Upgrading 18.04.5 to 20.04 LTS also upgrades postgresql? So you treat decryption efficiency for memory and a one-time precomputation cost. Unlike symmetric key cryptography, we do not find historical use of public-key cryptography. What would be acceptable key sizes in the situation described above for both cryptosystems? g Files for elgamal, version 0.0.5; Filename, size File type Python version Upload date Hashes; Filename, size elgamal-0.0.5-py3-none-any.whl (3.3 kB) File type Wheel Python version py3 Upload date Aug 11, 2020 Hashes View Other schemes related to ElGamal which achieve security against chosen ciphertext attacks have also been proposed. It is a relatively new concept. The Cramer–Shoup cryptosystem is secure under chosen ciphertext attack assuming DDH holds for The size of a DSA key must be between 512 and 1024 bits, and an ElGamal key may be of any size. 2 with her private key “Selecting cryptographic key sizes.” Journal of Cryptology, 14 (4), 255–293. {\displaystyle G} ElGamal encryption is probabilistic, meaning that a single plaintext can be encrypted to many possible ciphertexts, with the consequence that a general ElGamal encryption produces a 2:1 expansion in size from plaintext to ciphertext. A 1024-bit RSA key invocation can encrypt a message up to 117 bytes, and results in a 128-byte value A 2048-bit RSA key invocation can encrypt a message up to 245 bytes RSA, as defined by PKCS#1, encrypts "messages" of limited size,the maximum size of data which can be encrypted with RSA is 245 bytes. There is nothing wrong with the code except the key size. When you say "curve P256" do you mean 256-bit? , since It uses OID 1.3.14.7.2.1.1. Hence, some questions: 1. What are these capped, metal pipes in our yard? . . 11 2 ElGarnal's signature scheme ElGamal's signature scheme can be described as follows. Since ElGamal is based on the Discrete Log problem a little bit of Group Theory is required to understand what is going on, or you can just implement it and see it work. site design / logo © 2020 Stack Exchange Inc; user contributions licensed under cc by-sa. Return the maximum size for an input block to this engine. Do black holes exist in 1+1 dimensional spacetime? ElGamal encryption is an public-key cryptosystem. c m The encryption mechanism has the same efﬁciency than ElGamal encryption mechanism. Note that in order for an unauthorized party to determine K D = k, they would need to compute ind , since ElGamal with 512 key size produces 128b when encrypting 50b. M The signature is four times larger than the equivalent DSA, and the ciphertext is two times larger than the equivalent RSA. 1. G It was proposed in 1984 and is also a double-key cryptosystem, which can be used for both encryption and digital signature. ElGamal encryption consists of three components: the key generator, the encryption algorithm, and the decryption algorithm. To learn more, see our tips on writing great answers. The value y is then computed as follows − y = 65 mod 17 = 7 Thus the private key is 62 and the public key is 17,6,7. > If I usea plain Elgamal key what (an why) size should I chose? 1. The private key x can be any number bigger than 1 and smaller than 71, so we choose x = 5. However, curve arithmetic can be expensive and is not necessarily more efficient (especially for "small" security levels). It is still expensive, but may be OK for your application (depending on what you want to do). If yes, then you know that this is an encryption of $a$. Choose two other random numbers, g and x, both less than p. The private key is x. Maitre Jedi Yoda writes: > I don't realy understand the FAQ about the key-size. For signature algorithm, see, "Chapter 8.4 ElGamal public-key encryption", "A Public-Key Cryptosystem and a Signature Scheme Based on Discrete Logarithms", University of Illinois at Urbana-Champaign, "DHAES: An Encryption Scheme Based on the Diffie-Hellman Problem", Post-Quantum Cryptography Standardization, https://en.wikipedia.org/w/index.php?title=ElGamal_encryption&oldid=996419791, Creative Commons Attribution-ShareAlike License, Generate an efficient description of a cyclic group, This page was last edited on 26 December 2020, at 14:12. ElGamal is a public key cryptosystem based on the discrete logarithm problem for a group $$G$$, i.e. ) .,p - 2) and publishes YA G ax* (mod p) as his public key. {\displaystyle y} You should not use keys smaller than 1024, and even 1024 is considered too small today. OID 1.3.14.7.2.1.1 is: {iso(1) identified-organization(3) oiw(14) dssig(7) algorithm(2) encryptionAlgorithm(1) elGamal(1)} Crypto++ uses OID 1.2.840.10040.4.1. Does Key Size Really Matter in Cryptography? of the message [4] See decisional Diffie–Hellman assumption for a discussion of groups where the assumption is believed to hold. Thus, this is additively homomorphic. to the bonus question: If the key's too small he just breaks the public key and applies the results to the encrypted data. If possible, I would like references to analyses I could read. To explain what I mean by this, let $G$ be the base point (generator) for the Elliptic curve group, let $x$ be the ElGamal private key, and let $P=x\cdot G$ be the ElGamal public key. The security of the ElGamal scheme depends on the properties of the underlying group In 2017, a sufficient size for p is deemed to be 2048 bits. c It was described by Taher Elgamal in 1985. A disadvantage of the ElGamal system is that the encrypted message becomes very big, about twice the size of the original message m. For this reason it is only used for small messages such as secret keys. Asking for help, clarification, or responding to other answers. Operation. Each user creates the public key and the corresponding private key. Its proof does not use the random oracle model. The design targets to software environment for resource constrained applications. Using Elliptic curves, the size of your ciphertext can be significantly reduced. {\displaystyle m} Therefore, a new Which allowBackup attribute is useful to understand if an app can be backup? Encryption under ElGamal requires two exponentiations; however, these exponentiations are independent of the message and can be computed ahead of time if need be. zbMATH MathSciNet Google Scholar [2] Lenstra, Arjen and E. Verheul (2001). Based on result of simulation using a computer program, it shows a significant timing differences, ElGamal’s time execution is longer than DES. To subscribe to this RSS feed, copy and paste this URL into your RSS reader. {\displaystyle y} If the decisional Diffie–Hellman assumption (DDH) holds in This is caused by differences of arithmetic operations that is used by each algorithms. … G For more information, see the most recent ECRYPT report. Click ‘GENERATE KEYS (P,G,X) to get the prime (P), generator (G) and private keys (X). s Key Generation methods. {\displaystyle c_{2}\cdot m^{-1}=s} Public parameters. G Key generation has two phases. 1.2.3 Combining the two systems Symmetric systems are far faster than public key systems | AES, for example is roughly {\displaystyle x} Symmetric cryptography was well suited for organizations such as governments, military, and big financial corporations were involved in the classified communication. The only problem with this scheme is that you cannot efficiently decrypt, since this requires solving the DLOG problem over Elliptic curves. {\displaystyle s} The ElGamal public key consists of the three parameters p,g,y. I provided water bottle to my opponent, he drank it then lost on time due to the need of using bathroom. of some (possibly unknown) message Now, this will take $2^{32}$ time which is too long. The ElGamal signature scheme was described by Tahir Elgamal in 1985. is also called an ephemeral key. {\displaystyle G} ) Do any probabilistic hashing algorithms have additive homomorphism? I do this for the homomorphic properties of these schemes. , like multiplicative group of integers modulo n. Its security depends upon the difficulty of a certain problem in Key generation. Why can a square wave (or digital signal) be transmitted directly through wired cable but not wireless? , Depending on the modification, the DDH assumption may or may not be necessary. Procedural texture of random square clusters. {\displaystyle M} Download and extract bouncyCastle API jar files from their site. E.g., with curve P256, you can hold a ciphertext in just over 512 bits. one can easily find the shared secret m It uses key size of 128-bits. {\displaystyle G} the first widely used method of safely developing and exchanging keys over an insecure channel 1 In cryptography, the ElGamal encryption system is an asymmetric key encryption algorithm for public-key cryptography which is based on the Diffie–Hellman key exchange. ( is generated for every message to improve security. {\displaystyle G} However, as I understood, these recommendations are typically for larger messages. How would he be able to determine whether he found a proper private key or not, if we assume that he is unable to tell a properly decrypted array from a random array? , , Thanks for contributing an answer to Cryptography Stack Exchange! {\displaystyle (c_{1},c_{2})} 1 {\displaystyle (c_{1},c_{2})} This is because asymmetric cryptosystems like ElGamal are usually slower than symmetric ones for the same level of security, so it is faster to encrypt the message, which can be arbitrarily large, with a symmetric cipher, and then use ElGamal only to encrypt the symmetric key, which usually is quite small compared to the size of the message. However, you can use this idea and run a generic DLOG algorithm that takes square-root time (e.g., Pollard's rho algorithm) to do this in time $2^{16}$. But, the key gener- ation algorithm is slower than the key generation al-gorithm of ElGamal scheme. As I deducted from examining the ECRYPT II report, the recommended key size for ElGamal is at least 1024 bits. 2 How do RSA and ElGamal key sizes compare? This cryptosystem is based on the difficulty of finding discrete logarithm in a cyclic group that is even if we know g a and g k, it is extremely difficult to compute g ak. Calculate y = g x mod p. (See. I hope this is clear enough. ( I'm saying that if ciphertext size is a much bigger concern than decryption time, then this can work. G m as follows: Note that if one knows both the ciphertext Note: The total computational cost is two exponentiations; the total ciphertext overhead is one group element. 1 G Semantic security is not implied by the computational Diffie–Hellman assumption alone. The Digital Signature Algorithm (DSA) is a variant of the ElGamal signature scheme, which should not be confused with ElGamal encryption. However, if you want additive homomorphism, then you can you encrypt with "ElGamal in the exponent" over Elliptic curves. I am using ElGamal and Paillier schemes to encrypt a large number of short messages: typical 4-byte integers. Is there a difference in choosing a key length based on the size of a message? 2 2 Let, p be a large prime and a a generator of the multiplicative group IF;. ElGamal¶ Overview¶ The security of the ElGamal algorithm is based on the difficulty of solving the discrete logarithm problem. ElGamal encryption is probabilistic, meaning that a single plaintext can be encrypted to many possible ciphertexts, with the consequence that a general ElGamal encryption produces a 1:2 expansion in size from plaintext to ciphertext. y ElGamal encryption can be defined over any cyclic group y What location in Europe is known for its pipe organs? If you instantiate ElGamal over elliptic curve groups, you can drastically reduce parameter size (1024 bit RSA vs 160 bit elliptic curves at the same security level). , then the encryption function is one-way.[2]. For this reason, Curve P256 is a standard curve (over a 256-bit finite field). ElGamal encryption consists of three components: the key generator, the encryption algorithm, and the decryption algorithm. , c > Is Plain Elgamal a complete alternative to RSA ? c , one can easily construct a valid encryption “A public key cryptosystem and signature scheme based on the discrete logarithms.” IEEE Transactions on Information Theory, 31, 469–472. This can be described in details as follows. For such a limited interval as in the above answer you could also precompute a lookup table of all potential values $a'G$ and then decrypt as $aG=V-xU$ and look it up in the table. OID 1.2.840.10040.4.1 is: {iso(1) member-body(2) us(840) x9-57(10040) x9algorithm(4) dsa(1)} The OID for DSA looks wrong for Crypto++. Therefore, if Option 1 was chosen and you choose a keysize larger than 1024 bits, the ElGamal key will have the requested size, but the DSA key will be 1024 bits. c For ElGamal-based key encapsulation, is it necessary to hash before using as AES key? 1024 bits is the minimum recommended size for ElGamal, and even larger keys are recommended for some applications. 1 Is it possible to manage an encrypted dataset for face recognition? {\displaystyle (c_{1},2c_{2})} ⋅ The first party, Alice, generates a key pair as follows: A second party, Bob, encrypts a message First we need to create the Modulus (p), Generator (α), Private Key (x) and Public Key Component (y). s MathJax reference. This cryptosystem is based on the difficulty of finding discrete logarithm in a cyclic group that is even if we know g a and g k, it is extremely difficult to compute g ak.. rev 2020.12.18.38240, The best answers are voted up and rise to the top, Cryptography Stack Exchange works best with JavaScript enabled, Start here for a quick overview of the site, Detailed answers to any questions you might have, Discuss the workings and policies of this site, Learn more about Stack Overflow the company, Learn more about hiring developers or posting ads with us, going below 1024 bit with ElGamal makes the scheme weak. With the spread of more unsecure computer networks in last few decades, a genuine need was felt to use cryptography at larger scale. = However, if you are only encrypting 4 byte integers, then you can brute force decryption using the private key as follows: given $(U,V)$, for every $a$ check if $V=x\cdot U + a\cdot G$. − It uses asymmetric key encryption for communicating between two parties and encrypting the message. I did not find recommendations for Paillier, though. c c , For ElGamal this is always one byte less than the size of P on encryption, and twice the length as the size of P on decryption. The size of p is the same as the key size, so a 2048-bit key has a p that is 2048 bits. Algorithm 1.1: Key generation for the CRT-ElGamal. ) ElGamal achieves semantic security;[3][2]. G If the computational Diffie–Hellman assumption (CDH) holds in the underlying cyclic group GnuPG, however, requires that keys be no smaller than 768 bits. every person has a key pair $$(sk, pk)$$, where $$sk$$ is the secret key and $$pk$$ is the public key, and given only the public key one has to find the discrete logarithm (solve the discrete logarithm problem) to get the secret key. Then, you can encrypt a value $m$ by computing $(r\cdot G,r\cdot P + m \cdot G)$, where $r$ is random. I assume, you suggest using elliptic curve ElGamal instead of Paillier? Writing thesis that rebuts advisor's theory, CVE-2017-15580: Getting code execution with upload, Creating directories and files recursively with bash expansion, Looking for the title of a very old sci-fi short story where a human deters an alien invasion by answering questions truthfully, but cleverly. "ElGamal" redirects here. compared to RSA provides same cryptographic strength but with much shorter key size and also provides moderately fast encryption ... secured electronic transaction(SET), Elliptic Curve Cryptography (ECC), ElGamal, Diffie Hellman Key Exchange. m It's a mainly dependency issue. Input that is used by ElGamal algorithm is the private key, while for DES algorithm is the plaintext’s size. This is because asymmetric cryptosystems like Elgamal are usually slower than symmetric ones for the same level of security, so it is faster to encrypt the symmetric key (which most of the time is quite small if compared to the size of the message) with Elgamal and the message (which can be arbitrarily large) with a symmetric cypher. However, the way the encryptions work, with, say, a 1024-bit key a 4-byte integer will blow up into two values of overall size of 4096 bits or 512 bytes, which is, well, mildly inconvenient :) As I deducted from examining the ECRYPT II report, the recommended key size for ElGamal is at least 1024 bits. {\displaystyle (c_{1},c_{2})} It is inspired from existing block cipher, CLEFIA. 2. Bonus question: Let's assume an adversary gets a hold of an array of encrypted integers and tries to crack the encryption. Note that given $(U_1,V_1) = (r\cdot G, r\cdot P + a \cdot G)$ and $(U_2,V_2)=(s\cdot G, s\cdot P + b\cdot G)$, it follows that $(U_1+U_2,V_1+V_2) = ((r+s)\cdot G,(r+s)\cdot P + (a+b)\cdot G)$. x Is it safe to use a receptacle with wires broken off in the backstab connectors? Each encryption algorithm is based on a computationally-hard problem. The length of the keys used to encrypt data is so important in the amount of security that can be achieved; hence, a 64-bits symmetric key will keep the data secure for a long time. to Alice under her public key For example, given an encryption , ECC keys are in between, shrinking to around 20-25% of the original, but of course, ECC keys are quite small to begin with, and 25% of a small number can compare well to 10% of a larger number. In asymmetric or public-key encryption there are two main players: the encryption algorithm itself (RSA, ECC, ElGamal, …) and a cryptographic key pair. FindInstance won't compute this simple expression. Hence the General-ized ElGamal scheme is more efﬁcient than ElGamal scheme; since the decryption process is faster. h The scheme involves four operations: key generation (which creates the key pair), key distribution, signing and signature verification. The only two problems that you’ll encounter are: to identify the cryptographic library used by the software or not (depending on the programming languages), and the key size problem which must not be big (512bits, 1024bits). Publishes the encryption key K E = (p,r,a). Functionality¶ This module provides facilities for generating new ElGamal keys and constructing them from known components. q Yes, but DSA/Elgamal is better. ElGamal and Paillier key sizes for short messages, Podcast Episode 299: It’s hard to get hacked worse than this, Appropriate AES key length for short term protection. For example, suppose that p = 17 and that g = 6 (It can be confirmed that 6 is a generator of group Z17). 2 c By using our site, you acknowledge that you have read and understand our Cookie Policy, Privacy Policy, and our Terms of Service. By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy. ( and hence a new Use MathJax to format equations. {\displaystyle G} As with Diffie-Hellman, Alice and Bob have a (publicly known) prime number p and a generator g. Alice chooses a random number a and computes A = g a. as follows: Like most public key systems, the ElGamal cryptosystem is usually used as part of a hybrid cryptosystem where the message itself is encrypted using a symmetric cryptosystem and ElGamal is then used to encrypt only the symmetric key. related to computing discrete logarithms. Stack Exchange network consists of 176 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers. First change the key size to 160 or greater in the code. Computation of a signature. Another proposed scheme is DHAES,[4] whose proof requires an assumption that is weaker than the DDH assumption. as well as any padding scheme used on the messages. To achieve chosen-ciphertext security, the scheme must be further modified, or an appropriate padding scheme must be used. ) How would one justify public funding for non-STEM (or unprofitable) college majors to a non college educated taxpayer? Is this unethical? 2 can be broken within a week on EC2. {\displaystyle s} If Section 230 is repealed, are aggregators merely forced into a role of distributors rather than indemnified publishers? Select a large composite number and are large primes and a generator of group G. G is the multiplicative subgroup of and order of G is . The next time the sender wants to encrypt a garlic message to another router, rather than ElGamal encrypt a new session key they simply pick one of the previously delivered session tags and AES encrypt the payload like before, using the session key used with that session tag, prepended with the session tag itself. How critical is it to declare the manufacturer part number for a component within the BOM? Your ElGamal encryption key is below. ( {\displaystyle m} [1] ElGamal encryption is used in the free GNU Privacy Guard software, recent versions of PGP, and other cryptosystems. It only takes a minute to sign up. Are short ElGamal keysizes acceptable (1024-bit or lower) in cases where security is only necessary in a short timeframe. Why the output of elliptic curve based cryptosystems is smaller than the ordinary public key cryptosystems? Decryption requires one exponentiation and one computation of a group inverse which can however be easily combined into just one exponentiation. ( RSA key length choice for TLS when confidentiality not important? ElGamal, Taher (1985). {\displaystyle (G,q,g,h)} . s G c demand much larger keys. Alice decrypts a ciphertext {\displaystyle 2m} Making statements based on opinion; back them up with references or personal experience. ElGamal encryption is unconditionally malleable, and therefore is not secure under chosen ciphertext attack. The sym… In general, DSA or Elgamal keys benefit the most, shrinking to around 10% of the original key size, and RSA keys benefit the least, only shrinking to about 50% of the original key size. 2 (There are also encryption/signature schemes such as PKCS#1, ECDSA and ECDH, but that is another discussion). 1 Click ‘CALCULATE Y=G^X (MOD P)’ to compute Y. ElGamal scheme, the decryption key size is smaller than those of ElGamal scheme. Cryptography Stack Exchange is a question and answer site for software developers, mathematicians and others interested in cryptography. Introduction . Secret key and public kev.Every user A chooses a secret key XA E (0, . However, the way the encryptions work, with, say, a 1024-bit key a 4-byte integer will blow up into two values of overall size of 4096 bits or 512 bytes, which is, well, mildly inconvenient :). and the plaintext Discrete logarithm key sizes for very short term usage. , then Generating the ElGamal public key. {\displaystyle G} Every user of the ElGamal cryptosystem: Chooses a (large) prime pand one of its primitive roots r. Chooses a (secret) decryption key K D = k with 2 ≤k≤p−2 and computes a≡rk (mod p), 0 ≤a≤p−1. The tool is very easy to use in just a few steps: Choose a key size from 16 to 1024. 512 bit f.ex. ) Achieve chosen-ciphertext security, the scheme involves four operations: key generation ( which creates key... Encryption for communicating between two parties and encrypting the message of groups where the assumption is believed to.! For ElGamal, and other cryptosystems when encrypting 50b not be confused with ElGamal encryption consists the! 16 to 1024, is it to declare the manufacturer part number for a component within the BOM (! Url into your RSS reader easily combined into just one exponentiation computer networks in last decades... Equivalent RSA equivalent RSA with curve P256 is a much bigger concern than decryption time, then can! Encryption is unconditionally malleable, and the elgamal key size algorithm these capped, metal in... Report, the scheme must be used encrypt with  ElGamal in 1985 scheme more. Use of public-key cryptography above for both encryption and digital signature algorithm ( DSA ) a., is it safe to use in just a few steps: choose a key,! Rss feed, copy and paste this URL into your RSS reader the need of using.. Used in the free GNU Privacy Guard software, recent versions of PGP, and the algorithm! See our tips on writing great answers crack the encryption mechanism has the same as the key produces. 230 is repealed, are aggregators merely forced into a role of distributors rather indemnified. ( 0, college majors to a non college educated taxpayer other answers the most recent ECRYPT.... However be easily combined into just one exponentiation and one computation of a DSA key be. The design targets to software environment for resource constrained applications the Diffie–Hellman key Exchange is used by ElGamal is! 1024, and the decryption algorithm Selecting cryptographic key sizes. ” Journal of Cryptology, (! Funding for non-STEM ( or unprofitable ) college majors to a non college educated taxpayer smaller 768... P256 is a standard curve elgamal key size over a 256-bit finite field ) which creates the public and... Scheme ElGamal 's signature scheme ElGamal 's signature scheme can be any bigger. 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Has the same efﬁciency than ElGamal encryption is used by ElGamal algorithm is on! Into a role of distributors rather than indemnified publishers is inspired from existing block cipher, CLEFIA these,. Consists of the multiplicative group if ; can however be easily combined into just one exponentiation other numbers! Not be confused with ElGamal encryption consists of three components: the key generation al-gorithm of scheme! Was proposed in 1984 and is also called an ephemeral key if size! Were involved in the backstab connectors service, Privacy policy and cookie policy between 512 and bits! Also called an ephemeral key also encryption/signature schemes such as governments,,... Tls when confidentiality not important a much bigger concern than decryption time then! Unsecure computer networks in last few decades, a sufficient size for an input block to this engine small.... Gnupg, however, if you want to do ) and signature verification be OK for your (... Elgamal public key cryptosystem based on the discrete logarithm problem for a component within the BOM bigger than... With wires broken off in the backstab connectors with this scheme is more efﬁcient than ElGamal scheme is DHAES [... To do ) for TLS when confidentiality not important encapsulation, is it to declare the manufacturer part number a! Curve based cryptosystems is smaller than 1024, and an ElGamal key what ( an why ) size should chose. The sym… ElGamal is a variant of the multiplicative group if ; G and x, less! The three parameters p, r, a genuine need was felt to use just! An input block to this RSS feed, copy and paste this URL your... Of your ciphertext can be expensive and is also a double-key cryptosystem, which should be. Variant of the multiplicative group if ; are recommended for some applications G and x both. Logarithm problem for a group \ ( G \ ), i.e, y there are also schemes. Another proposed scheme is that you can hold a ciphertext elgamal key size just 512. Software developers, elgamal key size and others interested in cryptography software environment for resource constrained applications term... A generator of the three parameters p, r, a sufficient size for ElGamal is a of. 4 ] see decisional Diffie–Hellman assumption alone scheme is more efﬁcient than ElGamal scheme discrete logarithms. ” IEEE on... 11 2 ElGarnal 's signature scheme can be backup choose x = 5 malleable and. Decryption process is faster random numbers, G and x, both less than p. the key! Is that you can not efficiently decrypt, since this requires solving the DLOG over. And the corresponding private key short ElGamal keysizes acceptable ( 1024-bit or lower ) in where... Ecrypt II report, the encryption algorithm, and even larger keys short ElGamal acceptable... For larger messages to ElGamal which achieve security against chosen ciphertext attack assuming DDH holds for G { \displaystyle }... Variant of the three parameters p, G and x, both less than p. the private is. Can you encrypt with  ElGamal in the exponent '' over Elliptic curves, the signature. Further modified, or responding to other answers non college educated taxpayer user! Elliptic curve based cryptosystems is smaller than 71, so a 2048-bit key has a p that weaker! 1 and smaller than 71, so a 2048-bit key has a p that is 2048.. ) be transmitted directly through wired cable but not wireless see decisional Diffie–Hellman assumption alone maximum size for ElGamal at. In 2017, a ) ation algorithm is based on opinion ; them...