212-81 EC-Council Certified Encryption Specialist (ECES) Questions and Answers

Menezes-Qu-Vanstone

https://en.wikipedia.org/wiki/MQV

MQV (Menezes–Qu–Vanstone) is an authenticated protocol for key agreement based on the Diffie–Hellman scheme. Like other authenticated Diffie–Hellman schemes, MQV provides protection against an active attacker. The protocol can be modified to work in an arbitrary finite group, and, in particular, elliptic curve groups, where it is known as elliptic curve MQV (ECMQV).

MQV was initially proposed by Alfred Menezes, Minghua Qu and Scott Vanstone in 1995. It was modified with Law and Solinas in 1998.

Chosen Plaintext Attack

https://en.wikipedia.org/wiki/Chosen-plaintext_attack

A chosen-plaintext attack (CPA) is an attack model for cryptanalysis which presumes that the attacker can obtain the ciphertexts for arbitrary plaintexts. The goal of the attack is to gain information that reduces the security of the encryption scheme.

Explanation

The key expansion phase

https://en.wikipedia.org/wiki/Advanced_Encryption_Standard

KeyExpansion – round keys are derived from the cipher key using the AES key schedule. AES requires a separate 128-bit round key block for each round plus one more.

Substitution

https://en.wikipedia.org/wiki/Atbash

Atbash is a monoalphabetic substitution cipher originally used to encrypt the Hebrew alphabet. It can be modified for use with any known writing system with a standard collating order.

Correct answers: Transport mode and Tunnel mode

https://en.wikipedia.org/wiki/IPsec#Modes_of_operation

The IPsec protocols AH and ESP can be implemented in a host-to-host transport mode, as well as in a network tunneling mode.

Only the key needs to be secret, not the actual algorithm

https://en.wikipedia.org/wiki/Kerckhoffs%27s_principle

Kerckhoffs's principle of cryptography was stated by Netherlands born cryptographer Auguste Kerckhoffs in the 19th century: A cryptosystem should be secure even if everything about the system, except the key, is public knowledge.

Explanation

lbs

https://en.wikipedia.org/wiki/Bit_numbering#:~:text=In%20computing%2C%20the%20least%20significant,number%20is%20even%20or%20odd.

The least significant bit (LSB) is the bit position in a binary integer giving the units value, that is, determining whether the number is even or odd. The LSB is sometimes referred to as the low-order bit or right-most bit, due to the convention in positional notation of writing less significant digits further to the right. It is analogous to the least significant digit of a decimal integer, which is the digit in the ones (right-most) position.

Explanation

4

https://en.wikipedia.org/wiki/Feistel_cipher

Michael Luby and Charles Rackoff analyzed the Feistel cipher construction, and proved that if the round function is a cryptographically secure pseudorandom function, with Ki used as the seed, then 3 rounds are sufficient to make the block cipher a pseudorandom permutation, while 4 rounds are sufficient to make it a "strong" pseudorandom permutation (which means that it remains pseudorandom even to an adversary who gets oracle access to its inverse permutation). Because of this very important result of Luby and Rackoff, Feistel ciphers are sometimes called Luby–Rackoff block ciphers.

Explanation

RA (Registration Authority)

https://en.wikipedia.org/wiki/Registration_authority

Registration authorities exist for many standards organizations, such as ANNA (Association of National Numbering Agencies for ISIN), the Object Management Group, W3C, IEEE and others. In general, registration authorities all perform a similar function, in promoting the use of a particular standard through facilitating its use. This may be by applying the standard, where appropriate, or by verifying that a particular application satisfies the standard's tenants. Maintenance agencies, in contrast, may change an element in a standard based on set rules – such as the creation or change of a currency code when a currency is created or revalued (i.e. TRL to TRY for Turkish lira). The Object Management Group has an additional concept of certified provider, which is deemed an entity permitted to perform some functions on behalf of the registration authority, under specific processes and procedures documented within the standard for such a role.

3DES

https://en.wikipedia.org/wiki/Triple_DES

Triple DES (3DES) has a three different keys with same size (56-bit).

Explanation

DESX

https://en.wikipedia.org/wiki/DES-X

In cryptography, DES-X (or DESX) is a variant on the DES (Data Encryption Standard) symmetric-key block cipher intended to increase the complexity of a brute-force attack using a technique called key whitening.

Rijndael

https://en.wikipedia.org/wiki/Advanced_Encryption_Standard

The Advanced Encryption Standard (AES), also known by its original name Rijndael. The algorithm described by AES is a symmetric-key algorithm, meaning the same key is used for both encrypting and decrypting the data.

Explanation

128 bit and CCMP

Counter Mode with Cipher Block Chaining Message Authentication Code Protocol (CCMP) is an encryption protocol that forms part of the 802.11i standard for wireless local area networks (WLANs), particularly those using WiMax technology. CCMP employs 128-bit keys and a 48-bit initialization vector that minimizes vulnerability to replay attacks.

MQV

https://en.wikipedia.org/wiki/MQV

MQV (Menezes–Qu–Vanstone) is an authenticated protocol for key agreement based on the Diffie–Hellman scheme. Like other authenticated Diffie–Hellman schemes, MQV provides protection against an active attacker. The protocol can be modified to work in an arbitrary finite group, and, in particular, elliptic curve groups, where it is known as elliptic curve MQV (ECMQV).

IV

https://en.wikipedia.org/wiki/Initialization_vector

In cryptography, an initialization vector (IV) or starting variable (SV) is a fixed-size input to a cryptographic primitive that is typically required to be random or pseudorandom. Randomization is crucial for encryption schemes to achieve semantic security, a property whereby repeated usage of the scheme under the same key does not allow an attacker to infer relationships between segments of the encrypted message. For block ciphers, the use of an IV is described by the modes of operation. Randomization is also required for other primitives, such as universal hash functions and message authentication codes based thereon.

CRL

https://en.wikipedia.org/wiki/Certificate_revocation_list

In cryptography, a certificate revocation list (or CRL) is "a list of digital certificates that have been revoked by the issuing certificate authority (CA) before their scheduled expiration date and should no longer be trusted".

Explanation

It maintains letter and word frequency

https://en.wikipedia.org/wiki/Frequency_analysis

Frequency analysis (also known as counting letters) is the study of the frequency of letters or groups of letters in a ciphertext. The method is used as an aid to breaking classical ciphers.

Frequency analysis is based on the fact that, in any given stretch of written language, certain letters and combinations of letters occur with varying frequencies. Moreover, there is a characteristic distribution of letters that is roughly the same for almost all samples of that language. For instance, given a section of English language, E, T, A and O are the most common, while Z, Q, X and J are rare. Likewise, TH, ER, ON, and AN are the most common pairs of letters (termed bigrams or digraphs), and SS, EE, TT, and FF are the most common repeats. The nonsense phrase "ETAOIN SHRDLU" represents the 12 most frequent letters in typical English language text.

In some ciphers, such properties of the natural language plaintext are preserved in the ciphertext, and these patterns have the potential to be exploited in a ciphertext-only attack.

Instance Deduction

https://en.wikipedia.org/wiki/Cryptanalysis

The results of cryptanalysis can also vary in usefulness. For example, cryptographer Lars Knudsen (1998) classified various types of attack on block ciphers according to the amount and quality of secret information that was discovered:

Total break — the attacker deduces the secret key.

Global deduction — the attacker discovers a functionally equivalent algorithm for encryption and decryption, but without learning the key.

Instance (local) deduction — the attacker discovers additional plaintexts (or ciphertexts) not previously known.

Information deduction — the attacker gains some Shannon information about plaintexts (or ciphertexts) not previously known.

Distinguishing algorithm — the attacker can distinguish the cipher from a random permutation.

Explanation

Brute force

https://en.wikipedia.org/wiki/Brute-force_attack

A brute-force attack consists of an attacker submitting many passwords or passphrases with the hope of eventually guessing correctly. The attacker systematically checks all possible passwords and passphrases until the correct one is found. Alternatively, the attacker can attempt to guess the key which is typically created from the password using a key derivation function. This is known as an exhaustive key search.

A brute-force attack is a cryptanalytic attack that can, in theory, be used to attempt to decrypt any encrypted data (except for data encrypted in an information-theoretically secure manner). Such an attack might be used when it is not possible to take advantage of other weaknesses in an encryption system (if any exist) that would make the task easier.

Explanation

Salting

https://en.wikipedia.org/wiki/Salt_(cryptography)

A salt is random data that is used as an additional input to a one-way function that hashes data, a password or passphrase. Salts are used to safeguard passwords in storage. Historically a password was stored in plaintext on a system, but over time additional safeguards were developed to protect a user's password against being read from the system.

A new salt is randomly generated for each password. In a typical setting, the salt and the password (or its version after key stretching) are concatenated and processed with a cryptographic hash function, and the output hash value (but not the original password) is stored with the salt in a database. Hashing allows for later authentication without keeping and therefore risking exposure of the plaintext password in the event that the authentication data store is compromised.

Salts defend against a pre-computed hash attack, e.g. rainbow tables.Since salts do not have to be memorized by humans they can make the size of the hash table required for a successful attack prohibitively large without placing a burden on the users. Since salts are different in each case, they also protect commonly used passwords, or those users who use the same password on several sites, by making all salted hash instances for the same password different from each other.

Explanation

WPA2

https://en.wikipedia.org/wiki/Wi-Fi_Protected_Access#WPA2

WPA2 use the Counter Mode-Cipher Block Chaining (CBC)-Message Authentication Code (MAC) Protocol (CCMP).

TLS

https://en.wikipedia.org/wiki/Mutual_authentication

Mutual authentication or two-way authentication refers to two parties authenticating each other at the same time, being a default mode of authentication in some protocols (IKE, SSH) and optional in others (TLS).

By default the TLS protocol only proves the identity of the server to the client using X.509 certificate and the authentication of the client to the server is left to the application layer. TLS also offers client-to-server authentication using client-side X.509 authentication. As it requires provisioning of the certificates to the clients and involves less user-friendly experience, it's rarely used in end-user applications.

Explanation

Correct answers: Variable length input, fixed length output and Not reversible

https://en.wikipedia.org/wiki/Hash_function

A hash function is any function that can be used to map data of arbitrary size to fixed-size values. The values returned by a hash function are called hash values, hash codes, digests, or simply hashes. The values are used to index a fixed-size table called a hash table. Use of a hash function to index a hash table is called hashing or scatter storage addressing.

Correct answers: 128, 192, 256

https://en.wikipedia.org/wiki/Advanced_Encryption_Standard

The Advanced Encryption Standard (AES), also known by its original name Rijndael, is a specification for the encryption of electronic data established by the U.S. National Institute of Standards and Technology (NIST) in 2001.

AES is a subset of the Rijndael block cipher developed by two Belgian cryptographers, Vincent Rijmen and Joan Daemen, who submitted a proposal to NIST during the AES selection process. Rijndael is a family of ciphers with different key and block sizes. For AES, NIST selected three members of the Rijndael family, each with a block size of 128 bits, but three different key lengths: 128, 192 and 256 bits.

Entropy

https://en.wikipedia.org/wiki/Entropy_(information_theory)

In information theory, the entropy of a random variable is the average level of "information", "surprise", or "uncertainty" inherent in the variable's possible outcomes. The concept of information entropy was introduced by Claude Shannon in his 1948 paper "A Mathematical Theory of Communication".

Online Certificate Status Protocol (OCSP)

https://en.wikipedia.org/wiki/Online_Certificate_Status_Protocol

The Online Certificate Status Protocol (OCSP) is an Internet protocol used for obtaining the revocation status of an X.509 digital certificate. It is described in RFC 6960 and is on the Internet standards track. It was created as an alternative to certificate revocation lists (CRL), specifically addressing certain problems associated with using CRLs in a public key infrastructure (PKI).

X.509

https://en.wikipedia.org/wiki/X.509

In cryptography, X.509 is a standard defining the format of public key certificates. X.509 certificates are used in many Internet protocols, including TLS/SSL, which is the basis for HTTPS, the secure protocol for browsing the web. They are also used in offline applications, like electronic signatures. An X.509 certificate contains a public key and an identity (a hostname, or an organization, or an individual), and is either signed by a certificate authority or self-signed. When a certificate is signed by a trusted certificate authority, or validated by other means, someone holding that certificate can rely on the public key it contains to establish secure communications with another party, or validate documents digitally signed by the corresponding private key.

Whitening

https://en.wikipedia.org/wiki/Key_whitening

In cryptography, key whitening is a technique intended to increase the security of an iterated block cipher. It consists of steps that combine the data with portions of the key.

The most common form of key whitening is xor-encrypt-xor -- using a simple XOR before the first round and after the last round of encryption.

The first block cipher to use a form of key whitening is DES-X, which simply uses two extra 64-bit keys for whitening, beyond the normal 56-bit key of DES. This is intended to increase the complexity of a brute force attack, increasing the effective size of the key without major changes in the algorithm. DES-X's inventor, Ron Rivest, named the technique whitening.

ADFVGX Cipher

https://en.wikipedia.org/wiki/ADFGVX_cipher

ADFGVX cipher was a field cipher used by the German Army on the Western Front during World War I. ADFGVX was in fact an extension of an earlier cipher called ADFGX.

Invented by Lieutenant Fritz Nebel (1891–1977) and introduced in March 1918, the cipher was a fractionating transposition cipher which combined a modified Polybius square with a single columnar transposition.

They can form a part of viable encryption methods

for example - https://en.wikipedia.org/wiki/XOR_cipher

The XOR operator is extremely common as a component in more complex ciphers. By itself, using a constant repeating key, a simple XOR cipher can trivially be broken using frequency analysis. If the content of any message can be guessed or otherwise known then the key can be revealed. Its primary merit is that it is simple to implement, and that the XOR operation is computationally inexpensive. A simple repeating XOR (i.e. using the same key for xor operation on the whole data) cipher is therefore sometimes used for hiding information in cases where no particular security is required. The XOR cipher is often used in computer malware to make reverse engineering more difficult.

IDEA

https://en.wikipedia.org/wiki/International_Data_Encryption_Algorithm

In cryptography, the International Data Encryption Algorithm (IDEA), originally called Improved Proposed Encryption Standard (IPES), is a symmetric-key block cipher designed by James Massey of ETH Zurich and Xuejia Lai and was first described in 1991. The algorithm was intended as a replacement for the Data Encryption Standard (DES). IDEA is a minor revision of an earlier cipher Proposed Encryption Standard (PES).

The cipher was designed under a research contract with the Hasler Foundation, which became part of Ascom-Tech AG. The cipher was patented in a number of countries but was freely available for non-commercial use. The name "IDEA" is also a trademark. The last patents expired in 2012, and IDEA is now patent-free and thus completely free for all uses.

IDEA was used in Pretty Good Privacy (PGP) v2.0 and was incorporated after the original cipher used in v1.0, BassOmatic, was found to be insecure. IDEA is an optional algorithm in the OpenPGP standard.

Explanation

Wired Equivalent Privacy (WEP)

https://en.wikipedia.org/wiki/Wired_Equivalent_Privacy#Weak_security

In 2007, Erik Tews, Andrei Pychkine, and Ralf-Philipp Weinmann were able to extend Klein's 2005 attack and optimize it for usage against WEP. With the new attack it is possible to recover a 104-bit WEP key with probability 50% using only 40,000 captured packets. For 60,000 available data packets, the success probability is about 80% and for 85,000 data packets about 95%. Using active techniques like deauth and ARP re-injection, 40,000 packets can be captured in less than one minute under good conditions. The actual computation takes about 3 seconds and 3 MB of main memory on a Pentium-M 1.7 GHz and can additionally be optimized for devices with slower CPUs. The same attack can be used for 40-bit keys with an even higher success probability.

Explanation

RIPEMD

https://en.wikipedia.org/wiki/RIPEMD

RIPEMD (RIPE Message Digest) is a family of cryptographic hash functions developed in 1992 (the original RIPEMD) and 1996 (other variants). There are five functions in the family: RIPEMD, RIPEMD-128, RIPEMD-160, RIPEMD-256, and RIPEMD-320, of which RIPEMD-160 is the most common.

The original RIPEMD, as well as RIPEMD-128, is not considered secure because 128-bit result is too small and also (for the original RIPEMD) because of design weaknesses. The 256- and 320-bit versions of RIPEMD provide the same level of security as RIPEMD-128 and RIPEMD-160, respectively; they are designed for applications where the security level is sufficient but longer hash result is necessary.

PGP

https://en.wikipedia.org/wiki/Pretty_Good_Privacy

Pretty Good Privacy (PGP) is an encryption program that provides cryptographic privacy and authentication for data communication. PGP is used for signing, encrypting, and decrypting texts, e-mails, files, directories, and whole disk partitions and to increase the security of e-mail communications. Phil Zimmermann developed PGP in 1991.

CHAP

https://en.wikipedia.org/wiki/Challenge-Handshake_Authentication_Protocol

Challenge-Handshake Authentication Protocol (CHAP) is an identity verification protocol that does not rely on sending a shared secret between the access-requesting party and the identity-verifying party (the authenticator). CHAP is based on a shared secret, but in order to authenticate, the authenticator sends a “challenge” message to the access-requesting party, which responds with a value calculated using a “one-way hash” function that takes as inputs the challenge and the shared secret. The authenticator checks the response against its own calculation of the expected hash value. If the values match, the authentication succeeds, otherwise it fails. Following the establishment of an authenticated connection, the authenticator may send a challenge to the access-requesting party at random intervals, to which the access-requesting party will have to produce the correct response.

Explanation

RSA 

https://en.wikipedia.org/wiki/RSA_(cryptosystem)

RSA (Rivest–Shamir–Adleman) is a public-key cryptosystem that is widely used for secure data transmission. It is also one of the oldest. The acronym RSA comes from the surnames of Ron Rivest, Adi Shamir, and Leonard Adleman, who publicly described the algorithm in 1977.

Explanation

Finding any method that is more efficient than brute force

https://en.wikipedia.org/wiki/Cryptanalysis

Bruce Schneier notes that even computationally impractical attacks can be considered breaks: "Breaking a cipher simply means finding a weakness in the cipher that can be exploited with a complexity less than brute force."

Explanation

Skipjack

https://en.wikipedia.org/wiki/Skipjack_(cipher)

Skipjack uses an 80-bit key to encrypt or decrypt 64-bit data blocks. It is an unbalanced Feistel network with 32 rounds.

Explanation

Collision

https://en.wikipedia.org/wiki/Collision_(computer_science)

A collision or clash is a situation that occurs when two distinct pieces of data have the same hash value, checksum, fingerprint, or cryptographic digest.

Explanation

Alice's public key

https://en.wikipedia.org/wiki/Diffie%E2%80%93Hellman_key_exchange

In asymmetric (public key) cryptography, both communicating parties (i.e. both Alice and Bob) have two keys of their own — just to be clear, that's four keys total. Each party has their own public key, which they share with the world, and their own private key which they ... well, which they keep private, of course but, more than that, which they keep as a closely guarded secret. The magic of public key cryptography is that a message encrypted with the public key can only be decrypted with the private key. Alice will encrypt her message with Bob's public key, and even though Eve knows she used Bob's public key, and even though Eve knows Bob's public key herself, she is unable to decrypt the message. Only Bob, using his secret key, can decrypt the message ... assuming he's kept it secret, of course.

128

https://en.wikipedia.org/wiki/Advanced_Encryption_Standard

Rijndael is a family of ciphers with different key and block sizes. For AES, NIST selected three members of the Rijndael family, each with a block size of 128 bits, but three different key lengths: 128, 192 and 256 bits.

Explanation

Revoked certificates

https://en.wikipedia.org/wiki/Online_Certificate_Status_Protocol

The Online Certificate Status Protocol (OCSP) is an Internet protocol used for obtaining the revocation status of an X.509 digital certificate.It is described in RFC 6960 and is on the Internet standards track. It was created as an alternative to certificate revocation lists (CRL), specifically addressing certain problems associated with using CRLs in a public key infrastructure (PKI). Messages communicated via OCSP are encoded in ASN.1 and are usually communicated over HTTP. The "request/response" nature of these messages leads to OCSP servers being termed OCSP responders.

CRL

https://ru.wikipedia.org/wiki/Certificate_Revocation_List

Certificate Revocation List (or CRL) is "a list of digital certificates that have been revoked by the issuing certificate authority (CA) before their scheduled expiration date and should no longer be trusted".

SHA2

https://en.wikipedia.org/wiki/Collision_resistance

Collision resistance is a property of cryptographic hash functions: a hash function H is collision-resistant if it is hard to find two inputs that hash to the same output; that is, two inputs a and b where a ≠ b but H(a) = H(b). The pigeonhole principle means that any hash function with more inputs than outputs will necessarily have such collisions; the harder they are to find, the more cryptographically secure the hash function is.

Due to the Birthday Problem, for a hash function that produces an output of length n bits, the probability of getting a collision is 1/2^n/2.

So, just looking for a hash function with larger "n".

The SHA-2 family consists of six hash functions with digests (hash values) that are 224, 256, 384 or 512 bits: SHA-224, SHA-256, SHA-384, SHA-512, SHA-512/224, SHA-512/256.

Chosen plaintext

https://en.wikipedia.org/wiki/Chosen-plaintext_attack

A chosen-plaintext attack (CPA) is an attack model for cryptanalysis which presumes that the attacker can obtain the ciphertexts for arbitrary plaintexts. The goal of the attack is to gain information that reduces the security of the encryption scheme.

FISH

https://en.wikipedia.org/wiki/FISH_(cipher)

The FISH (FIbonacci SHrinking) stream cipher is a fast software based stream cipher using Lagged Fibonacci generators, plus a concept from the shrinking generator cipher. It was published by Siemens in 1993. FISH is quite fast in software and has a huge key length. However, in the same paper where he proposed Pike, Ross Anderson showed that FISH can be broken with just a few thousand bits of known plaintext.

Explanation

Nonce

https://en.wikipedia.org/wiki/Cryptographic_nonce

A nonce is an arbitrary number that can be used just once in a cryptographic communication. It is similar in spirit to a nonce word, hence the name. It is often a random or pseudo-random number issued in an authentication protocol to ensure that old communications cannot be reused in replay attacks.

Explanation

FORK-256

https://en.wikipedia.org/wiki/FORK-256

FORK-256 was introduced at the 2005 NIST Hash workshop and published the following year.[6] FORK-256 uses 512-bit blocks and implements preset constants that change after each repetition. Each block is hashed into a 256-bit block through four branches that divides each 512 block into sixteen 32-bit words that are further encrypted and rearranged.

Explanation

FISH

https://en.wikipedia.org/wiki/FISH_(cipher)

The FISH (FIbonacci SHrinking) stream cipher is a fast software based stream cipher using Lagged Fibonacci generators, plus a concept from the shrinking generator cipher. It was published by Siemens in 1993. FISH is quite fast in software and has a huge key length. However, in the same paper where he proposed Pike, Ross Anderson showed that FISH can be broken with just a few thousand bits of known plaintext.

Explanation

y^2 = x^3 + Ax + B

https://en.wikipedia.org/wiki/Elliptic-curve_cryptography

For current cryptographic purposes, an elliptic curve is a plane curve over a finite field (rather than the real numbers) which consists of the points satisfying the equation:

Atbash

https://en.wikipedia.org/wiki/Atbash

Atbash is a monoalphabetic substitution cipher originally used to encrypt the Hebrew alphabet. It can be modified for use with any known writing system with a standard collating order.

Explanation

CBC-MAC

https://en.wikipedia.org/wiki/CBC-MAC

A cipher block chaining message authentication code (CBC-MAC) is a technique for constructing a message authentication code from a block cipher. The message is encrypted with some block cipher algorithm in CBC mode to create a chain of blocks such that each block depends on the proper encryption of the previous block. This interdependence ensures that a change to any of the plaintext bits will cause the final encrypted block to change in a way that cannot be predicted or counteracted without knowing the key to the block cipher. Using in WPA2 for integrity check and provides security against a replay attack.

Null Ciphers

https://en.wikipedia.org/wiki/Null_cipher

A null cipher, also known as concealment cipher, is an ancient form of encryption where the plaintext is mixed with a large amount of non-cipher material. Today it is regarded as a simple form of steganography, which can be used to hide ciphertext.

Explanation

Symmetric algorithm

https://en.wikipedia.org/wiki/Triple_DES

Triple DES (3DES or TDES), officially the Triple Data Encryption Algorithm (TDEA or Triple DEA), is a symmetric-key block cipher, which applies the DES cipher algorithm three times to each data block. The Data Encryption Standard's (DES) 56-bit key is no longer considered adequate in the face of modern cryptanalytic techniques and supercomputing power. However, an adapted version of DES, Triple DES (3DES), uses the same algorithm to produce a more secure encryption.

DES

https://en.wikipedia.org/wiki/Data_Encryption_Standard

DES is insecure due to the relatively short 56-bit key size. In January 1999, distributed.net and the Electronic Frontier Foundation collaborated to publicly break a DES key in 22 hours and 15 minutes.