Encryption device, decryption device, encryption method, decryption method, and computer readable medium
An encryption device divides a plaintext M to generate a value M[1], . . . , and a value M[m]. The encryption device generates an n-bit value B[i] by encrypting a value B[i−1] by a block cipher with a value T[i−1] as a key, for each integer i of i=1, . . . , m in ascending order, generates a value C[i] from the value B[i] and a value M[i], and generates an n-bit value T[i] from a value P(T[i−1]) obtained by converting the value T[i−1] using a replacement function P, a value F(B[i]) obtained by converting the value B[i] using a replacement function F, and the value C[i]. The encryption device generates a ciphertext C by connecting the values C[i] for i=1, . . . , m. The encryption device generates from a value H[m] and the value B[m], an authenticator Tag for detecting an alteration of the ciphertext C.
1 . An encryption device comprising:
processing circuitry:
to sequentially divide a plaintext M into each n bits to generate a value M[1], . . . , and a value M[m], wherein m is an integer >=1;
to set an n-bit value Ht to a value T[0] and set an n-bit value Hb to a value B[0], to generate an n-bit value B[i] by encrypting a value B[i−1] by a block cipher with a value T[i−1] as a key, for each integer i of i=1, . . . , m in ascending order, to generate a value C[i] from the value B[i] and a generated value M[i], and to generate an n-bit value T[i] from a value P (T[i−1]) obtained by converting the value T[i−1] using a replacement function P, a value F (B[i]) obtained by converting the value B[i] using a replacement function F, and the value C[i];
to generate a ciphertext C by connecting the generated values C[i] for i=1, . . . , m; and
to generate from a value T[m] and a value B[m], an authenticator Tag for detecting an alteration of the generated ciphertext C, wherein
the processing circuitry maintains a total memory size of 2n bits as a sum of memory sizes for the value T and the value B, during the generation of the value T[i] using the replacement function P and the value F(B[i]) using the replacement function F.
2 . The encryption device according to claim 1 , wherein
the processing circuitry generates the value C[i] by computing an exclusive OR between the value B[i] and the value M[i] for each integer i of i=1, . . . , m−1 in ascending order, and generates a value C[m] by computing an exclusive OR between the value M[m] and a value B′[m] obtained by extracting only a bit length |M[m] | of the value M[m] from a value R(B[m]) obtained by converting the value B[m] using a replacement function R.
3 . The encryption device according to claim 1 , wherein
the processing circuitry generates an n-bit value B[m+1] by encrypting the value B[m] by the block cipher with the value T[m] as a key, and generates the authenticator Tag from a value P(T[m]) obtained by converting the value T[m] using the replacement function P and a value F(B[m+1]) obtained by converting the value B[m+1] using the replacement function F.
4 . The encryption device according to claim 1 , wherein
the processing circuitry generates an n-bit value B[m+1] by encrypting the value B[m] by the bock cipher with the value T[m] as a key, and sets the value B[m+1] to the authenticator Tag.
5 . The encryption device according to claim 1 , wherein
the processing circuitry sequentially divides a public data A into each 2n bits to generate a value A[1], . . . , and a value A[a], wherein a is an integer >=1, and
sets an n-bit value IVt as a value T*[0] and sets an n-bit value IVb as a value B*[0], generates an n-bit value B*[i] from a value E (B*[i−1]) obtained by encrypting a value B*[i−1] by the block cipher with a value T*[i−1] as a key, and an n-bit value A[i, b] of a value A[i] wherein b is an integer >=1, for each integer i of i=1, . . . , a−1 in ascending order, generates an n-bit value T*[i] from a value P(T*[i−1]) obtained by converting the value T*[i−1] using the replacement function P, a value F(E(B*[i−1])) obtained by converting the value E(B*[i−1]) using the replacement function F, and a value A[i, t] which is n bits of the value A[i] other than the value A[i, b], and generates the value Ht and the value Hb from a value T*[a−1], a value B*[a−1], and the value A[a].
6 . The encryption device according to claim 5 , wherein
the processing circuitry generates the value Bt from a value Q(E(B*[a−1])) obtained by converting using a replacement function Q, a value E(B*[a−1]) obtained by encrypting the value B*[a−1] by the block cipher with the value T*[a−1] as a key, and an n-bit value A′[a, b] of a 2n-bit value A′[a] obtained by padding the value A[a] with bits, and generates the value Ht from a value F(Q(E(B*[a−1]))) obtained by converting the value Q(E(B*[a−1])) using the replacement function F, and an n-bit value A′[a, t] of the value A′[a] other than the value A′[a, b], wherein t is an integer >=1.
7 . The encryption device according to claim 5 , wherein
the processing circuitry generates the value IVb from a value E(N) obtained by encrypting an n-bit nonce N by a block cipher E using an n-bit key K, and a value id depending on the public data A and the plaintext M, and generates the value IVt from a value P(K) obtained by converting the key K using the replacement function P and a value F(E[N]) obtained by converting the value E(N) using the replacement function F.
8 . A decryption device comprising:
processing circuitry:
to sequentially divide a ciphertext C into each n bits to generate a value C[1], . . . , and a value C[c], wherein c is an integer >=1;
to set an n-bit value Ht to a value T[0] and set an n-bit value Hb to a value B[0], to generate an n-bit value B[i] by encrypting a value B[i−1] by a block cipher with a value T[i−1] as a key, for each integer i of i=1, . . . , c in ascending order, to generate a value M[i] from the value B[i] and a generated value C[i], and to generate an n-bit value T[i] from a value P(T[i−1]) obtained by converting the value T[i−1] using a replacement function P, a value F (B[i]) obtained by converting the value B[i] using a replacement function F, and the value C[i];
to generate a plaintext M by connecting the generated values M[i] for i=1, . . . , c; and
to generate from a value T[c] and a value B[c], an authenticator Tag′ for detecting an alteration of the generated plaintext M, wherein
the processing circuitry maintains a total memory size of 2n bits as a sum of memory sizes for the value T and the value B, during the generation of the value T[i] using the replacement function P and the value F(B[i]) using the replacement function F.
9 . The decryption device according to claim 8 , wherein
the processing circuitry generates the value M[i] by computing an exclusive OR between the value B[i] and the value C[i] for each integer i of i=1, . . . , c−1 in ascending order, and generates a value M[c] by computing an exclusive OR between the value C[c] and a value B′[c] obtained by extracting only a bit length |C[c]| of the value C[c] from a value R(B[c]) obtained by converting the value B[c] using a replacement function R.
10 . The decryption device according to claim 8 , wherein
the processing circuitry generates an n-bit value B[c+1] by encrypting the value B[c] by the block cipher with the value T[c] as a key, and generates the authenticator Tag′ from a value P(T[c]) obtained by converting the value T[c] using the replacement function P, and a value F(B[c+1]) obtained by converting the value B[c+1] using the replacement function F.
11 . The decryption device according to claim 8 , wherein
the processing circuitry generates an n-bit value B[c+1] by encrypting the value B[c] by the bock cipher with the value T[c] as a key, and sets the value B[c+1] to the authenticator Tag′.
12 . The decryption device according to claim 8 , wherein
the processing circuitry sequentially divides a public data A into each 2n bits to generate a value A[1], . . . , and a value A[a], wherein a is an integer >=1, and
sets an n-bit value IVt as a value T*[0] and sets an n-bit value IVb as a value B*[0], generates an n-bit value B*[i] from a value E(B*[i−1]) obtained by encrypting a value B*[i−1] by the block cipher with a value T*[i−1] as a key, and an n-bit value A[i, b] of a value A[i] wherein b is an integer >=1, for each integer i of i=1, . . . , a−1 in ascending order, generates an n-bit value T*[i] from a value P(T*[i−1]) obtained by converting the value T*[i−1] using the replacement function P, a value F(E(B*[i−1])) obtained by converting the value E(B*[i−1]) using the replacement function F, and a value A[i, t] which is n bits of the value A[i] other than the value A[i, b], wherein tis an integer >=1, and generates the value Ht and the value Hb from a value T*[a−1], a value B*[a−1], and the value A[a].
13 . The decryption device according to claim 12 , wherein
the processing circuitry generates the value Bt from a value Q(E (B*[a−1])) obtained by converting using a replacement function Q, a value E(B*[a−1]) obtained by encrypting the value B*[a−1] by the block cipher with the value T*[a−1] as a key, and an n-bit value A′[a, b] of a 2n-bit value A′[a] obtained by padding the value A[a] with bits, and generates the value Ht from a value F(Q(E(B*[a−1]))) obtained by converting the value Q(E(B*[a−1])) using the replacement function F, and an n-bit value A′[a, t] of the value A′[a] other than the value A′[a, b].
14 . The decryption device according to claim 12 , wherein
the processing circuitry generates the value IVb from a value E(N) obtained by encrypting an n-bit nonce N by a block cipher E using an n-bit key K, and a value id depending on the public data A and the plaintext M, and generates the value IVt from a value P(K) obtained by converting the key K using the replacement function P and a value F(E[N]) obtained by converting the value E(N) using the replacement function F.
15 . An encryption method comprising:
sequentially dividing a plaintext M into each n bits to generate a value M[1], . . . , and a value M[m], wherein m is an integer >=1;
setting an n-bit value Ht to a value T[0] and setting an n-bit value Hb to a value B[0], generating an n-bit value B[i] by encrypting a value B[i−1] by a block cipher with a value T[i−1] as a key, for each integer i of i=1, . . . , m in ascending order, generating a value C[i] from the value B[i] and a value M[i], and generating an n-bit value T[i] from a value P (T[i−1]) obtained by converting the value T[i−1] using a replacement function P, a value F(B[i]) obtained by converting the value B[i] using a replacement function F, and the value C[i];
generating a ciphertext C by connecting the values C[i] for i=1, . . . , m; and
generating from a value T[m] and a value B[m], an authenticator Tag for detecting an alteration of the ciphertext C, wherein
the encryption method further comprises maintaining a total memory size of 2n bits as a sum of memory sizes for the value T and the value B, during the generation of the value T[i] using the replacement function P and the value F(B[i]) using the replacement function F.
16 . A non-transitory computer readable medium storing an encryption program for causing a computer to function as an encryption device to execute:
a division process to sequentially divide a plaintext M into each n bits to generate a value M[1], . . . , and a value M[m], wherein m is an integer >=1;
an encryption element generation process to set an n-bit value Ht to a value T[0] and set an n-bit value Hb to a value B[0], to generate an n-bit value B[i] by encrypting a value B[i−1] by a block cipher with a value T[i−1] as a key, for each integer i of i=1, . . . , m in ascending order, to generate a value C[i] from the value B[i] and a value M[i] generated by the division process, and to generate an n-bit value T[i] from a value P (T[i−1]) obtained by converting the value T[i−1] using a replacement function P, a value F(B[i]) obtained by converting the value B[i] using a replacement function F, and the value C[i];
a ciphertext generation process to generate a ciphertext C by connecting the values C[i] for i=1, . . . , m generated by the encryption element generation process; and
an authenticator generation process to generate from a value T[m] and a value B[m], an authenticator Tag for detecting an alteration of the ciphertext C generated by the ciphertext generation process, wherein
the encryption program causes the computer to further execute the encryption element generation process to maintain a total memory size of 2n bits as a sum of memory sizes for the value T and the value B, during the generation of the value T[i] using the replacement function P and the value F(B[i]) using the replacement function F.
17 . A decryption method comprising:
sequentially dividing a ciphertext C into each n bits to generate a value C[1], . . . , and a value C[c], wherein c is an integer >=1;
setting an n-bit value Ht to a value T[0] and setting an n-bit value Hb to a value B[0], generating an n-bit value B[i] by encrypting a value B[i−1] by a block cipher with a value T[i−1] as a key, for each integer i of i=1, . . . , c in ascending order, generating a value M[i] from the value B[i] and a value C[i], and generating an n-bit value T[i] from a value P (T[i−1]) obtained by converting the value T[i−1] using a replacement function P, a value F (B[i]) obtained by converting the value B[i] using a replacement function F, and the value C[i];
generating a plaintext M by connecting the values M[i] for i=1, . . . , c; and
generating from a value T[c] and a value B[c], an authenticator Tag′ for detecting an alteration of the plaintext M, wherein
the decryption method further comprises maintaining a total memory size of 2n bits as a sum of memory sizes for the value T and the value B, during the generation of the value T[i] using the replacement function P and the value F (B[i]) using the replacement function F.
18 . A non-transitory computer readable medium storing a decryption program for causing a computer to function as a decryption device to execute:
a division process to sequentially divide a ciphertext C into each n bits to generate a value C[1], . . . , and a value C[c], wherein c is an integer >=1;
a plaintext element generation process to set an n-bit value Ht to a value T[0] and set an n-bit value Hb to a value B[0], to generate an n-bit value B[i] by encrypting a value B[i−1] by a block cipher with a value T[i−1] as a key, for each integer i of i=1, . . . , c in ascending order, to generate a value M[i] from the value B[i] and a value C[i] generated by the division process, and to generate an n-bit value T[i] from a value P(T[i−1]) obtained by converting the value T[i−1] using a replacement function P, a value F(B[i]) obtained by converting the value B[i] using a replacement function F, and the value C[i];
a plaintext generation process to generate a plaintext M by connecting the values M[i] for i=1, . . . , c generated by the plaintext element generation process; and
an authenticator generation process to generate from a value T[c] and a value B[c], an authenticator Tag′ for detecting an alteration of the plaintext M generated by the plaintext generation process, wherein
the decryption program causes the computer to further execute the plaintext element generation process to maintain a total memory size of 2n bits as a sum of memory sizes for the value T and the value B, during the generation of the value T[i] using the replacement function P and the value F(B[i]) using the replacement function F.