Decryption. If there has been proper receipt pursuant to Section 2.1 the receiving party shall attempt to decrypt the Transaction. If the Transaction decryption is unsuccessful, the receiving party shall send the applicable error message to the sending party. The sending party shall attempt to correct the error and promptly retransmit the Transaction or notify the receiving party in an attempt to solve the problem. If the Transaction can not be authenticated an applicable error message will be sent to the sending party however, if the sending party’s identity can not be ascertained, then the transmission will not be deemed a Transaction.
Decryption. The recipient optionally can verify the encrypted DSRC key with the public key KS-PUB of the originator and decrypts the DSRC key with his private key KR-PRIV. Signature verification KS-PUB OK / not OK RSA decryption KR-PRIV DSRC Key opy Signature encrypted Key Figure 7: Signature Verification and Decryption (optional part in grey)
Decryption. After receiving a ciphertext (c1, c2, c3), anyone with a valid message-signature pair (s, σ) can extract =
Decryption. Acronis cannot decrypt your files if Reseller has elected to encrypt. However, You have selected the location of your backup and understand that local laws where the selected data centers are located may be different than the laws of the country in which you reside. Acronis will comply with the local laws of the jurisdiction You reside and also the jurisdiction where the data center housing Your data is located. As a result, You acknowledge that Acronis or Acronis affiliates may use servers and other equipment to provide the Acronis Backup Cloud Product and Platform that are located in the United States or in other countries where litigants, law enforcement, courts, and other agencies of the government may have the right to access data stored within their jurisdictions upon terms and conditions provided by local law.
Decryption. In decryption process, user B decrypts the ciphertext message Ci = [C1, C2, …, Ci] using its own private key (d, n) to get the original corresponding plaintext blocks Mi as Mi = Ci (mod n). After that, user B concatenates all decrypted ciphertext blocks Mi to get the message M. -Elliptic Curve Cryptography (ECC) : ECC is a public key encryption technique based on elliptic curve theory which is the set of the point that satisfies the specific mathematical equation: y2= x3+ ax + b (Stallings, 2006; Yu, 2012). Before talking about the ECC encryption/decryption, we will discuss in a brief elliptic curve equation. -Elliptic Curve with Finite Field : A finite field or Galois Field (GF) is a field that contains a finite number of elements which called its order, such as the fields of prime order GF(p) (also denoted Zp or Fp), which is a field of prime number of order p (size of field). The finite field with elliptic curve defined as follow: Let a and b ϵ Zp, where Zp = {0, 1,… p - 1 } and p > 3 be a prime, such that 4a³ + 27b² != 0 (mod p). A non-singular elliptic curve y² = x3 + ax + b over the finite field GF (p) is the set Ep (a, b) of solutions (x,y) ϵ Zp × Zp to the congruence y² = x³ + ax + b (mod p), where a and b ϵ Zp are constants such that 4a³ + 27b² € 0 (mod p). Together with a special point Ҩ called the point at infinity or zero points (Xxxxx et al., 2015; Xxxxxxxxx, 2006; Yu, 2012). Let P (Xp, Yp) and Q (XQ, YQ) be two point on an elliptic curve y² = x³ + ax + b (mod p), and let G be the base point on Ep (a, b) whose order be n, that is nG = G + G + … + G (n times) = Ҩ, R (XR, YR) = P + Q is computed as follows: XR = ( €²- Xp – XQ) (mod p), YR = ( €( Xp – XR) – Yp) (mod p), p Where €= (YQ – Yp)/( XQ – Xp) (mod p), if P € Q and €= (2X ² + a )/( 2YP) (mod p), if P = Q. Figure 2-1 explain the elliptic curve. y -R y2 = x3 + ax + b Q x P R = P + Q Figure 2-1. Elliptic Curve. -ECC Encryption/Decryption : Before encryption and decryption process in elliptic curve algorithm, the plaintext message m will be encoded to be sent as an elliptic curve point Pm ϵ Ep (a, b). This point Pm then will be encrypted as a cipher text and then subsequently decrypted. Key generation : In the key generation process, user B has the elliptic curve Ep (a, b) defined over a finite field GF (p), and a base point G ϵ Ep (a, b) whose order is n, that nG = Ҩ. User B selects a private key nB randomly on the interval [ 1, n – 1 ] and computes his/her public key PB = nB G.
Decryption. After receiving a ciphertext (c1, c2, c3), anyone with a valid message-signature pair (s, σ) can extract c3 m = . e(σ, c1)e(H(s), c2) ⊗ ⊙ ⊗ ⊗ ⊙ ⊙ The correctness of the proposed ASBB scheme follows from a direct verifica- tion. Define by (R1, A1) (R2, A2)= (R1R2, A1A2) and by σ1 σ2 = σ1σ2. For security, we have the following claims in which Claim 2 follows from the definition of and , and the security proof of Claim 3 can be found in the full version of the paper [23]. O
Decryption. Let c with 0 c < n be the number encoding one block of the ciphertext, which is received by Bob and also by the eavesdropper Xxxxx. Bob decrypts c by using his private key d and the following decryption function Dd(c) = cd mod n . Theorem 7.13 states that the RSA protocol described above indeed is a cryp- tosystems in the sense of Definition 7.1. The proof of Theorem 7.13 is left to the reader as Exercise 7.3-1. Theorem 7.13 Let (n, e) be the public key and d be the private key in the RSA protocol. Then, for each message m with 0 ≤ m < n, m = (me)d mod n . Hence, RSA is a public-key cryptosystem. To make RSA encryption and (authorised) decryption efficient, the algorithm Square-and-Multiply algorithm is again employed for fast exponentiation. − − How should one choose the prime numbers p and q in the RSA protocol? First of all, they must be large enough, since otherwise Xxxxx would be able to factor the number n in Bob’s public key (n, e) using the extended Euclidean algorithm. Knowing the prime factors p and q of n, he could then easily determine Bob’s private key d, which is the unique inverse of e mod ϕ(n), where ϕ(n) = (p 1)(q 1). To keep the prime numbers p and q secret, they thus must be sufficiently large. In practice, p and q should have at least 80 digits each. To this end, one generates numbers of this size randomly and then checks using one of the known randomised primality tests whether the chosen numbers are primes indeed. By the Prime Number Theorem, there are about N/ ln N prime numbers not exceeding N . Thus, the odds are good to hit a prime after reasonably few trials. In theory, the primality of p and q can be decided even in deterministic polyno- mial time. Xxxxxxx et al. [1, 2] recently showed that the primality problem, which is defined by PRIMES = {bin(n) | n is prime} , O O is a member of the complexity class P. Their breakthrough solved a longstanding open problem in complexity theory: Among a few other natural problems such as the graph isomorphism problem, the primality problem was considered to be one of the rare candidates of problems that are neither in P nor NP-complete.2 For practical purposes, however, the known randomised algorithms are more useful than the deterministic algorithm by Xxxxxxx et al. The running time of (n12) obtained in their original paper [1, 2] could be improved to (n6) meanwhile, applying a more sophisticated analysis, but this running time is still not as good as that of the randomised algorithms.
Decryption. Each instance of any Licensed Program shall be decrypted solely: (a) for the purpose of playback, (b) in a manner so that no more than 10 seconds of video exists in unencrypted form at any given time and is deleted immediately after the playback of such content frame and (c) by the Security Solution client/component of the Authorized App/Player. To the extent supported by the Security Solution, such Security Solution license and decryption keys shall be keyed to work on only a single instance of the Authorized App/Player on a single Authorized Internet Device and shall be incapable of being used by a different device or transferred between devices. Any Security Solution license and decryption keys shall be held securely on the Authorized Internet Device and only for as long as necessary to decrypt and exhibit the Licensed Program and must be deleted immediately thereafter.
Decryption. P : the generator of an given cyclic addition group G, where G consists of all points on a given elliptic curve
Decryption. Given , the plaintext can be retrieved using the private key:
