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"The generation of random numbers is too important to be left to chance.” 1 -- Robert R. Coveyou Oak Ridge National Laboratory

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n (modulus) = product of secret primes p and q e (public key) = relatively prime to (p-1)(q-1) d (private key) = e -1 mod ((p-1)(q-1))) Encrypt c=m e mod n Decrypt m=c d mod n Eve gets ciphertext message c from Alice, wants to read it i.e., she wants to find m = c d Choose random r < n, and use Alice’s public key e x=r e mod n y=xc mod n t=r -1 mod n Note if x=r e mod n, then r=x d mod n ! Eve tricks Alice into encrypting (signing) y with her d Alice sends Eve u=y d mod n Eve then calculates tu mod n = r -1 y d mod n = r -1 x d c d mod n = c d mod n = m 2 Chosen ciphertext attack against RSA -Schneier

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ECRYPT 2012 Key Length Advice 3 See

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Captured One-Time Pads

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Russian One-Time Pad captured by MI5 5

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Don’t reuse those one-time pads! If C1=P1 K1 C2=P2 K1 C3=P3 K1 Then try C1 C2 => P1 K1 P2 K1 => P1 P2 C1 C3 => P1 K1 P3 K1 => P1 P3 C2 C3 => P2 K1 P3 K1 => P2 P3 and (P1 P2) (P1 P3) => (P2 P3) (P1 P2) (P2 P3) => (P1 P3) … 6

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From Rick Smith: Don’t reuse those one-time pads!

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Key? What Key? Alice encrypts: P K=>C Bob knows the key and decrypts: C K=>P They agree on a dummy plaintext D and if they’re ever captured, they will give up the key K’=C D If the authorities decrypt C K’ => D 8

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Case study: Heartbleed SSL Bug struct { HeartbeatMessageType type; uint16 payload_length; uchar payload [HeartbeatMessage.payload_length]; uchar padding[padding_length]; } HeartbeatMessage; 9

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Power Analysis 11

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Simple Power Analysis: `DES Parity Check DES-CheckParity(byte Key[8]) for i = 8 down to 1 parity=0; for j = 8 down to 1 if (bit j of Key[i] is set) // CONDITIONAL parity = parity+1 // OPERATION endif endfor if (parity is even) parity_error(); endfor end DES-CheckParity 12

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SPA Attack on DES-Parity 13

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EM History Classified TEMPEST standards. Some parts declassified Jan '01, Published work – EM Leakages from Peripherals, E.g., Monitors: Van Eck, Anderson & Kuhn. – EM Leakage from smart-cards during Computation. J.-J. Quisquater & David Samyde, E-smart 2001, Gemplus Team [GMO ’01], CHES ’01. – SEMA/DEMA attacks. Best results require "decapsulation" of chip packaging and/or precise micro-antennas positioning on chip surface

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Rao et.al.’s Work` Deeper understanding of the EM leakages. – Similar to declassified TEMPEST literature. Key Insights/Results – Plenty of EM signals are available, provided you know what to look for and where. Superior signals and attacks possible without micro- antennas or decapsulation. Some attacks possible from a distance. – EM side-channel(s) >> Power side-channel EM can break DPA-resistant implementations.

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EM Emanations Background Origin/Types of EM Emanations – Direct emanations from intended currents. Maxwell’s equations, Ampere’s and Faraday’s laws. – Unintentional emanations from coupling effects. Depend on physical factors, e.g., circuit geometry. Most couplings ignored by circuit designers. Manifest as modulation of carriers (e.g. clock harmonics) present/generated/introduced in device. – AM or Angle (FM/Phase) Modulation. Compromising signals available via demodulation. Propagation of EM – Radiation, Conduction, Combination of both. E.g., Faint EM signals riding on power line.

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EM Capturing Equipment Antennas (Far-field) and Near-field probes Current probes. Analog processing: Filters/Amplifiers, Tunable wideband receiver or equivalent $$ Digital sampling hardware.

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ICOM wideband radio receiver with IF output

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MAKE YOUR OWN

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EM vs. Power Sometimes, EM is the only side-channel available. – Filtered power supplies, restricted access… – E.g. Crypto Tokens, SSL Accelerators,...

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Time (10ns) Amplitude EM Signal from SSL Accelerator S at 15 feet

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EM vs. Power Is EM useful in the presence of power? Yes, several EM carriers: Generated, Ambient, Introduced… – Experimentally verified: Different carriers carry different information. Some EM leakages substantially different from Power leakages.

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Bad Instructions Instructions where some EM leakage >> Power leakage. Typically CPU intensive rather than bus intensive. All architectures have BAD Instructions. Example: Bit-test on several 6805 based systems leaks tested bit.

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EM Attack Example 2 signals, different data, same exp & modulus 24

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O TESTED BIT = 0 IN BOTH TRACES

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O TESTED BIT DIFFERENT

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Countermeasures Require sound vulnerability assessment. Countermeasures include: – Circuit redesign to reduce unintentional emanations. – Reducing S/N ratio EM Shielding Noise introduction Physically secure zones. – Randomization based software countermeasures similar to DPA countermeasures.

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29 Xkcd

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Netscape 1.1 Seeding Process 30 RNG_CreateContext() { (seconds, microseconds) = time of day; /* Time elapsed since 1970 */ pid = process ID; ppid = parent process ID; a = mklcpr(microseconds); b = mklcpr(pid + seconds + (ppid << 12)); seed = MD5(a, b); /* seed is a global variable */ } mklcpr(x) { /* not cryptographically significant; shown for completeness */ return ((0xDEECE66D * x + 0x2BBB62DC) >> 1); } From Goldberg and Wagner, “Randomness and the Netscape Browser”, Dr. Dobb’s, January 1996.

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Netscape 1.1 Key Generation 31 From Goldberg and Wagner, “Randomness and the Netscape Browser”, Dr. Dobb’s, January RNG_GenerateRandomBytes() { x = MD5(seed); seed = seed + 1; return x; } global variable challenge, secret_key; create_key() { RNG_CreateContext(); tmp = RNG_GenerateRandomBytes(); challenge = RNG_GenerateRandomBytes(); secret_key = RNG_GenerateRandomBytes(); }

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Jone’s RNG Rules 1.Don’t use system generators 2.Use a known good RNG you implemented 3.Properly seed the RNG 32

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KISS Generator (G. Marsaglia) static unsigned int /* Seed variables */ x = , y = , z = , c = ; unsigned int KISS() { unsigned long long t, a = ULL; x = 69069*x+12345; // y never == 0! */ y ^= (y >17); y ^= (y >32); // Also avoid setting z=c=0! return x+y+(z=t); } 33

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