 b4ce 6f3b ef7c 4bb2 b4ce 6f3b Fix: cascade blocks together (chaining) see later: encryption modes! 12

7 Attacking Messages replay and/or reordering of cipher blocks individual ciphertext blocks (typ 64bit) can be replayed in subsequent messages, re-concatenated with others, or reordered pre-computation or forward searches when set of possible M messages is small, pre-compute set of all possible ciphertexts E(M) and build a look-up table (mi, E(mi)) when a ciphertext E(mk)) appears, use table to find mk can it be used with any kind of cipher? known-challenge pre-computation when a challenge X is known or can be chosen and presented to victim for encryption, for fixed X, pre-compute set of all possible ciphertexts Eki(X) as a function of ki and build a look-up table (ki, Eki(X)) when a ciphertext Eki(X) is obtained, use table to find ki can it be used with any kind of cipher? 13 Attacking Messages EXAMPLES of message attacks : understanding of block meaning through KPT or CPT attacks Intersection, reordering or forgery of messages, e.g. bank deposit order changing genuine account number with hacker s account number encryption mode should prevent this. How? OBSERVATIONS : pre-computation can only be used with asymmetric crypto one should encrypt each block with random information, padding, and /or create dependence from previous block, e.g. by chaining 14

8 Pre-computation example Cathy knows Alice will send Bob one of two messages: encrypted BUY, or encrypted SELL Using public key Ku Bob, Cathy pre-computes a table of possible messages including: m 1 = E Ku Bob (BUY) m 2 = E Ku Bob (SELL) Cathy sniffs m 2 when Alice sends it to Bob she looks the message up in her table and knows Alice sent SELL! 15 Reordering example Alice sends Bob message n Bob = 77, e Bob = 17, d Bob = 53 message is LIVE ( ) encrypted message is Eve intercepts it, rearranges blocks now encrypted message is Bob gets encrypted message, decrypts it he sees EVIL 16

9 Attacking Protocol Execution attacker studies the protocol and performs active attacks to make it take wrong decisions, such as: surrendering a shared secret key letting attacker into a server without completing his authentication reproduction intruder repeats sequences of interactions, eventually modified in order to penetrate the system confusion intruder inserts interactions at chosen steps that confuse protocol code (expected message i, gets message k, decides wrongly) OBSERVATIONS : a protocol can only be made as resilient as the underlying algorithm use good engineering practice to make protocol robust validate protocol against some formal specification of the algorithm using nonces and time-dependent info makes reproduction difficult a spoofing attack can undermine an otherwise correct crypto system 17 Attacking Keys weak keys e.g., obtained from naïve passwords groups of weak keys (happens in some algorithms) EXAMPLE: intruder captures ciphertext messages and tries a dictionary-based guessing attack with probable weak keys until a match is found OBSERVATIONS : carefully draft keys (long, nonce, random, are sacred words here) make guessing attacks ineffective by rendering recovered cleartext unintelligible» e.g., looking for english words in deciphered blocks is incredibly easier than trying to find them in a compressed or obfuscated file 18

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